Transient electromagnetic wave logging response calculation method and device, electronic equipment and medium

Abstract

The invention discloses a transient electromagnetic wave logging response calculation method and device, electronic equipment and a storage medium. The method comprises the following steps: determining a target function from at least two reference functions associated with a target cased well radial stratification model, wherein the at least two reference functions comprise a first function and a second function; the signal receiving time of a receiving coil in the target cased well is determined, and a three-component transmitting coil and a three-component receiving coil are placed in a borehole of the target cased well; substituting the time of receiving the signal into the target function to obtain a target result, wherein the target result is a solving result used for indicating a derivative term of time domain magnetic field intensity to time in a frequency-time transformation equation of the target function; and determining the induced electromotive force of the receiving coil position at the borehole middle position of the target cased well according to the target result. According to the technical scheme, high-precision and efficient calculation of transient electromagnetic wave logging response can be achieved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of oil and gas exploration and development, and particularly relates to a transient electromagnetic wave logging response calculation method and device, an electronic device and a medium. BACKGROUND

[0002] The transient electromagnetic logging technology has the core advantages of penetrating high conductivity casing to obtain the real conductivity of the formation and detecting the casing quality by metal detection of the casing well, and thus occupies a key position in production well evaluation and provides important technical support for formation parameter interpretation and casing integrity evaluation. At present, the transient electromagnetic logging numerical simulation mainly includes a frequency domain conversion method and a direct time domain method. The frequency domain conversion method needs to solve the full frequency electromagnetic field first, and then obtain the time domain solution through frequency-time conversion. The direct time domain method directly solves in the time domain. However, in the actual application of the frequency-time conversion algorithm, the fast Fourier transform needs to meet the sampling theorem, and multiple sampling leads to low calculation efficiency. The sine and cosine transform algorithm has high precision but slow operation speed. The Gaver-Stehfest algorithm has high speed but insufficient precision. In the frequency domain-time domain conversion process of the numerical filtering algorithm and the fast Fourier transform, a large number of frequency sampling points are needed, and the frequency field corresponding to different times needs to be repeatedly calculated. SUMMARY

[0003] The present application provides a transient electromagnetic wave logging response calculation method to solve the problem that the calculation efficiency and precision of the transient electromagnetic wave logging response are difficult to be considered.

[0004] According to an aspect of the present application, a transient electromagnetic wave logging response calculation method is provided, which includes:

[0005] determining a target function from at least two reference functions associated with a target casing radial layered model, the target casing radial layered model being a radial layered formation resistivity model formed based on wellbore parameters, casing parameters and formation parameters corresponding to a target casing well, a three-component transmitting coil and a three-component receiving coil being arranged in the wellbore of the target casing radial layered model, the at least two reference functions including a first function and a second function, the first function being used to indicate a frequency-time conversion equation of the receiving coil of the target casing radial layered model established when the transmitting coil of the target casing radial layered model obtained through spectral analysis uses a lower step current as a transmitting source excitation of the transient electromagnetic logging, the frequency-time conversion equation of the first function including a derivative term of the time domain magnetic field intensity with respect to time and an integral function term using the frequency domain magnetic field intensity function and the trigonometric function; the second function being obtained by introducing a cubic spline interpolation method to approximately fit the frequency domain magnetic field intensity function in the integral function term of the first function into a polynomial interpolation function;

[0006] determining a time of receiving a signal at a receiving coil in a target cased hole, the target cased hole having a three-component transmitting coil and a three-component receiving coil placed in a middle of a borehole of the target cased hole;

[0007] substituting the time of receiving the signal into the objective function to obtain an objective result, the objective result being a solution result of a derivative term of a time-domain magnetic field intensity with respect to time in a frequency-time transform equation of the objective function;

[0008] determining, according to the objective result, an induced electromotive force of a receiving coil position in the middle of the borehole of the target cased hole.

[0009] According to another aspect of the present application, there is provided a transient electromagnetic wave logging response calculation device, the device comprising:

[0010] an objective function determination module configured to determine an objective function from at least two reference functions associated with a target cased hole radial layered model, the target cased hole radial layered model being a radial layered formation resistivity model formed based on corresponding borehole parameters, casing parameters and formation parameters of a target cased hole, the three-component transmitting coil and the three-component receiving coil being placed in the middle of the borehole of the target cased hole radial layered model, the at least two reference functions including a first function and a second function, the first function being configured to indicate a frequency-time transform equation of a receiving coil of the target cased hole radial layered model established when a transmitting coil of the target cased hole radial layered model is excited by a lower step current as a transient electromagnetic logging transmitting source through spectrum analysis, the frequency-time transform equation of the first function including a derivative term of a time-domain magnetic field intensity with respect to time and an integral function term using a frequency-domain magnetic field intensity function and a trigonometric function; the second function being obtained by introducing a cubic spline interpolation method to approximately fit the frequency-domain magnetic field intensity function in the integral function term of the first function into a polynomial interpolation function;

[0011] a time determination module configured to determine a time of receiving a signal at a receiving coil in a target cased hole, the target cased hole having a three-component transmitting coil and a three-component receiving coil placed in a middle of a borehole of the target cased hole;

[0012] an objective result determination module configured to substitute the time of receiving the signal into the objective function to obtain an objective result, the objective result being a solution result of a derivative term of a time-domain magnetic field intensity with respect to time in a frequency-time transform equation of the objective function;

[0013] a logging response determination module configured to determine, according to the objective result, an induced electromotive force of a receiving coil position in the middle of the borehole of the target cased hole.

[0014] According to another aspect of the present application, there is provided an electronic device, the electronic device comprising:

[0015] at least one processor; and

[0016] a memory communicatively connected with the at least one processor; wherein

[0017] The memory stores a computer program executable by the at least one processor, and the computer program is executed by the at least one processor to enable the at least one processor to perform the transient electromagnetic wave logging response calculation method according to any one of the embodiments of the present application.

[0018] According to another aspect of the present application, a computer readable storage medium is provided, which stores computer instructions for enabling a processor to implement the transient electromagnetic wave logging response calculation method according to any one of the embodiments of the present application when executed by the processor.

[0019] The technical scheme of the embodiments of the present application determines a target function from at least two reference functions associated with a target casing well radial layered model, wherein the target casing well radial layered model is constructed based on wellbore parameters, casing parameters and formation parameters corresponding to the target casing well, can accurately depict a radial non-uniform medium, and ensures that the electromagnetic response calculation is consistent with the actual physical field distribution, thereby improving the accuracy of the logging response calculation; the frequency-time transform equation of the first function includes a derivative term for indicating the time-domain magnetic field intensity with respect to time and an integral function term for adopting the frequency-domain magnetic field intensity function and the trigonometric function, and can accurately describe the frequency-time transform characteristics of the transient electromagnetic response; the second function performs polynomial approximation on the frequency-domain magnetic field intensity function through the cubic spline interpolation method, can convert the integral function term into a form that can be directly integrated and solved, thereby solving the high-frequency sampling and convergence control problem required for numerical integration of high oscillation kernels in the frequency-time transform process, and can improve the accuracy and efficiency of the frequency-time transform; the time of the received signal at the receiving coil in the target casing well is determined and substituted into the target function to obtain a target result, and the target result is the solution result of the derivative term for indicating the time-domain magnetic field intensity with respect to time in the frequency-time transform equation of the target function; and the induced electromotive force of the receiving coil position at the middle position of the wellbore of the target casing well is determined according to the target result. Based on the above technical scheme, the problem that the efficiency and accuracy of the transient electromagnetic wave logging response calculation cannot be considered can be solved, high-precision and high-efficiency calculation of the transient electromagnetic wave logging response can be realized, and thus the application effect of the transient electromagnetic wave logging technology in the casing well metal flaw detection, formation evaluation and other scenes can be improved.

[0020] It should be understood that the content described in this part is not intended to identify key or important features of the embodiments of the present application, nor to limit the scope of the present application. Other features of the present application will become apparent from the following description. BRIEF DESCRIPTION OF DRAWINGS

[0021] In order to make the technical solutions in the embodiments of the present application clearer, the drawings needed in the embodiment description will be briefly introduced as follows. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without any creative effort on the basis of these drawings.

[0022] Figure 1 is a flow chart of a transient electromagnetic wave logging response calculation method according to an embodiment of the present application;

[0023] Figure 2 is a schematic diagram of a target casing radial layered model according to an embodiment of the present application;

[0024] Figure 3 is a comparison diagram of transient electromagnetic wave logging responses calculated by using a second function and a SinTran401 algorithm under the condition of a two-layered formation with a radial layer and a formation resistivity from 100 to 1000 Ωm according to an embodiment of the present application; to

[0025] Figure 4 is a comparison diagram of transient electromagnetic wave logging responses calculated by using a second function and a SinTran401 algorithm under the condition of a two-layered formation with a radial layer and a formation resistivity from 100 to 1000 Ωm according to an embodiment of the present application; to

[0026] Figure 5 is a flow chart of another transient electromagnetic wave logging response calculation method according to an embodiment of the present application;

[0027] Figure 6 is a comparison diagram of transient electromagnetic wave logging responses calculated by using a second function and a Gaussian integral under the condition of a formation resistivity of 100 Ωm and a target source distance of 1 m according to an embodiment of the present application;

[0028] Figure 7 is a comparison diagram of transient electromagnetic wave logging responses calculated by using a second function and a Gaussian integral under the condition of a formation resistivity of 100 Ωm and a target source distance of 2.5 m according to an embodiment of the present application;

[0029] Figure 8 is a comparison diagram of transient electromagnetic wave logging responses calculated by using a second function and a Gaussian integral under the condition of a formation resistivity of 1000 Ωm and a target source distance of 1 m according to an embodiment of the present application;

[0030] Figure 9 is a comparison diagram of transient electromagnetic wave logging responses calculated by using a second function and a Gaussian integral under the condition of a formation resistivity of 1000 Ωm and a target source distance of 2.5 m according to an embodiment of the present application; ​​​​​The comparison chart of the second function and the result of the transient electromagnetic wave logging response calculated by the Gaussian integral under the condition of a target source distance of 2.5 m;

[0031] Figure 10 It is a structural schematic diagram of a transient electromagnetic wave logging response calculation device provided by an embodiment of the present application;

[0032] Figure 11 It is a structural schematic diagram of an electronic device for implementing a transient electromagnetic wave logging response calculation method of an embodiment of the present application. DETAILED DESCRIPTION

[0033] In order for those skilled in the art to better understand the present application, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor should fall within the scope of protection of the present application.

[0034] It should be noted that the terms "first", "second", and the like in the specification and claims of the present application and the above-mentioned drawings are used to distinguish similar objects, and do not necessarily have to be used to describe a specific order or sequence. It should be understood that the data thus used can be interchanged under appropriate circumstances, so that the embodiments of the present application described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "include" and "have" and any variations thereof are intended to cover non-exclusive inclusion, for example, a process, method, system, product or device that includes a series of steps or units does not have to be limited to those steps or units clearly listed, but can include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0035] Figure 1 A flowchart of a transient electromagnetic wave logging response calculation method provided by an embodiment of the present application is provided. The embodiment can be applicable to the case where transient electromagnetic wave logging response needs to be calculated in a radial non-uniform medium. The method can be executed by a transient electromagnetic wave logging response calculation device, which can be realized in the form of hardware and / or software, and can be configured in any electronic device with network communication function. As shown in the figure, the transient electromagnetic wave logging response calculation method provided by the embodiment can include the following processes: Figure 1

[0036] ​S110. Determine the target function from at least two reference functions associated with the radial stratification model of the target casing well. The radial stratification model of the target casing well is a radial stratification formation resistivity model constructed based on the wellbore parameters, casing parameters, and formation parameters corresponding to the target casing well. A three-component transmitting coil and a three-component receiving coil are configured in the middle of the wellbore of the radial stratification model of the target casing well. The at least two reference functions include a first function and a second function. The first function is used to indicate the frequency-time transformation equation at the receiving coil of the radial stratification model of the target casing well when the transmitting coil of the radial stratification model of the target casing well, obtained through spectrum analysis, is excited by a step current as the transmitting source of transient electromagnetic logging. The frequency-time transformation equation of the first function includes a term indicating the derivative of the time-domain magnetic field strength with respect to time and an integrand term using the frequency-domain magnetic field strength function and trigonometric functions. The second function is obtained by introducing a cubic spline interpolation method to approximately fit the frequency-domain magnetic field strength function in the integrand term of the first function into a polynomial interpolation function.

[0037] A radially stratified formation resistivity model for a target casing well refers to a radially stratified formation resistivity model established by accurately characterizing the wellbore, casing, and formation parameters of the target casing well in a radially stratified manner, centered on the wellbore's central axis. See also... Figure 2 The target casing well radial stratification model includes at least the wellbore, casing, and formation, wherein the casing conductivity is greater than 100%. The conductivity of the wellbore mud is approximately The formation conductivity is approximately The target casing well radial stratification model has a three-component transmitting coil and a three-component receiving coil configured in the middle of the wellbore, which are used for transmitting and receiving current excitation, respectively.

[0038] The reference function can refer to the frequency-time transformation equation used to transform the frequency-domain induced signal of the target casing well radial layering model into the time-domain induced signal. In this embodiment, the target casing well radial layering model is associated with at least two reference functions, including a first function and a second function, which correspond to the integrand form under different approximation strategies, respectively.

[0039] The first function can refer to the transformation equations of the time-domain and frequency-domain induced signals under step current excitation determined based on spectral analysis theory. The integrand in the first function includes the imaginary part of the frequency-domain magnetic field strength function and a trigonometric oscillation kernel; the integral result is the derivative of the time-domain magnetic field strength with respect to time. The second function can refer to the frequency-time transformation equation formed by locally approximating the frequency-domain magnetic field strength function to a polynomial interpolation function using cubic spline interpolation, based on the first function.

[0040] By constructing a radial stratification model of the target casing well based on the parameters of the target casing well, the environment of the target casing well can be accurately characterized. Based on the radial stratification model of the target casing well and at least two reference functions associated with the radial stratification model of the target casing well, an objective function is determined. The objective function is used to realize the frequency-time transformation of the transient electromagnetic response in the radial stratification model of the target casing well.

[0041] As an optional but not limited implementation, the transient electromagnetic wave logging response calculation method provided in this embodiment further includes steps A1-A3:

[0042] Step A1: Construct a radial stratification model of the target casing well for transient electromagnetic wave logging. The radial stratification formation structure of the target casing well remains unchanged in both the circumferential and longitudinal directions.

[0043] See Figure 2 Based on the radial stratification model of the target casing well, the central axis of the wellbore can be used to establish a spatial direction definition in a cylindrical coordinate system. This definition can be used to clarify the spatial distribution of physical quantities such as electromagnetic fields and formation structure. The spatial direction definition in the cylindrical coordinate system includes axial, radial, and circumferential directions. The axial direction can refer to a linear direction coinciding with the central axis of the wellbore, i.e. Figure 2 The z-direction is shown; radial direction can refer to the radial dimension extending outward from the center axis of the wellbore along a direction perpendicular to the axis, i.e. Figure 2 The direction r is shown; the circumferential direction can refer to the circumferential direction of rotation around the central axis of the wellbore, a ring-shaped direction perpendicular to both the radial and axial directions, i.e. Figure 2 As shown Direction. The radial stratification structure of the target casing well remains unchanged in both the circumferential and longitudinal directions, accurately reproducing the stratification characteristics along the radial direction. This ensures the physical authenticity and rationality of the target casing well's radial stratification model and effectively reflects the electromagnetic propagation characteristics of the formation.

[0044] Step A2: For the radial layered model of the target casing well, the frequency domain electromagnetic field of the three-dimensional radial layer is converted into a one-dimensional spectral domain field by Fourier transform to obtain the frequency domain electromagnetic field spectral domain expansion equation of the radial layered medium. The pseudo-analytical solution of the frequency domain electromagnetic field spectral domain expansion equation of the radial layered medium is solved by Maxwell's equations to obtain the distribution of frequency domain electric field intensity and frequency domain magnetic field intensity.

[0045] Since the radial stratification structure and circumferential and vertical formation properties remain unchanged in the target casing well radial stratification model, therefore see Figure 2 ,exist In the coordinate system, the directional wave number k is introduced along the axis through Fourier transform. zExpanding circumferentially into circumferential harmonics v, the three-dimensional radial layer frequency domain electromagnetic field is transformed into a one-dimensional spectral domain field. Solving the electromagnetic field by dimensionality reduction avoids the enormous computational burden caused by high-dimensional solutions or finite difference methods, thus improving the speed and accuracy of frequency domain electromagnetic field solutions.

[0046] Specifically, the frequency-domain electromagnetic field spectral expansion equation of the radially layered medium can be expressed as: Where p represents direction, i.e. Coordinate direction, v represents the circumferential harmonic number, k z E is the wave number in the z-direction. p H p For the scalar electric and magnetic fields in different directions at the field point, , The electric and magnetic fields in the spectral domain are represented. After Fourier transform, the spectral field... , and The relationship between z and circumferential harmonic components is reflected by the superposition of circumferential harmonic components and the wavenumber integral in the z direction. The relationship is as follows. By solving the pseudo-analytical solution of the frequency domain electromagnetic field spectral domain expansion equation of the radially layered medium using Maxwell's equations, the distribution of the frequency domain electric field intensity and frequency domain magnetic field intensity can be obtained.

[0047] Step A3: Configure the transmitted wave waveform of the transmitting coil in the radial layering model of the target casing well as the lower step current, and then construct the frequency-time transformation equation satisfied by the receiving coil of the radial layering model of the target casing well under the excitation of the lower step current based on the Fourier transform theory in spectrum analysis, so as to obtain the first function.

[0048] The lower step current refers to the current waveform of the transmitting coil outputting current that drops instantaneously from a preset stable value to zero and remains constant. The first function is the frequency-time transformation equation corresponding to the receiving coil in the radial layering model of the target casing well under the excitation of the lower step current. In the first function, by performing a continuous Gaussian integral on the frequency domain magnetic field strength obtained by pseudo-analysis, the derivative of the time domain magnetic field strength with respect to time can be obtained, which can preserve the field distribution characteristics of the entire frequency domain.

[0049] Specifically, the first function can be expressed as ,in, Represents angular frequency. This indicates the time it takes for the receiving coil to sense the transient electromagnetic wave response signal and complete signal acquisition. Represents the frequency domain magnetic field strength, Im represents the value of... The imaginary part, Represents the magnetic field strength in the time domain. It represents the derivative of the magnetic field strength in the time domain with respect to time.

[0050] As an optional but not limited implementation, the transient electromagnetic wave logging response calculation method provided in this embodiment further includes steps B1-B2:

[0051] Step B1: Separate the non-oscillatory frequency-domain magnetic field strength function and the oscillatory trigonometric function included in the integrand term of the frequency-time transformation equation of the first function.

[0052] The integrand can be the composite expression within the integral sign in the frequency-time transform equation of the first function, consisting of the product of a frequency-domain magnetic field strength function that varies smoothly with frequency and a rapidly oscillating trigonometric function. The non-oscillating frequency-domain magnetic field strength function is relatively smooth in the integrand, and it changes monotonically or slowly with angular frequency. The oscillating trigonometric function oscillates more strongly with increasing frequency and exhibits periodicity. Therefore, the oscillation of the integrand originates from the oscillating trigonometric function, which is the fundamental reason for the slow convergence of the integrand during direct integration. While maintaining the integration path, the product can be separated from the oscillating trigonometric function using the property of product decomposition. This allows treating the non-oscillating frequency-domain magnetic field strength function and the oscillating trigonometric function as two independent integrands, ensuring the integrity of electromagnetic information while isolating the oscillating behavior. This enables targeted processing of the functions based on their different characteristics.

[0053] Step B2: Introduce the cubic spline interpolation method to approximate the non-oscillating frequency domain magnetic field strength function part of the integrand term, and at the same time obtain the strict equation solution of the oscillating trigonometric function in the integrand term through algebraic transformation to obtain the second function.

[0054] Cubic spline interpolation refers to a function fitting method that uses piecewise cubic polynomials to locally smooth the non-oscillating frequency domain magnetic field strength function at selected frequency points, resulting in a continuous derivative of the overall curve of the non-oscillating frequency domain magnetic field strength function and controllable fitting error. A strictly equal solution refers to a closed algebraic result obtained by using integration tables or residue operations on the oscillating trigonometric function part, without any approximations. The second function can refer to the frequency-time transformation equation formed by replacing the non-oscillating frequency domain magnetic field strength function in the integrand term of the first function with a polynomial interpolation function and combining it with the oscillating trigonometric function.

[0055] Based on the separation of the non-oscillatory frequency-domain magnetic field strength function and the oscillatory trigonometric function in the integrand term, cubic spline interpolation is performed on the non-oscillatory frequency-domain magnetic field strength function. The resulting polynomial interpolation function is then used to replace the non-oscillatory frequency-domain magnetic field strength function. The replacement process can be expressed as follows: ,in, The first function is a polynomial interpolation function. The integrand in the second function is the product of the polynomial interpolation function and the oscillatory trigonometric function. The integration interval is discretized according to the interpolation node sequence of cubic spline interpolation, and the integral is solved by integration by parts. The obtained integral result is approximately equal to the derivative of the magnetic field strength in the time domain with respect to time.

[0056] Optionally, an interpolation node sequence is constructed for the integration interval at logarithmic intervals. The integration interval is then discretized into multiple sub-intervals based on this sequence, and the integration by parts method is used to solve the problem within each sub-interval. Specifically, the frequency-time transform equation of the second function can be expressed as:

[0057]

[0058] in, N represents the derivative of the magnetic field strength in the time domain with respect to time. N can represent the length of the interpolation node sequence or the number of discrete integration intervals. It is a polynomial interpolation function. , , and These are the first, second, third, and fourth derivatives of the polynomial interpolation function with respect to the angular frequency, respectively. In this embodiment, cubic spline interpolation is used for fitting. It is a cubic polynomial. .

[0059] S120. Determine the time for receiving the signal at the receiving coil in the target casing well. Place a three-component transmitting coil and a three-component receiving coil in the middle of the wellbore of the target casing well.

[0060] The signal reception time refers to the specific moment when the receiving coil in the target casing well senses the transient electromagnetic response signal and completes signal acquisition. A three-component transmitting coil can refer to a coil structure placed in the center of the target casing wellbore that can transmit transient electromagnetic signals along three orthogonal directions in space, enabling omnidirectional electromagnetic excitation. A three-component receiving coil can refer to a coil structure corresponding to the three-component transmitting coil, placed in the center of the wellbore, and capable of receiving electromagnetic response signals along three orthogonal directions in space, comprehensively capturing spatial electromagnetic signal characteristics.

[0061] S130. Substitute the time of the received signal into the objective function to obtain the target result. The target result is the solution result of the derivative term of the time-domain magnetic field strength with respect to time in the frequency-time transformation equation of the objective function.

[0062] The target result refers to the result obtained by substituting the time of the received signal into the objective function and solving for the derivative term of the time-domain magnetic field strength with respect to time in the frequency-time transformation equation. It can be used to reflect the transient electromagnetic response characteristics at the receiving coil during the time of the received signal.

[0063] S140. Determine the induced electromotive force at the receiving coil position at the middle position of the target casing well based on the target result.

[0064] Induced electromotive force (EMF) refers to the electromotive force generated at the two terminals of the receiving coil in the target casing well due to the change in magnetic flux passing through the well. Therefore, based on the target results and the characteristics of the receiving coil itself, the induced EMF at the receiving coil position in the middle of the target casing wellbore is determined. The induced EMF at the receiving coil position in the middle of the target casing wellbore is the core characteristic of transient electromagnetic wave logging response.

[0065] As an optional but not limited implementation, the induced electromotive force at the receiving coil position at the center of the target casing well is determined based on the target result, including steps C1-C2:

[0066] Step C1: Determine the number of turns and area of ​​the receiving coil in the target casing well, as well as the permeability of the receiving coil.

[0067] Step C2: Determine the induced electromotive force at the position of the receiving coil at the middle position of the target casing well based on the number of coil turns and coil area of ​​the receiving coil, the magnetic permeability of the receiving coil, and the target result.

[0068] The number of turns, coil area, and permeability of the receiving coil are all inherent characteristics of the receiving coil itself. The number of turns refers to the total number of turns of the conductor in the coil windings; it is directly proportional to the induced voltage. The coil area refers to the geometric cross-sectional area enclosed by a single turn of the coil winding; it determines the coil's ability to capture magnetic flux. The permeability of the receiving coil refers to the permeability of the material constituting the coil core or frame; it reflects the coil's ability to concentrate magnetic flux and amplifies the induced signal.

[0069] Transient electromagnetic wave logging response refers to the induced electromotive force at the receiving coil position in the middle of the target casing wellbore, expressed by the formula... The calculation can obtain the transient electromagnetic wave logging response at different times for the receiving coil position at the middle position of the target casing wellbore, where, This indicates the time it takes for the receiving coil to sense the transient electromagnetic wave response signal and complete signal acquisition. The induced electromotive force at time t is the value of the receiving coil located at the center of the target casing wellbore. The number of coil turns. The area of ​​the coil, Permeability, The target result is for time t.

[0070] To verify the accuracy of the second function in calculating the transient electromagnetic field of the radial layer model, the second function and the conventional sine transform algorithm SinTran401 were used to analyze the transient electromagnetic wave logging response under different radial two-layer formation conditions.

[0071] For example, a two-layer radial formation model I is established, where the target source distance is 1m, the radial layer interface is 0.5m, and the formation resistivity is... arrive That is, with the wellbore center axis as the center, the formation resistivity within a radial distance of 0.5m is The resistivity of the strata 0.5m away is The transient electromagnetic wave logging response was calculated using the second function and the conventional sine transform algorithm SinTran401, respectively. A comparison chart of the calculation results was then plotted. (See attached image.) Figure 3 The solid black line represents the formation resistivity. The transient electromagnetic wave logging response curve of a homogeneous medium at time t, where the black dashed line represents the formation resistivity. The graph shows the transient electromagnetic wave logging response curves in a uniform medium. The red hollow circles represent the calculation results using the second function, and the blue solid dots represent the calculation results using the SinTran401 algorithm. The overlap of the curves in the graph verifies the accuracy of the calculation results using the second function, proving that the second function is applicable to radial formations ranging from low resistivity to high resistivity.

[0072] A two-layer radial stratigraphic model II was established, with a target source distance of 1m, a radial layer interface of 0.5m, and a stratigraphic resistivity of [missing value]. arrive That is, with the wellbore center axis as the center, the formation resistivity within a radial distance of 0.5m is The resistivity of the strata 0.5m away is The transient electromagnetic wave logging response was calculated using the second function and the conventional sine transform algorithm SinTran401, respectively. A comparison chart of the calculation results was then plotted. (See attached image.) Figure 4 The solid black line represents the formation resistivity. The transient electromagnetic wave logging response curve of a homogeneous medium at time t, where the black dashed line represents the formation resistivity. The transient electromagnetic wave logging response curves in a uniform medium are shown. The red hollow circles represent the calculation results using the second function, and the blue solid dots represent the calculation results using the SinTran401 algorithm. The overlap of the curves in the figure can verify the accuracy of the calculation results of the second function, proving that the second function is applicable to radial formations with resistivity ranging from high to low.

[0073] In addition, to verify the computational efficiency of the second function in the transient electromagnetic field of the radial layer model, the second function and the conventional sine transform algorithm SinTran401 were used to calculate the transient electromagnetic wave logging response under the conditions of homogeneous medium and radial layer non-homogeneous medium, respectively, and the computation time was analyzed.

[0074] For example, when the second function is calculated using the spline interpolation algorithm, the frequency domain sampling points are set to 401 points, consistent with the sine transform algorithm for 401-point numerical filtering. The computation time was recorded under both homogeneous and radially inhomogeneous media conditions, and the results are shown in Table 1. Analysis of Table 1 shows that for homogeneous media, the computational efficiency of the second function and the conventional sine transform algorithm SinTran401 is similar. This is because frequency domain electromagnetic field calculation is faster and less time-consuming in homogeneous media. However, for radially layered media, when the number of time samples is 1, the computation time of the two algorithms is similar; as the number of time samples increases, the computation time of the second function remains basically unchanged, while the computation time of the SinTran401 algorithm increases proportionally to the number of time samples; when the number of samples is 50, the computation time of the SinTran401 algorithm is much greater than that of the second function, proving that the second function is more suitable for radially layered inhomogeneous media under the same frequency domain sampling density and has higher computational efficiency.

[0075] Table 1 Comparison of computation time for frequency-time transformation algorithms

[0076]

[0077] The technical solution of this invention determines the target function from at least two reference functions associated with the radial stratification model of the target casing well. The radial stratification model of the target casing well is constructed based on the wellbore parameters, casing parameters, and formation parameters corresponding to the target casing well, which can accurately characterize the radially non-uniform medium and ensure that the electromagnetic response calculation fits the actual physical field distribution, thereby improving the accuracy of the logging response calculation. The frequency-time transformation equation of the first function includes a term indicating the derivative of the time-domain magnetic field strength with respect to time and an integrand term using the frequency-domain magnetic field strength function and trigonometric functions, which can accurately describe the frequency-time transformation characteristics of the transient electromagnetic response. The second function approximates the frequency-domain magnetic field strength function using a cubic spline interpolation method, transforming the integrand into a directly integrateable form. This addresses the high-frequency sampling and convergence control issues required for high-oscillation kernel numerical integration during frequency-time transformation, improving the accuracy and efficiency of the transformation. The receiving time of the signal at the receiving coil in the target casing well is determined and substituted into the objective function to obtain the target result. The target result is the solution of the derivative term of the time-domain magnetic field strength with respect to time in the frequency-time transformation equation of the objective function. Based on the target result, the induced electromotive force at the receiving coil position in the middle of the target casing well is determined. This technical solution solves the problem of balancing efficiency and accuracy in transient electromagnetic wave logging response calculations, achieving high-precision and efficient calculation of transient electromagnetic wave logging responses. This improves the application effect of transient electromagnetic wave logging technology in scenarios such as casing well metal flaw detection and formation evaluation.

[0078] Figure 5 This is a flowchart of another transient electromagnetic wave logging response calculation method provided by an embodiment of the present invention. This embodiment further optimizes the method of determining the objective function from at least two reference functions associated with the radial stratification model of the target casing well in the above embodiment. Figure 5 As shown, the transient electromagnetic wave logging response calculation method provided in this embodiment may include the following process:

[0079] S210. Determine the formation conductivity and magnetic permeability corresponding to the target casing well, as well as the target source distance. The target source distance is the axial distance between the transmitting coil and the receiving coil in the target casing well.

[0080] Formation conductivity refers to the physical quantity that allows the target casing well to conduct electrical current through the formation medium, reflecting the inherent property of the formation medium in conducting electromagnetic signals. Formation magnetic permeability refers to the physical quantity that allows the target casing well to magnetize the formation medium, characterizing the inherent characteristic of the formation medium undergoing magnetization under the influence of an electromagnetic field. Target-source distance refers to the distance along the wellbore axis between the transmitting coil used to transmit transient electromagnetic signals and the receiving coil used to receive electromagnetic response signals in the target casing well. By determining the formation conductivity and magnetic permeability corresponding to the target casing well, as well as the target-source distance, the electromagnetic propagation characteristics around the target casing well can be accurately characterized.

[0081] S220. Based on the formation conductivity and magnetic permeability and the target source distance, determine the integral discriminant factor corresponding to the target casing well. The integral discriminant factor is used to determine the feasibility of solving the integral of the first function by characterizing the oscillation intensity of the integrand term in the first function associated with the radial stratification model of the target casing well.

[0082] The integral discriminant factor refers to a quantitative index constructed based on formation electromagnetic characteristic parameters and coil spatial layout parameters. It can be used to characterize the oscillation intensity of the integrand term in the first function associated with the radial stratification model of the target casing well, thereby determining the feasibility of solving the integral of the first function. The oscillation intensity of the integrand term refers to the degree of fluctuation in the integral value of the integrand term as the angular frequency changes. The oscillation intensity of the integrand term is a key characteristic affecting the efficiency and accuracy of the integral solution. The feasibility of the integral solution refers to the possibility of obtaining the integral result efficiently and accurately by using the corresponding integration method based on the characteristics of the integrand term. The lower the oscillation intensity of the integrand term in the first function associated with the radial stratification model of the target casing well, the higher the feasibility of solving the integral of the first function.

[0083] The oscillation of the integrand term in the first function mainly stems from the trigonometric functions of oscillation, according to the integrand term... The oscillation characteristics of the integrand are as follows: when t is small, the oscillation of the integrand term with the angular frequency is low, and the calculation accuracy of general integration methods such as Gaussian integral is not significantly affected by the sampling density. When t is large, the oscillation of the integrand term with the angular frequency is high, and the calculation accuracy of general integration methods such as Gaussian integral is significantly affected by the sampling density. In order to maintain the calculation accuracy, high-density sampling is required, which seriously affects the calculation efficiency.

[0084] Based on the obtained formation conductivity, magnetic permeability, and target source distance, a preset logical correlation can be used to determine the integral discrimination factor. This allows for a quantitative characterization of the oscillation intensity of the integrand term in the first function and a scientific assessment of the feasibility of solving the integral of the first function, avoiding the limitations of relying on subjective experience to judge the feasibility of the integral solution. Optionally, the preset logical correlation can refer to... ,in, Denotes the integral discriminant factor. Indicates the target-source distance. Indicates the magnetic permeability of the formation. This indicates the electrical conductivity of the formation.

[0085] Optionally, a preset logical relationship is determined based on the Green's function of time-domain response. Specifically, the Green's function of time-domain response can be expressed as follows: ,in, Indicates the target-source distance. Indicates the magnetic permeability of the formation. Let represent the formation conductivity, t represent time, and u(t) represent the step function. When t is greater than or equal to 0, u(t) = 1; when t is less than 0, u(t) = 0. In this embodiment, based on the non-ferromagnetic properties of most formations such as rocks, water, and casing mud at the conventional geophysical logging or laboratory scale, the formation magnetic permeability is... Based on the fact that the amplitude of the Green's function in the time domain response can reflect the spatiotemporal distribution characteristics of the electromagnetic field response intensity, the derivative of the Green's function in the time domain response with respect to t is taken, and the derivative is set to zero. The resulting time expression for the formation conductivity, magnetic permeability, and target source distance is then determined as a preset logical correlation.

[0086] S230. Determine the target function from at least two reference functions associated with the radial stratification model of the target casing well, based on the integral discrimination factor corresponding to the target casing well.

[0087] By using the quantitative characterization results of the integral discriminant factor as the screening criterion to determine the objective function, we can avoid situations such as low efficiency in integral solving and excessive error caused by improper function selection. We can also avoid the inability to adapt to the different oscillation characteristics of the integrand term in different time intervals due to the use of a single objective function, thereby improving the computational accuracy and efficiency across the entire time interval.

[0088] As an optional but not limited implementation, the objective function is determined from at least two reference functions associated with the radial stratification model of the target casing well, based on the integral discriminant factor corresponding to the target casing well, including steps D1-D2:

[0089] Step D1: In response to the fact that the time for receiving the signal at the receiving coil in the target casing well is not greater than the integral discrimination factor corresponding to the target casing well, the first function among the at least two reference functions associated with the radial stratification model of the target casing well is determined as the target function.

[0090] When the time of receiving the signal is determined to be no greater than the integral discrimination factor, it indicates that the oscillation intensity of the integrand term of the first function is low and the integral solution is feasible with high efficiency and high accuracy. Therefore, the first function among the at least two reference functions associated with the radial layering model of the target casing well is determined as the target function for subsequent logging response calculation.

[0091] Step D2: In response to the fact that the time for receiving the signal at the receiving coil in the target casing well is greater than the integral discrimination factor corresponding to the target casing well, the second function among the at least two reference functions associated with the radial stratification model of the target casing well is determined as the target function.

[0092] When the time of receiving the signal is greater than the integral discrimination factor, it indicates that the oscillation intensity of the integrand of the first function is high. Direct integration is prone to problems of low efficiency or poor accuracy. The second function, after polynomial approximation, is more suitable for integration in high oscillation scenarios. Therefore, the second function in the reference function associated with the radial layering model of the target casing well is determined as the target function for subsequent logging response calculation.

[0093] To verify that determining the target function from at least two reference functions associated with the radial stratification model of the target casing well based on the integral discriminant factor corresponding to the target casing well can effectively improve the calculation accuracy and efficiency throughout the entire time range, this embodiment provides the results analysis of calculating the transient electromagnetic wave logging response using the second function and Gaussian integral under different formation resistivity and different target source distances.

[0094] Specifically, see Figure 6 The formation resistivity provided in the embodiments of the present invention is The graph compares the results of the transient electromagnetic wave logging response calculated by the second function and the Gaussian integral when the target source distance is 1m. The results from the second function and the Gaussian integral overlap for a portion of the time, and their relative errors are both less than 1% during this period. Before this period, the relative error of the Gaussian integral is significantly smaller than that of the second function; after this period, the relative error of the Gaussian integral is significantly larger than that of the second function. According to the formula... and The integral discriminant factor can be calculated. Furthermore, the obtained integral discriminant factor falls within the time period where the calculation results of the second function and the Gaussian integral overlap. Therefore, when the time is not greater than the integral discriminant factor, using the first function as the objective function (i.e., using the Gaussian integral method) and when the time is greater than the integral discriminant factor, using the second function as the objective function is reasonable and can keep the relative error of the calculation results below 1%, effectively improving the calculation accuracy and efficiency throughout the entire time period.

[0095] See Figure 7 The formation resistivity provided in the embodiments of the present invention is A comparison of the results of the second function and the Gaussian integral used to calculate the transient electromagnetic wave logging response under the condition of a target source distance of 2.5m. Similarly, according to the formula... and The integral discriminant factor can be calculated. And the obtained integral discriminant factor belongs to Figure 7 The time period during which the calculation results of the second function indicated in the text coincide with the calculation results of the Gaussian integral.

[0096] See Figure 8 The formation resistivity provided in the embodiments of the present invention is A comparison of the results of the second function and the Gaussian integral used to calculate the transient electromagnetic wave logging response under the condition of a target source distance of 1m is shown in the figure. Similarly, according to the formula... and The integral discriminant factor can be calculated. And the obtained integral discriminant factor belongs to Figure 8 The time period during which the calculation results of the second function indicated in the text coincide with the calculation results of the Gaussian integral.

[0097] See Figure 9 The formation resistivity provided in the embodiments of the present invention is A comparison of the results of the second function and the Gaussian integral used to calculate the transient electromagnetic wave logging response under the condition of a target source distance of 2.5m. Similarly, according to the formula... and The integral discriminant factor can be calculated. And the obtained integral discriminant factor belongs to Figure 9 The time period during which the calculation results of the second function indicated in the text coincide with the calculation results of the Gaussian integral.

[0098] S240. Determine the time for receiving the signal at the receiving coil in the target casing well. Place a three-component transmitting coil and a three-component receiving coil in the middle of the wellbore of the target casing well.

[0099] S250. Substitute the time of the received signal into the objective function to obtain the target result. The target result is the solution result of the derivative term of the time-domain magnetic field strength with respect to time in the frequency-time transformation equation of the objective function.

[0100] S260. Determine the induced electromotive force at the receiving coil position at the middle position of the target casing well based on the target result.

[0101] The technical solution of this invention, by determining the formation conductivity and permeability of the target casing well and the target source distance, can accurately characterize the electromagnetic propagation characteristics around the target casing well. Based on the formation conductivity, permeability, and target source distance, the integration discrimination factor is calculated in real time, which can quantitatively characterize the oscillation intensity of the integrand of the first function, thus providing a basis for judging the feasibility of the integral solution and avoiding the uncertainty caused by subjective experience. Determining the objective function based on the integration discrimination factor corresponding to the target casing well allows the objective function to match the oscillation characteristics of the integrand, avoiding low integration efficiency or insufficient accuracy due to improper selection of the objective function, effectively improving the calculation accuracy and efficiency across the entire time range. The time of signal reception at the receiving coil in the target casing well is determined and substituted into the objective function to obtain the target result, which is the solution result of the derivative term of the time-domain magnetic field strength with respect to time in the frequency-time transformation equation of the objective function. Based on the target result, the induced electromotive force at the receiving coil position at the middle position of the wellbore in the target casing well is determined. Based on the above technical solution, the problem of balancing efficiency and accuracy in transient electromagnetic wave logging response calculation can be solved. It can achieve high-precision and efficient calculation of transient electromagnetic wave logging response, thereby improving the application effect of transient electromagnetic wave logging technology in scenarios such as casing well metal flaw detection and formation evaluation.

[0102] Figure 10 This is a schematic diagram of a transient electromagnetic wave logging response calculation device provided in an embodiment of the present invention. Figure 10 As shown, the transient electromagnetic wave logging response calculation device provided in this embodiment may include the following:

[0103] The objective function determination module 310 is used to determine the objective function from at least two reference functions associated with the radial stratification model of the target casing well. The radial stratification model of the target casing well is a radial stratification formation resistivity model constructed based on the wellbore parameters, casing parameters, and formation parameters corresponding to the target casing well. A three-component transmitting coil and a three-component receiving coil are configured in the middle of the wellbore of the radial stratification model of the target casing well. The at least two reference functions include a first function and a second function. The first function is used to indicate the frequency-time transformation equation at the receiving coil of the radial stratification model of the target casing well, which is established by using a step current as the transmitting source for transient electromagnetic logging, as obtained through spectrum analysis. The frequency-time transformation equation of the first function includes a term indicating the derivative of the time-domain magnetic field strength with respect to time and an integrand term using the frequency-domain magnetic field strength function and trigonometric functions. The second function is obtained by introducing a cubic spline interpolation method to approximately fit the frequency-domain magnetic field strength function in the integrand term of the first function into a polynomial interpolation function.

[0104] The timing determination module 320 is used to determine the time of signal reception at the receiving coil in the target casing well, wherein a three-component transmitting coil and a three-component receiving coil are placed in the middle of the wellbore of the target casing well.

[0105] The target result determination module 330 is used to substitute the time of the received signal into the target function to obtain the target result, wherein the target result is the solution result of the term indicating the derivative of the time-domain magnetic field strength with respect to time in the frequency-time transformation equation of the target function;

[0106] The logging response determination module 340 is used to determine the induced electromotive force of the receiving coil position at the middle position of the wellbore of the target casing well based on the target result.

[0107] Based on the above embodiments, optionally, the objective function determination module is specifically used for:

[0108] Determine the formation conductivity and magnetic permeability corresponding to the target casing well, as well as the target source distance, wherein the target source distance is the axial distance between the transmitting coil and the receiving coil in the target casing well;

[0109] Based on the formation conductivity and magnetic permeability and the target source distance, the integral discriminant factor corresponding to the target casing well is determined. The integral discriminant factor is used to determine the feasibility of solving the integral of the first function by characterizing the oscillation intensity of the integrand term in the first function associated with the radial stratification model of the target casing well.

[0110] Based on the integral discriminant factor corresponding to the target casing well, the target function is determined from at least two reference functions associated with the radial stratification model of the target casing well.

[0111] Based on the above embodiments, optionally, a target function is determined from at least two reference functions associated with the radial stratification model of the target casing well, according to the integral discriminant factor corresponding to the target casing well, including:

[0112] In response to the fact that the time for receiving the signal at the receiving coil in the target casing well is not greater than the integral discrimination factor corresponding to the target casing well, the first function among at least two reference functions associated with the radial stratification model of the target casing well is determined as the target function;

[0113] In response to the fact that the time for receiving the signal at the receiving coil in the target casing well is greater than the integral discrimination factor corresponding to the target casing well, the second function among at least two reference functions associated with the radial stratification model of the target casing well is determined as the target function.

[0114] Optionally, based on the above embodiments, the transient electromagnetic wave logging response calculation device further includes:

[0115] The model building module is used to build a radial stratification model of the target casing well for transient electromagnetic wave logging. The radial stratification structure of the target casing well remains unchanged in both the circumferential and longitudinal stratification properties.

[0116] The frequency domain electromagnetic field intensity distribution acquisition module is used to convert the three-dimensional radial layer frequency domain electromagnetic field into a one-dimensional spectral domain field for the target casing well radial layer model through Fourier transform to obtain the frequency domain electromagnetic field spectral domain expansion equation of the radial layer medium, and use Maxwell's equations to solve the pseudo-analytical solution of the frequency domain electromagnetic field spectral domain expansion equation of the radial layer medium to obtain the distribution of frequency domain electric field intensity and frequency domain magnetic field intensity.

[0117] The first function determination module is used to configure the transmitted wave waveform of the transmitting coil in the radial layering model of the target casing well as a lower step current, and then construct the frequency-time transformation equation satisfied at the receiving coil of the radial layering model of the target casing well under the excitation of the lower step current based on the Fourier transform theory in spectrum analysis, so as to obtain the first function.

[0118] Optionally, based on the above embodiments, the transient electromagnetic wave logging response calculation device further includes:

[0119] The integrand term separation module is used to separate the non-oscillatory frequency-domain magnetic field strength function and the oscillatory trigonometric function included in the integrand term of the frequency-time transformation equation of the first function;

[0120] The second function determination module is used to introduce the cubic spline interpolation method to approximately fit the non-oscillatory frequency domain magnetic field strength function part in the integrand term, and at the same time, obtain the strict equation solution of the oscillatory trigonometric function in the integrand term through algebraic transformation, so as to obtain the second function.

[0121] Based on the above embodiments, optionally, the well logging response determination module is specifically used for:

[0122] Determine the number of turns and area of ​​the receiving coil in the target casing well, as well as the permeability of the receiving coil;

[0123] The induced electromotive force at the position of the receiving coil at the middle position of the borehole of the target casing well is determined based on the number of turns and coil area of ​​the receiving coil, the magnetic permeability of the receiving coil, and the target result.

[0124] The technical solution of this invention determines the target function from at least two reference functions associated with the radial stratification model of the target casing well. The radial stratification model of the target casing well is constructed based on the wellbore parameters, casing parameters, and formation parameters corresponding to the target casing well, which can accurately characterize the radially non-uniform medium and ensure that the electromagnetic response calculation fits the actual physical field distribution, thereby improving the accuracy of the logging response calculation. The frequency-time transformation equation of the first function includes a term indicating the derivative of the time-domain magnetic field strength with respect to time and an integrand term using the frequency-domain magnetic field strength function and trigonometric functions, which can accurately describe the frequency-time transformation characteristics of the transient electromagnetic response. The second function approximates the frequency-domain magnetic field strength function using a cubic spline interpolation method, transforming the integrand into a directly integrateable form. This addresses the high-frequency sampling and convergence control issues required for high-oscillation kernel numerical integration during frequency-time transformation, improving the accuracy and efficiency of the transformation. The receiving time of the signal at the receiving coil in the target casing well is determined and substituted into the objective function to obtain the target result. The target result is the solution of the derivative term of the time-domain magnetic field strength with respect to time in the frequency-time transformation equation of the objective function. Based on the target result, the induced electromotive force at the receiving coil position in the middle of the target casing well is determined. This technical solution solves the problem of balancing efficiency and accuracy in transient electromagnetic wave logging response calculations, achieving high-precision and efficient calculation of transient electromagnetic wave logging responses. This improves the application effect of transient electromagnetic wave logging technology in scenarios such as casing well metal flaw detection and formation evaluation.

[0125] The transient electromagnetic wave logging response calculation device provided in this embodiment of the invention can execute the transient electromagnetic wave logging response calculation method provided in any of the above embodiments of the invention, and has the corresponding functions and beneficial effects of executing the transient electromagnetic wave logging response calculation method. For detailed process, please refer to the relevant operations of the transient electromagnetic wave logging response calculation method in the foregoing embodiments.

[0126] It is worth noting that the various units and modules included in the above-mentioned device are only divided according to functional logic, but are not limited to the above division, as long as the corresponding functions can be realized; in addition, the specific names of each functional unit are only for easy differentiation and are not used to limit the protection scope of the embodiments of the present invention.

[0127] Figure 11A schematic diagram of an electronic device 10, which can be used to implement embodiments of the present invention, is shown. The electronic device is intended to represent various forms of digital computers, such as laptop computers, desktop computers, workstations, personal digital assistants, servers, blade servers, mainframe computers, and other suitable computers. The electronic device can also represent various forms of mobile devices, such as personal digital processors, cellular phones, smartphones, wearable devices (e.g., helmets, glasses, watches, etc.), and other similar computing devices. The components shown herein, their connections and relationships, and their functions are merely illustrative and are not intended to limit the implementation of the invention described and / or claimed herein.

[0128] like Figure 11 As shown, the electronic device 10 includes at least one processor 11 and a memory, such as a read-only memory (ROM) 12 or a random access memory (RAM) 13, communicatively connected to the at least one processor 11. The memory stores computer programs executable by the at least one processor. The processor 11 can perform various appropriate actions and processes based on the computer program stored in the ROM 12 or loaded from storage unit 18 into the RAM 13. The RAM 13 can also store various programs and data required for the operation of the electronic device 10. The processor 11, ROM 12, and RAM 13 are interconnected via a bus 14. An input / output (I / O) interface 15 is also connected to the bus 14.

[0129] Multiple components in electronic device 10 are connected to I / O interface 15, including: input unit 16, such as keyboard, mouse, etc.; output unit 17, such as various types of displays, speakers, etc.; storage unit 18, such as disk, optical disk, etc.; and communication unit 19, such as network card, modem, wireless transceiver, etc. Communication unit 19 allows electronic device 10 to exchange information / data with other devices through computer networks such as the Internet and / or various telecommunications networks.

[0130] Processor 11 can be a variety of general-purpose and / or special-purpose processing components with processing and computing capabilities. Some examples of processor 11 include, but are not limited to, central processing unit (CPU), graphics processing unit (GPU), various special-purpose artificial intelligence (AI) computing chips, various processors running machine learning model algorithms, digital signal processors (DSPs), and any suitable processor, controller, microcontroller, etc. Processor 11 performs the various methods and processes described above, such as transient electromagnetic wave logging response calculation methods.

[0131] In particular, according to embodiments of the present invention, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of the present invention include a computer program product comprising a computer program carried on a non-transitory computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via communication unit 19, or installed from storage unit 18, or installed from ROM 12. When the computer program is executed by processor 11, it performs the functions defined in the methods of the embodiments of the present invention.

[0132] In some embodiments, the transient electromagnetic wave logging response calculation method can be implemented as a computer program tangibly contained in a computer-readable storage medium, such as storage unit 18. In some embodiments, part or all of the computer program can be loaded and / or installed on electronic device 10 via ROM 12 and / or communication unit 19. When the computer program is loaded into RAM 13 and executed by processor 11, one or more steps of the transient electromagnetic wave logging response calculation method described above can be performed. Alternatively, in other embodiments, processor 11 can be configured to execute the transient electromagnetic wave logging response calculation method by any other suitable means (e.g., by means of firmware).

[0133] Various embodiments of the systems and techniques described above herein can be implemented in digital electronic circuit systems, integrated circuit systems, field-programmable gate arrays (FPGAs), application-specific integrated circuits (ASICs), application-specific standard products (ASSPs), systems-on-a-chip (SoCs), complex programmable logic devices (CPLDs), computer hardware, firmware, software, and / or combinations thereof. These various embodiments may include implementations in one or more computer programs that can be executed and / or interpreted on a programmable system including at least one programmable processor, which may be a dedicated or general-purpose programmable processor, capable of receiving data and instructions from a storage system, at least one input device, and at least one output device, and transmitting data and instructions to the storage system, the at least one input device, and the at least one output device.

[0134] Computer programs used to implement the methods of the present invention may be written in any combination of one or more programming languages. These computer programs may be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when executed by the processor, the computer programs cause the functions / operations specified in the flowcharts and / or block diagrams to be performed. The computer programs may be executed entirely on a machine, partially on a machine, or as a standalone software package, partially on a machine and partially on a remote machine, or entirely on a remote machine or server.

[0135] In the context of this invention, a computer-readable storage medium can be a tangible medium that may contain or store a computer program for use by or in conjunction with an instruction execution system, apparatus, or device. A computer-readable storage medium may include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, apparatus, or devices, or any suitable combination thereof. Alternatively, a computer-readable storage medium may be a machine-readable signal medium. More specific examples of machine-readable storage media include electrical connections based on one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0136] To provide interaction with a user, the systems and techniques described herein can be implemented on an electronic device having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to the user; and a keyboard and pointing device (e.g., a mouse or trackball) through which the user provides input to the electronic device. Other types of devices can also be used to provide interaction with the user; for example, feedback provided to the user can be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user can be received in any form (including sound input, voice input, or tactile input).

[0137] The systems and technologies described herein can be implemented in computing systems that include backend components (e.g., as data servers), or middleware components (e.g., application servers), or frontend components (e.g., user computers with graphical user interfaces or web browsers through which users can interact with implementations of the systems and technologies described herein), or any combination of such backend, middleware, or frontend components. The components of the system can be interconnected via digital data communication of any form or medium (e.g., communication networks). Examples of communication networks include local area networks (LANs), wide area networks (WANs), blockchain networks, and the Internet.

[0138] A computing system can include clients and servers. Clients and servers are generally located far apart and typically interact through communication networks. The client-server relationship is created by computer programs running on the respective computers and having a client-server relationship with each other. The server can be a cloud server, also known as a cloud computing server or cloud host, which is a hosting product within the cloud computing service system to address the shortcomings of traditional physical hosts and VPS services, such as high management difficulty and weak business scalability.

[0139] It should be understood that the various forms of processes shown above can be used, with steps reordered, added, or deleted. For example, the steps described in this invention can be executed in parallel, sequentially, or in different orders, as long as the desired result of the technical solution of this invention can be achieved, and this is not limited herein.

[0140] The specific embodiments described above do not constitute a limitation on the scope of protection of this invention. Those skilled in the art should understand that various modifications, combinations, sub-combinations, and substitutions can be made according to design requirements and other factors. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this invention should be included within the scope of protection of this invention.

Claims

1. A method for calculating the response of transient electromagnetic wave logging, characterized in that, The method includes: The target function is determined from at least two reference functions associated with the radial stratification model of the target casing well. The radial stratification model of the target casing well is a radial stratification formation resistivity model constructed based on the wellbore parameters, casing parameters, and formation parameters corresponding to the target casing well. A three-component transmitting coil and a three-component receiving coil are configured in the middle of the wellbore of the radial stratification model of the target casing well. The at least two reference functions include a first function and a second function. The first function is used to indicate the frequency-time transformation equation at the receiving coil of the radial stratification model of the target casing well, which is established by using a step current as the transmitting source for transient electromagnetic logging, as obtained through spectral analysis. The frequency-time transformation equation of the first function includes a term indicating the derivative of the time-domain magnetic field strength with respect to time and an integrand term using the frequency-domain magnetic field strength function and trigonometric functions. The second function is obtained by introducing a cubic spline interpolation method to approximately fit the frequency-domain magnetic field strength function in the integrand term of the first function into a polynomial interpolation function. Determine the time when the signal is received at the receiving coil in the target casing well. A three-component transmitting coil and a three-component receiving coil are placed in the middle of the wellbore of the target casing well. Substituting the time of the received signal into the objective function yields the objective result, which is the solution result of the derivative term of the time-domain magnetic field strength with respect to time in the frequency-time transformation equation of the objective function. Based on the target result, determine the induced electromotive force at the receiving coil position at the middle position of the wellbore of the target casing well.

2. The method according to claim 1, characterized in that, The objective function is determined from at least two reference functions associated with the radial stratification model of the target casing well, including: Determine the formation conductivity and magnetic permeability corresponding to the target casing well, as well as the target source distance, wherein the target source distance is the axial distance between the transmitting coil and the receiving coil in the target casing well; Based on the formation conductivity and magnetic permeability and the target source distance, the integral discriminant factor corresponding to the target casing well is determined. The integral discriminant factor is used to determine the feasibility of solving the integral of the first function by characterizing the oscillation intensity of the integrand term in the first function associated with the radial stratification model of the target casing well. Based on the integral discriminant factor corresponding to the target casing well, the target function is determined from at least two reference functions associated with the radial stratification model of the target casing well.

3. The method according to claim 2, characterized in that, Based on the integral discriminant factor corresponding to the target casing well, the target function is determined from at least two reference functions associated with the radial stratification model of the target casing well, including: In response to the fact that the time for receiving the signal at the receiving coil in the target casing well is not greater than the integral discrimination factor corresponding to the target casing well, the first function among at least two reference functions associated with the radial stratification model of the target casing well is determined as the target function; In response to the fact that the time for receiving the signal at the receiving coil in the target casing well is greater than the integral discrimination factor corresponding to the target casing well, the second function among at least two reference functions associated with the radial stratification model of the target casing well is determined as the target function.

4. The method according to claim 1, characterized in that, The method further includes: A radial stratification model of the target casing well is constructed for transient electromagnetic wave logging, wherein the radial stratification formation structure of the target casing well remains unchanged in both the circumferential and longitudinal directions; For the target casing well radial layering model, the frequency domain electromagnetic field of the three-dimensional radial layer is converted into a one-dimensional spectral domain field by Fourier transform to obtain the frequency domain electromagnetic field spectral domain expansion equation of the radial layering medium. Then, the pseudo-analytical solution of the frequency domain electromagnetic field spectral domain expansion equation of the radial layering medium is solved by Maxwell's equations to obtain the distribution of frequency domain electric field intensity and frequency domain magnetic field intensity. The transmitted wave waveform of the transmitting coil in the radial layering model of the target casing well is configured as a lower step current. Then, based on the Fourier transform theory in spectrum analysis, the frequency-time transformation equation satisfied by the receiving coil of the radial layering model of the target casing well under the excitation of the lower step current is constructed to obtain the first function.

5. The method according to claim 1, characterized in that, The method further includes: Separate the non-oscillatory frequency-domain magnetic field strength function and the oscillatory trigonometric function included in the integrand term of the frequency-time transformation equation of the first function; A cubic spline interpolation method is introduced to approximate the non-oscillating frequency-domain magnetic field strength function part of the integrand term. At the same time, through algebraic transformation, a strict equation solution of the oscillating trigonometric function in the integrand term is obtained to obtain the second function.

6. The method according to claim 1, characterized in that, Determining the induced electromotive force at the receiving coil position at the middle position of the target casing well based on the target result includes: Determine the number of turns and area of ​​the receiving coil in the target casing well, as well as the permeability of the receiving coil; The induced electromotive force at the position of the receiving coil at the middle position of the borehole of the target casing well is determined based on the number of turns and coil area of ​​the receiving coil, the magnetic permeability of the receiving coil, and the target result.

7. A transient electromagnetic wave logging response calculation device, characterized in that, The device includes: The objective function determination module is used to determine the objective function from at least two reference functions associated with the radial stratification model of the target casing well. The radial stratification model of the target casing well is a radial stratification formation resistivity model constructed based on the wellbore parameters, casing parameters, and formation parameters corresponding to the target casing well. A three-component transmitting coil and a three-component receiving coil are configured in the middle of the wellbore of the radial stratification model of the target casing well. The at least two reference functions include a first function and a second function. The first function is used to indicate the frequency-time transformation equation at the receiving coil of the radial stratification model of the target casing well, which is established by using a step current as the transmitting source for transient electromagnetic logging, as obtained through spectrum analysis. The frequency-time transformation equation of the first function includes a term indicating the derivative of the time-domain magnetic field strength with respect to time and an integrand term using the frequency-domain magnetic field strength function and trigonometric functions. The second function is obtained by introducing a cubic spline interpolation method to approximately fit the frequency-domain magnetic field strength function in the integrand term of the first function into a polynomial interpolation function. The timing determination module is used to determine the time when the signal is received at the receiving coil in the target casing well. A three-component transmitting coil and a three-component receiving coil are placed in the middle of the wellbore of the target casing well. The target result determination module is used to substitute the time of the received signal into the target function to obtain the target result, wherein the target result is the solution result of the term indicating the derivative of the time-domain magnetic field strength with respect to time in the frequency-time transformation equation of the target function; The logging response determination module is used to determine the induced electromotive force at the receiving coil position at the middle position of the wellbore of the target casing well based on the target result.

8. The apparatus according to claim 7, characterized in that, The objective function determination module is specifically used for: Determine the formation conductivity and magnetic permeability corresponding to the target casing well, as well as the target source distance, wherein the target source distance is the axial distance between the transmitting coil and the receiving coil in the target casing well; Based on the formation conductivity and magnetic permeability and the target source distance, the integral discriminant factor corresponding to the target casing well is determined. The integral discriminant factor is used to determine the feasibility of solving the integral of the first function by characterizing the oscillation intensity of the integrand term in the first function associated with the radial stratification model of the target casing well. Based on the integral discriminant factor corresponding to the target casing well, the target function is determined from at least two reference functions associated with the radial stratification model of the target casing well.

9. An electronic device, characterized in that, The electronic device includes: At least one processor; and, A memory communicatively connected to the at least one processor; wherein, The memory stores a computer program that can be executed by the at least one processor, the computer program being executed by the at least one processor to enable the at least one processor to perform the transient electromagnetic wave logging response calculation method according to any one of claims 1-6.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer instructions that cause a processor to execute the transient electromagnetic wave logging response calculation method according to any one of claims 1-6.

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