Wave number domain incident field stripping method and apparatus

Abstract

The application provides a wave number domain incident field stripping method and device, which is suitable for two-dimensional stratum while-drilling electromagnetic wave response simulation. The method comprises the following steps: obtaining two-dimensional stratum model parameters and while-drilling electromagnetic wave logging instrument parameters according to simulation requirements; using the two-dimensional stratum model parameters and the while-drilling electromagnetic wave logging instrument parameters, constructing a spatial domain wave equation for describing electromagnetic fields in space and the relationship between the electromagnetic fields and while-drilling electromagnetic wave logging instrument transmission signals from a differential form of Maxwell equation set; calculating a spatial domain incident electric field through stratum resistivity at an instrument site and a transmission antenna signal, and performing stripping processing on the spatial domain wave equation according to the spatial domain incident electric field; calculating and obtaining a spatial domain scattered electric field according to the spatial domain wave equation after the stripping processing, and superimposing the spatial domain scattered electric field and the spatial domain incident electric field to obtain a spatial domain total field.

Description

Technical Field

[0001] This application relates to the field of oil exploration and development, and falls under the category of electrical logging methods. Specifically, it relates to a wavenumber domain incident field stripping method and apparatus suitable for two-dimensional formation electromagnetic wave response simulation during drilling. Background Technology

[0002] Simulation of logging-while-drilling (LMD) electromagnetic wave (EMWL) response is a crucial foundation for instrument design, software development, and data interpretation. Achieving efficient and accurate simulation of logging responses has become a key research focus in the industry. In recent years, the detection depth of MWD instruments has been continuously increasing. To better simulate the logging response of complex formations, 2.5D numerical simulation algorithms are required. The basic principle of the 2.5D algorithm is to transform the three-dimensional electromagnetic field calculation problem in the spatial domain into a two-dimensional problem in the wavenumber domain. Therefore, the key to 2.5D MWD simulation lies in solving the two-dimensional problem in the wavenumber domain. Traditional MWD 2.5D algorithms typically apply point sources using a pseudo-delta function approach when solving the two-dimensional field in the wavenumber domain, that is, simulating point sources by applying electric fields to multiple grid nodes. However, this method may lead to point source singularities and large calculation errors in the electromagnetic field near the source. Therefore, there is an urgent need to establish a wavenumber domain point source application method that does not require approximation, which can facilitate accurate and rapid simulation of two-dimensional formation MWD responses. Summary of the Invention

[0003] The purpose of this application is to provide a wavenumber domain incident field stripping method and apparatus, based on a 2.5D finite difference simulation method for logging while drilling using discontinuous grids, to adapt to the simulation of logging while drilling response in complex formations and improve the speed and accuracy of numerical calculation.

[0004] To achieve the above objectives, the wavenumber domain incident field stripping method provided in this application is applicable to two-dimensional formation electromagnetic wave response simulation while drilling. The method includes: obtaining two-dimensional formation model parameters and electromagnetic wave logging instrument parameters while drilling according to simulation requirements; using the two-dimensional formation model parameters and the electromagnetic wave logging instrument parameters while drilling, constructing a spatial domain wave equation describing the electromagnetic field in space and its relationship with the transmitted signal of the electromagnetic wave logging instrument from the differential form of Maxwell's equations; calculating the spatial domain incident electric field through the resistivity of the formation where the instrument is located and the transmitted antenna signal; stripping the spatial domain wave equation based on the spatial domain incident electric field; calculating the spatial domain scattered electric field based on the stripped spatial domain wave equation; and superimposing the spatial domain scattered electric field and the spatial domain incident electric field to obtain the spatial domain total field.

[0005] In the above wavenumber domain incident field stripping method, optionally, before stripping the spatial domain wave equation based on the spatial domain incident electric field, the method further includes: analyzing the formation conditions within the instrument's detection range based on the two-dimensional formation model parameters and the drilling electromagnetic wave logging instrument parameters; when the formation within the instrument's detection range is a homogeneous medium, the spatial domain scattered electric field is set to zero.

[0006] In the above wavenumber domain incident field stripping method, optionally, constructing a spatial domain wave equation describing the electromagnetic field in space and its relationship with the transmission signal of the drilling electromagnetic wave logging instrument, starting from the differential form of Maxwell's equations, includes: constructing a first Maxwell's equations for the time harmonic electromagnetic field for a general lossy medium, starting from the differential form of Maxwell's equations; and eliminating the magnetic field of the first Maxwell's equations to obtain the spatial domain wave equation.

[0007] In the above wavenumber domain incident field stripping method, optionally, the stripping of the spatial domain wave equation based on the spatial domain incident electric field includes: starting from the differential form of Maxwell's equations, constructing a second Maxwell's equations for a homogeneous lossy medium; subtracting the first Maxwell's equations from the second Maxwell's equations, and eliminating the magnetic field to obtain the spatial domain wave equation stripped of the spatial domain incident electric field.

[0008] In the above-mentioned wavenumber domain incident field stripping method, optionally, the calculation of the spatial domain scattered electric field based on the stripped spatial domain wave equation includes: using the spatial domain incident electric field as the signal source of the spatial domain electromagnetic field; generating a two-dimensional wavenumber domain electric field by performing a Fourier transform on the processed spatial domain wave equation along a direction invariant to the stratum properties; constructing the relationship between the wavenumber domain scattered electric field and the wavenumber domain incident electric field using a wavenumber domain electric field difference scheme based on the two-dimensional wavenumber domain electric field, and establishing a linear equation system; substituting a preset analytical expression of the wavenumber domain incident field into the linear equation system to obtain the wavenumber domain scattered electric field; and obtaining the spatial domain scattered electric field through analysis of the wavenumber domain scattered electric field.

[0009] Optionally, in the above wavenumber domain incident field stripping method, the method further includes: constructing a spatial domain scalar Green's function starting from the Green's function, and obtaining the magnetic dipole-generated electric field by scalarizing the spatial domain scalar Green's function; and performing an inverse Fourier transform on the magnetic dipole-generated electric field to obtain a preset analytical expression for the wavenumber domain incident field.

[0010] In the above-mentioned wavenumber domain incident field stripping method, optionally, the wavenumber domain scattered electric field is obtained by substituting the preset analytical expression of the wavenumber domain incident field into the linear equation system, and the spatial domain scattered electric field is obtained by analyzing the wavenumber domain scattered electric field. This includes: substituting the preset analytical expression of the wavenumber domain incident field into the linear equation system, and solving the linear equation system using the LU decomposition method to obtain the wavenumber domain scattered electric field; and performing an inverse Fourier transform on the wavenumber domain scattered electric field to obtain the spatial domain scattered electric field.

[0011] This application also provides a wavenumber domain incident field stripping device suitable for two-dimensional formation drilling electromagnetic wave response simulation. The device includes an acquisition module, a construction module, a stripping module, and a generation module. The acquisition module is used to obtain two-dimensional formation model parameters and drilling electromagnetic wave logging instrument parameters according to simulation requirements. The construction module is used to construct a spatial domain wave equation describing the electromagnetic field in space and its relationship with the transmitted signal of the drilling electromagnetic wave logging instrument, starting from the differential form of Maxwell's equations, using the two-dimensional formation model parameters and the drilling electromagnetic wave logging instrument parameters. The stripping module is used to calculate the spatial domain incident electric field through the resistivity of the formation where the instrument is located and the transmitted antenna signal, and strip the spatial domain wave equation according to the spatial domain incident electric field. The generation module is used to calculate the spatial domain scattered electric field according to the stripped spatial domain wave equation, and superimpose the spatial domain scattered electric field and the spatial domain incident electric field to obtain the spatial domain total field.

[0012] In the aforementioned wavenumber domain incident field stripping device, optionally, the generation module includes a conversion unit, which is used to use the spatial domain incident electric field as a signal source for the spatial domain electromagnetic field; to generate a two-dimensional wavenumber domain electric field by performing a Fourier transform on the processed spatial domain wave equation along a direction in which the strata properties remain unchanged; to construct the relationship between the wavenumber domain scattered electric field and the wavenumber domain incident electric field using a wavenumber domain electric field difference scheme based on the two-dimensional wavenumber domain electric field, and to establish a linear equation system; to obtain the wavenumber domain scattered electric field by substituting a preset analytical expression of the wavenumber domain incident field into the linear equation system; and to obtain the spatial domain scattered electric field by analyzing the wavenumber domain scattered electric field.

[0013] This application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described method.

[0014] This application also provides a computer-readable storage medium storing a computer program that performs the above-described methods.

[0015] This application also provides a computer program product, including a computer program / instructions that, when executed by a processor, implement the steps of the above-described method.

[0016] The beneficial technical effects of this application are as follows: During the simulation process, the incident field of the wavenumber domain electric field is extracted, and an equivalent wavenumber domain point source is used to solve for the wavenumber domain electric field scattering field. This not only effectively avoids point source singularities by using the analytical solution of the wavenumber domain incident field to obtain an equivalent wavenumber domain point source, but also, by extracting the incident field, only an inverse Fourier transform needs to be performed on the scattering field during the simulation, effectively reducing the impact of inverse Fourier transform errors. Overall, the scheme of using an equivalent point source in the wavenumber domain incident field can effectively improve the algorithm accuracy. Attached Figure Description

[0017] The accompanying drawings, which are included to provide a further understanding of this application and form part of this application, do not constitute a limitation thereof. In the drawings:

[0018] Figure 1 This is a schematic flowchart of a wavenumber domain incident field stripping method provided in an embodiment of this application;

[0019] Figure 2 A schematic diagram of the application process of the wavenumber domain incident field stripping method provided in an embodiment of this application;

[0020] Figure 3 This is a schematic diagram of a fault model provided in an embodiment of this application;

[0021] Figure 4 This is a schematic diagram of the spatial domain wave equation construction process provided in an embodiment of this application;

[0022] Figure 5 This is a schematic diagram of the spatial domain incident electric field stripping process provided in an embodiment of this application;

[0023] Figure 6 This is a schematic diagram of the spatial domain scattering electric field conversion process provided in an embodiment of this application;

[0024] Figure 7 This is a schematic diagram illustrating the verification of the wavenumber domain incident field analytical results provided in an embodiment of this application;

[0025] Figure 8 This is a schematic diagram comparing the electromagnetic logging response results of a fault model provided in an embodiment of this application.

[0026] Figure 9 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0027] The following will describe in detail the implementation methods of this application with reference to the accompanying drawings and embodiments, so as to fully understand how this application uses technical means to solve technical problems and achieve technical effects, and to implement it accordingly. It should be noted that, as long as there is no conflict, the various embodiments and features in each embodiment of this application can be combined with each other, and the resulting technical solutions are all within the protection scope of this application.

[0028] Furthermore, the steps shown in the flowchart in the accompanying drawings can be executed in a computer system such as a set of computer-executable instructions, and although a logical order is shown in the flowchart, in some cases the steps shown or described may be executed in a different order than that shown here.

[0029] Please refer to Figure 1 As shown, the wavenumber domain incident field stripping method provided in this application is applicable to two-dimensional formation drilling electromagnetic wave response simulation. The method includes:

[0030] S101 obtains two-dimensional formation model parameters and drilling electromagnetic logging instrument parameters according to simulation requirements;

[0031] S102 uses the two-dimensional formation model parameters and the drilling electromagnetic wave logging instrument parameters to construct a spatial domain wave equation describing the electromagnetic field in space and its relationship with the transmission signal of the drilling electromagnetic wave logging instrument, starting from the differential form of Maxwell's equations.

[0032] S103 calculates the incident electric field in the spatial domain using the resistivity of the stratum where the instrument is located and the transmitted antenna signal, and performs stripping processing on the spatial domain wave equation based on the incident electric field in the spatial domain.

[0033] S104 calculates the spatial domain scattered electric field based on the spatial domain wave equation after stripping, and superimposes the spatial domain scattered electric field and the spatial domain incident electric field to obtain the spatial domain total field.

[0034] The process of stripping the spatial domain wave equation based on the spatial domain incident electric field includes: analyzing the formation conditions within the instrument's detection range based on the two-dimensional formation model parameters and the parameters of the drilling electromagnetic wave logging instrument; and setting the spatial domain scattered electric field to zero when the formation within the instrument's detection range is a homogeneous medium. Further, calculating the spatial domain scattered electric field based on the stripped spatial domain wave equation includes: using the spatial domain incident electric field as the signal source of the spatial domain electromagnetic field; generating a wavenumber domain two-dimensional electric field by performing a Fourier transform on the processed spatial domain wave equation along a direction invariant to the formation properties; constructing the relationship between the wavenumber domain scattered electric field and the wavenumber domain incident electric field using a wavenumber domain electric field difference scheme based on the wavenumber domain two-dimensional electric field, and establishing a linear equation system; substituting a preset analytical expression for the wavenumber domain incident field into the linear equation system to obtain the wavenumber domain scattered electric field; and obtaining the spatial domain scattered electric field through analysis of the wavenumber domain scattered electric field.

[0035] For details, please refer to Figure 2 As shown, in practical work, the specific implementation process of the wavenumber domain incident field stripping method provided in this application is as follows:

[0036] S201 According to the simulation requirements, input the two-dimensional stratigraphic structure. Under normal circumstances, the corresponding stratigraphic model can be designed in two-dimensional visualization software, and the key parameters of the model can be exported and then input into the algorithm of this application.

[0037] S202 According to the simulation requirements, input the parameters of the logging-while-drilling electromagnetic wave instrument. There are many types of logging-while-drilling electromagnetic wave instruments and the parameters of the instruments vary greatly. When using this application to simulate the logging response, it is necessary to input specific parameters such as coil spacing and working frequency according to the actual simulation instrument.

[0038] S203 starts from the differential form of Maxwell's equations and establishes a spatial domain wave equation to describe the electromagnetic field in space and its relationship with the signal transmitted by the drilling electromagnetic wave logging instrument.

[0039] S204 ignores the heterogeneity of the strata and calculates the spatial domain incident field based on the resistivity of the strata where the instrument is located and the transmitted antenna signal.

[0040] S205 determines whether the strata within the instrument's detection range are a homogeneous medium. If yes, the scattered field is set to zero, and the process proceeds directly to step S211; otherwise, the process proceeds to step S206.

[0041] S206 processes the spatial domain wave equation by separating the spatial domain incident field from the total field and using the incident field as the signal source of the spatial domain electromagnetic field.

[0042] S207 considers the strata to be two-dimensional. A Fourier transform is performed on the spatial domain electric field wave equation along the direction where the strata properties remain unchanged. This transformation can transform the three-dimensional electric field in the spatial domain into a two-dimensional electric field in the wavenumber domain.

[0043] S208 derives the wavenumber domain electric field difference scheme, establishes the relationship between the wavenumber domain scattered electric field and the wavenumber domain incident electric field, and establishes a linear system of equations;

[0044] S209 Derive the analytical expression of the incident field in the wavenumber domain, substitute it into the linear equations established in step S208, and solve the linear equations using the LU decomposition method to obtain the scattered electric field.

[0045] S210 performs an inverse Fourier transform on the wavenumber domain scattered electric field to obtain the spatial domain scattered electric field.

[0046] S211 superimposes the scattered electric field with the incident electric field in the spatial domain to obtain the total field in the spatial domain, and outputs it.

[0047] In step S201, the two-dimensional formation structure input in the drilling electromagnetic wave response simulation is mainly the resistivity distribution of the formation, including the formation boundaries and the resistivity of each layer. In this embodiment, a structure is established as follows: Figure 3 The fault model shown contains four formations in both the hanging wall and footwall, with resistivity of 3 Ω·m, 10 Ω·m, 2 Ω·m, and 5 Ω·m from top to bottom, and a fault dip angle of 60°. In step S202, inputting the instrument coil spacing is mainly to determine the relative positional relationship between the instrument's transmitting and receiving antennas. Combined with the wellbore trajectory, the specific depths of the transmitting source and receiving point can be determined. Inputting the instrument operating frequency is to calculate the logging response at the corresponding frequency. In this embodiment, only a single-transmitter, single-receiver instrument structure is considered, where the transmitting coil is located below and the receiving coil is located above, the coil spacing is 5m, and the instrument operating frequency is 48kHz.

[0048] Please refer to Figure 4 As shown, in the above embodiments, constructing a spatial domain wave equation describing the electromagnetic field in space and its relationship with the transmitted signal of the drilling electromagnetic wave logging instrument, starting from the differential form of Maxwell's equations, may include:

[0049] S401 starts from the differential form of Maxwell's equations and constructs the first Maxwell's equations for harmonic electromagnetic fields in general lossy media.

[0050] S402 eliminates the magnetic field of the first Maxwell's equations to obtain the space domain wave equation.

[0051] Specifically, in practical work, the established two-dimensional strata are taken as general silt media, and the time-harmonic electromagnetic field satisfies Maxwell's equations:

[0052]

[0053] In the formula, E(H) represents the electric field (magnetic field) in space, and M... i (J i Let ω be the magnetic flux density (current density), ω be the angular frequency, μ(ε) be the permeability (dielectric constant) of the medium, and σ′ be the conductivity tensor of the medium. Eliminating the magnetic field, we obtain the wave equation for the electric field in the spatial domain:

[0054]

[0055] Subsequently, ignoring the heterogeneity of the formation, the spatial domain incident field is calculated based on the resistivity of the formation where the instrument is located and the transmitting antenna signal. In this embodiment, the instrument drills into the formation from top to bottom. During this process, the resistivity of the formation where the transmitting antenna is located will change with depth. Therefore, when calculating the spatial domain incident field, it is necessary to combine the specific depth of the logging point. For example, when the transmitting antenna is located in the uppermost layer, the incident field under a 3Ω·m background is calculated.

[0056] In this embodiment, the input stratum is a two-dimensional fault structure, and the medium within the instrument's detection range is not homogeneous. Therefore, step S206 is performed to separate the spatial domain incident field from the total field; see reference. Figure 5 As shown, in one embodiment of this application, the stripping process of the spatial domain wave equation based on the incident electric field in the spatial domain includes:

[0057] S501 starts from the differential form of Maxwell's equations and constructs a second set of Maxwell's equations for a homogeneous lossy medium.

[0058] S502 subtracts the first Maxwell's equations from the second Maxwell's equations and eliminates the magnetic field to obtain the spatial domain wave equation stripped of the incident electric field in the spatial domain.

[0059] Specifically, when the transmitting antenna is located in a certain stratum, ignoring the heterogeneity of the stratum, the antenna is located in a homogeneous silicic medium. In this case, the time-harmonic Maxwell's equations can be expressed as:

[0060]

[0061] In the formula, the superscript i in the electric field and magnetic field indicates the incident field.

[0062] Subtracting Maxwell's equations for a general gyped medium from those for a homogeneous gyped medium, and eliminating the magnetic field, the incident field can be separated from the total field, yielding the wave equations in the spatial domain:

[0063]

[0064] In the equation, the superscript 's' of the electric field indicates the scattered field. Therefore, the left side of the wave equation does not include the incident field, while the right side represents the signal source in terms of the incident field.

[0065] Please refer to Figure 6 As shown, in one embodiment of this application, the wavenumber domain incident field analytical expression is substituted into the linear equation system to obtain the wavenumber domain scattered electric field. The spatial domain scattered electric field is obtained through the analysis of the wavenumber domain scattered electric field, including:

[0066] S601 substitutes the preset analytical expression of the incident field in the wavenumber domain into the linear equation set and uses the LU decomposition method to solve the linear equation set to obtain the wavenumber domain scattered electric field.

[0067] S602 performs an inverse Fourier transform on the wavenumber domain scattered electric field to obtain the spatial domain scattered electric field.

[0068] Specifically, considering the strata as two-dimensional, a Fourier transform is performed on the spatial domain electric field wave equation along the direction where the strata properties remain unchanged. This transform converts the three-dimensional electric field in the spatial domain into a two-dimensional electric field in the wavenumber domain. Since the strata parameters remain unchanged along the strata strike, the inverse Fourier transform of the electric field wave equation only affects the electric field term and not the strata parameters. Therefore, the wavenumber domain electric field wave equation is formally identical to that in the spatial domain. Subsequently, by deriving the wavenumber domain electric field difference scheme, the relationship between the wavenumber domain scattered electric field and the wavenumber domain incident electric field is established, and a system of linear equations is established. The analytical expression of the wavenumber domain incident field is derived, substituted into the linear equations, and the LU decomposition method is used to solve the linear equations to obtain the wavenumber domain scattered electric field. An inverse Fourier transform is performed on the wavenumber domain scattered electric field to obtain the spatial domain scattered electric field. Furthermore, in another embodiment of this application, the method further includes: constructing a spatial domain scalar Green's function starting from the Green's function, and obtaining the magnetic dipole-generated electric field by scalarizing the spatial domain scalar Green's function; and performing an inverse Fourier transform on the magnetic dipole-generated electric field to obtain a preset wavenumber domain incident field analytical expression.

[0069] In practical work, the analytical expression of the incident field in the wavenumber domain is the core of the wavenumber domain incident field stripping in this application, and the spatial domain scalar Green's function can be expressed as:

[0070]

[0071] In the formula, r is the field point and r' is the source point. The dyadic Green's function can be expressed as:

[0072]

[0073] Thus, the electric field generated by the magnetic dipole is obtained:

[0074]

[0075] In the formula, |ρ-ρ′| is the distance from the field point to the source point, k is the wave number, and the subscript indicates the wave number direction.

[0076] A portion of the integrand in the right-hand side of the electric field generated by a magnetic dipole is denoted as:

[0077]

[0078] And by expanding them separately, we get:

[0079]

[0080] According to the definition of the inverse Fourier transform, k in the equation... y Replace with -k y back, This refers to the spectral electric field of the magnetic dipole source in a homogeneous medium, i.e., the incident field of the magnetic dipole source in the wavenumber domain. After obtaining the analytical expression for the wavenumber domain field, the background resistivity of the formation and the instrument operating frequency can be substituted to calculate the incident field at all grid nodes. To verify the correctness of the wavenumber domain incident field of this application, the spatial domain incident field is first calculated, then transformed to the wavenumber domain using Fourier transform, and finally compared with the calculated wavenumber domain incident field results of this application. Figure 7 The diagram shows the analytical solution in the wavenumber domain and the transformation results in the spatial domain. It can be seen that the two solutions are in agreement, verifying the correctness of the incident field in the wavenumber domain.

[0081] Finally, the scattered electric field in the spatial domain is superimposed with the incident electric field in the spatial domain to obtain the total field in the spatial domain, which is then output. That is, by superimposing the incident field and the scattered electric field in the spatial domain, the total field can be obtained. In this embodiment, drilling electromagnetic wave logging utilizes magnetic field signals; therefore, the electric field is further converted into a magnetic field and output. Figure 8 A comparison of the 2.5D FDFD (Finite Difference Frequency Array) simulation results based on wavenumber domain incident field stripping and the 3D FEM (Finite Element Model) simulation results shows that the two are in good agreement, verifying the correctness and rationality of this application.

[0082] This application also provides a wavenumber domain incident field stripping device suitable for two-dimensional formation drilling electromagnetic wave response simulation. The device includes an acquisition module, a construction module, a stripping module, and a generation module. The acquisition module is used to obtain two-dimensional formation model parameters and drilling electromagnetic wave logging instrument parameters according to simulation requirements. The construction module is used to construct a spatial domain wave equation describing the electromagnetic field in space and its relationship with the transmitted signal of the drilling electromagnetic wave logging instrument, starting from the differential form of Maxwell's equations, using the two-dimensional formation model parameters and the drilling electromagnetic wave logging instrument parameters. The stripping module is used to calculate the spatial domain incident electric field through the resistivity of the formation where the instrument is located and the transmitted antenna signal, and strip the spatial domain wave equation according to the spatial domain incident electric field. The generation module is used to calculate the spatial domain scattered electric field according to the stripped spatial domain wave equation, and superimpose the spatial domain scattered electric field and the spatial domain incident electric field to obtain the spatial domain total field.

[0083] The generation module includes a conversion unit, which is used to use the incident electric field in the spatial domain as a signal source for the electromagnetic field in the spatial domain; to generate a two-dimensional electric field in the wavenumber domain by performing a Fourier transform on the processed wave equation in the spatial domain along a direction in which the geological properties remain unchanged; to construct the relationship between the scattered electric field in the wavenumber domain and the incident electric field in the wavenumber domain using a wavenumber domain electric field difference scheme based on the two-dimensional electric field in the wavenumber domain, and to establish a system of linear equations; to obtain the scattered electric field in the wavenumber domain by substituting the preset analytical expression of the incident electric field in the wavenumber domain into the system of linear equations; and to obtain the scattered electric field in the spatial domain by analyzing the scattered electric field in the wavenumber domain.

[0084] Since the principle by which this device solves the problem is similar to that of the wavenumber domain incident field stripping method, the implementation of this device can be found in the implementation of the wavenumber domain incident field stripping method, and the repetitions will not be repeated.

[0085] The beneficial technical effects of this application are as follows: During the simulation process, the incident field of the wavenumber domain electric field is extracted, and an equivalent wavenumber domain point source is used to solve for the wavenumber domain electric field scattering field. This not only effectively avoids point source singularities by using the analytical solution of the wavenumber domain incident field to obtain an equivalent wavenumber domain point source, but also, by extracting the incident field, only an inverse Fourier transform needs to be performed on the scattering field during the simulation, effectively reducing the impact of inverse Fourier transform errors. Overall, the scheme of using an equivalent point source in the wavenumber domain incident field can effectively improve the algorithm accuracy.

[0086] This application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the computer program to implement the above-described method.

[0087] This application also provides a computer-readable storage medium storing a computer program that performs the above-described methods.

[0088] This application also provides a computer program product, including a computer program / instructions that, when executed by a processor, implement the steps of the above-described method.

[0089] like Figure 9 As shown, the electronic device 600 may also include: a communication module 110, an input unit 120, an audio processor 130, a display 160, and a power supply 170. It is worth noting that the electronic device 600 does not necessarily need to include these components. Figure 9 All components shown; in addition, the electronic device 600 may also include Figure 9 For components not shown, please refer to existing technology.

[0090] like Figure 9 As shown, the central processing unit 100, sometimes also referred to as a controller or operating control, may include a microprocessor or other processor device and / or logic device. The central processing unit 100 receives inputs and controls the operation of various components of the electronic device 600.

[0091] The memory 140 may be, for example, one or more of a cache, flash memory, hard drive, removable media, volatile memory, non-volatile memory, or other suitable devices. It may store the aforementioned failure-related information, and also store a program for executing that information. The central processing unit 100 may execute the program stored in the memory 140 to perform information storage or processing, etc.

[0092] Input unit 120 provides input to central processing unit 100. Input unit 120 may be, for example, a keypad or touch input device. Power supply 170 provides power to electronic device 600. Display 160 displays images and text. Display may be, for example, an LCD display, but is not limited thereto.

[0093] The memory 140 can be a solid-state memory, such as a read-only memory (ROM), random access memory (RAM), a SIM card, etc. It can also be a memory that retains information even when power is off, can be selectively erased, and contains more data; examples of this type of memory are sometimes referred to as EPROMs. The memory 140 can also be some other type of device. The memory 140 includes a buffer memory 141 (sometimes referred to as a buffer). The memory 140 may include an application / function storage unit 142 for storing application programs and function programs or processes for executing the operation of the electronic device 600 via the central processing unit 100.

[0094] The memory 140 may also include a data storage unit (data 143) for storing data, such as contacts, digital data, pictures, sounds, and / or any other data used by the electronic device. The driver storage unit (driver 144) of the memory 140 may include various drivers for the electronic device's communication functions and / or for performing other functions of the electronic device (such as messaging applications, address book applications, etc.).

[0095] The communication module 110 is a transmitter / receiver 110 that transmits and receives signals via antenna 111. The communication module (transmitter / receiver) 110 is coupled to the central processing unit 100 to provide input signals and receive output signals, which can be the same as in a conventional mobile communication terminal.

[0096] Based on different communication technologies, multiple communication modules 110 can be configured in the same electronic device, such as cellular network modules, Bluetooth modules, and / or wireless LAN modules. The communication module (transmitter / receiver) 110 is also coupled to a speaker 131 and a microphone 132 via an audio processor 130 to provide audio output via the speaker 131 and receive audio input from the microphone 132, thereby enabling typical telecommunications functions. The audio processor 130 may include any suitable buffer, decoder, amplifier, etc. Additionally, the audio processor 130 is coupled to a central processing unit 100, enabling on-device recording via the microphone 132 and on-device playback of stored audio via the speaker 131.

[0097] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0098] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0099] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0100] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0101] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of this application. It should be understood that the above descriptions are merely specific embodiments of this application and are not intended to limit the scope of protection of this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the scope of protection of this application.

Claims

1. A wavenumber domain incident field stripping method, applicable to two-dimensional formation drilling electromagnetic wave response simulation, characterized in that, The method includes: The parameters of the two-dimensional formation model and the parameters of the electromagnetic logging-while-drilling instrument are obtained according to the simulation requirements. Using the parameters of the two-dimensional formation model and the parameters of the logging-while-drilling (LWD) instrument, a spatial domain wave equation describing the electromagnetic field in space and its relationship with the transmitted signal of the LWD instrument is constructed from the differential form of Maxwell's equations. The incident electric field in the spatial domain is calculated using the resistivity of the stratum where the instrument is located and the transmitted antenna signal. The spatial domain wave equation is then stripped based on the incident electric field in the spatial domain. The spatial domain scattered electric field is calculated based on the spatial domain wave equation after stripping, and the spatial domain scattered electric field and the spatial domain incident electric field are superimposed to obtain the spatial domain total field.

2. The wavenumber domain incident field stripping method according to claim 1, characterized in that, Before stripping the spatial domain wave equation based on the spatial domain incident electric field, the process also includes: The formation conditions within the instrument's detection range are analyzed based on the parameters of the two-dimensional formation model and the parameters of the electromagnetic logging-while-drilling instrument. When the strata within the instrument's detection range are homogeneous media, the spatial domain scattered electric field is set to zero.

3. The wavenumber domain incident field stripping method according to claim 1, characterized in that, Starting from the differential form of Maxwell's equations, a spatial domain wave equation describing the electromagnetic field in space and its relationship with the signal emitted by the drilling electromagnetic logging instrument is constructed, including: Starting from the differential form of Maxwell's equations, the first Maxwell's equations are used to construct harmonic electromagnetic fields for general lossy media. The spatial domain wave equation is obtained by eliminating the magnetic field of the first Maxwell's equations.

4. The wavenumber domain incident field stripping method according to claim 3, characterized in that, The stripping process of the spatial domain wave equation based on the incident electric field in the spatial domain includes: Starting from the differential form of Maxwell's equations, a second set of Maxwell's equations is constructed for a homogeneous lossy medium. Subtracting the first Maxwell's equations from the second Maxwell's equations and eliminating the magnetic field yields the spatial domain wave equation stripped of the incident electric field in the spatial domain.

5. The wavenumber domain incident field stripping method according to claim 1, characterized in that, The spatial domain scattered electric field, calculated based on the spatial domain wave equation after stripping, includes: The incident electric field in the spatial domain is used as the signal source of the electromagnetic field in the spatial domain. A two-dimensional electric field in the wavenumber domain is generated by performing a Fourier transform on the processed spatial domain wave equation along a direction in which the strata properties remain unchanged. Based on the two-dimensional electric field in the wavenumber domain, the relationship between the wavenumber domain scattered electric field and the wavenumber domain incident electric field is constructed through a wavenumber domain electric field difference scheme, and a linear system of equations is established. The wavenumber domain incident field analytical expression is substituted into the linear equation system to obtain the wavenumber domain scattered electric field, and the spatial domain scattered electric field is obtained through the analysis of the wavenumber domain scattered electric field.

6. The wavenumber domain incident field stripping method according to claim 5, characterized in that, The method further includes: A spatial domain scalar Green's function is constructed by starting with the Green's function, and the electric field generated by the magnetic dipole is obtained by scalarizing the spatial domain scalar Green's function. The electric field generated by the magnetic dipole is processed by inverse Fourier transform to obtain the analytical expression of the incident field in the preset wavenumber domain.

7. The wavenumber domain incident field stripping method according to claim 5, characterized in that, Substituting the pre-defined analytical expression for the incident field in the wavenumber domain into the linear equations yields the wavenumber domain scattered electric field. Analysis of this wavenumber domain scattered electric field reveals the spatial domain scattered electric field, which includes: The pre-defined analytical expression of the incident field in the wavenumber domain is substituted into the linear equations, and the wavenumber domain scattered electric field is obtained by solving the linear equations using the LU decomposition method. The spatial domain scattered electric field is obtained by performing an inverse Fourier transform on the wavenumber domain scattered electric field.

8. A wavenumber domain incident field stripping device, suitable for two-dimensional formation drilling electromagnetic wave response simulation, characterized in that, The device includes a data acquisition module, a construction module, a stripping module, and a generation module; The acquisition module is used to obtain two-dimensional formation model parameters and drilling electromagnetic logging instrument parameters according to simulation requirements. The construction module is used to construct a spatial domain wave equation describing the electromagnetic field in space and its relationship with the transmitted signal of the drilling electromagnetic wave logging instrument, starting from the differential form of Maxwell's equations, using the parameters of the two-dimensional formation model and the parameters of the drilling electromagnetic wave logging instrument. The stripping module is used to calculate the incident electric field in the spatial domain using the resistivity of the stratum where the instrument is located and the transmitted antenna signal, and to strip the spatial domain wave equation based on the incident electric field in the spatial domain. The generation module is used to calculate the spatial domain scattered electric field based on the spatial domain wave equation after stripping, and to superimpose the spatial domain scattered electric field and the spatial domain incident electric field to obtain the spatial domain total field.

9. The wavenumber domain incident field stripping device according to claim 8, characterized in that, The generation module includes a conversion unit, which is used to take the incident electric field in the spatial domain as the signal source of the electromagnetic field in the spatial domain; to generate a two-dimensional electric field in the wavenumber domain by performing a Fourier transform on the processed wave equation in the direction where the strata properties remain unchanged; and to construct the relationship between the scattered electric field in the wavenumber domain and the incident electric field in the wavenumber domain using a wavenumber domain electric field difference scheme based on the two-dimensional electric field in the wavenumber domain, and to establish a linear equation system. The wavenumber domain incident field analytical expression is substituted into the linear equation system to obtain the wavenumber domain scattered electric field, and the spatial domain scattered electric field is obtained through the analysis of the wavenumber domain scattered electric field.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the method of any one of claims 1 to 7.

11. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the method of any one of claims 1 to 7.

12. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instructions are executed by the processor, they implement the steps of the method according to any one of claims 1 to 7.

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