Virtual wave field imaging method based on transient electromagnetic multiple components

Abstract

The invention belongs to the technical field of artificial source electromagnetic detection, and discloses a transient electromagnetic multi-component-based virtual wave field imaging method, which comprises the following steps of solving an electric source transient electromagnetic electric field horizontal component and a magnetic induction intensity vertical component based on a transient electromagnetic one-dimensional forward modeling theory; converting the multi-component transient electromagnetic diffusion field into a virtual wave field based on a fine integration method; on the basis of the multi-component virtual wave field, a second-order Born approximation method is used, the speed disturbance quantity of an electrical interface is obtained, and interface information is obtained; and comprehensive geological information is obtained by integrating imaging results of the electric field horizontal component and the magnetic induction intensity vertical component. According to the virtual wave field imaging method based on the transient electromagnetic multiple components, the magnetic induction intensity vertical component and the electric field horizontal component are received at the same time under the condition of the transient electromagnetic diffusion field generated through excitation of the electrical source, and more comprehensive geological information is obtained compared with a traditional single-component imaging method; the purpose of accurately and rapidly explaining electromagnetic data is achieved.

Description

Technical Field

[0001] The invention relates to the technical field of artificial source electromagnetic detection, and in particular to a virtual wave field imaging method based on transient electromagnetic multi-components. Background Art

[0002] Transient electromagnetic method is a time domain electromagnetic exploration method, which is widely used in oil and gas resource detection, groundwater investigation, metal mine exploration and goaf detection. There are two types of devices: loop source and electrical source. Among them, the electrical source transient electromagnetic method has the characteristics of large exploration depth, high vertical resolution, and sensitive detection of abnormal bodies; and it can collect electric field and magnetic field components at the same time, and has good resolution for good conductors and high-resistance targets, which can provide richer geoelectric information.

[0003] Transient electromagnetic diffusion field has the characteristics of inductive diffusion, which is not easy to image; and transient electromagnetic three-dimensional inversion has large computational complexity, slow speed, and high requirements for computer memory. It is known that a mathematical relationship can be established between the diffusion field and the wave field. Based on the above situation, the transient electromagnetic diffusion field can be first converted into a virtual wave field, and then the virtual wave field imaging method can be used to quickly image and interpret the geological interface. The seismic migration imaging method based on the reverse extrapolation of the wave field is a process of back-transmitting the data observed on the ground and then obtaining the image of the underground medium. The final effect of its application is determined by the migration data, migration velocity, and migration algorithm. Therefore, high-quality migration data and accurate and reasonable velocity models are necessary conditions for the successful implementation of the seismic migration imaging method. It is known that the Born approximation algorithm is applicable to both pre-stack data and post-stack data; by obtaining the velocity perturbation amount, the depth profile can be directly obtained, overcoming the defect that the velocity model is given in advance by the migration algorithm; and the calculation speed is fast and the computer memory requirement is not high.

[0004] In order to linearize the formal solution of the wave equation, the conventional Born approximation algorithm ignores the scattered field and only retains the first term in the scattering sequence, which loses some useful information. This makes the algorithm only applicable to the imaging problem of small perturbation models. For large perturbation models, the conventional Born approximation algorithm will produce large errors and cannot accurately reflect the position and morphological characteristics of the geological interface. In addition, multiple components of electromagnetic field responses can be collected in electrical source transient electromagnetic forward simulation and field exploration, and electromagnetic fields of different components can reflect geological target information of different offset distances and different electrical properties. Traditional transient electromagnetic virtual wave field imaging methods are all interpreted for single-component electromagnetic field data. Summary of the invention

[0005] The object of the present invention is to provide a virtual wavefield imaging method based on transient electromagnetic multi-components. Under the condition of the transient electromagnetic diffusion field excited by an electrical source, the vertical component of the magnetic induction intensity and the horizontal component of the electric field are simultaneously received. The wavefield inverse transformation is performed on the two components respectively by using the precise integration method, and the multi-component pseudo-seismic imaging is carried out by using the second-order Born approximation algorithm to determine the position and shape of the underground geological interface. Compared with the traditional single-component imaging method, the present invention obtains more comprehensive geological information and improves the ability to accurately and quickly interpret electromagnetic data.

[0006] To achieve the above object, the present invention provides a virtual wavefield imaging method based on transient electromagnetic multi-components, including the following steps:

[0007] S1. Based on the existing open-source code of one-dimensional transient electromagnetic forward modeling, the horizontal component of the electric field and the vertical component of the magnetic induction intensity are respectively obtained to obtain the electromagnetic field response, and the signal intensity magnitudes of the two components in a homogeneous half-space and their sensitivities to resistivity and offset are analyzed;

[0008] S2. Based on the precise integration method, the multi-component transient electromagnetic diffusion field is converted into a virtual wavefield;

[0009] S3. Based on the multi-component virtual wavefield, the velocity perturbation amount of the electrical interface is obtained by using the second-order Born approximation method to obtain the interface information;

[0010] S4. By using Green's theorem and through derivation, the relationship expression between the scattered wavefield and the velocity perturbation amount is established to achieve the purpose of imaging the underground electrical interface.

[0011] Preferably, in step S2, the relationship formula based on the transient electromagnetic diffusion field and the virtual wavefield is established as follows:

[0012]

[0013] where f(r,t) represents the electromagnetic field component, t represents time, with the unit of s; U(r,τ) represents the virtual wavefield, τ represents the virtual time, and its unit is

[0014] Preferably, based on the above relationship formula between the transient electromagnetic diffusion field and the virtual wavefield, the wavefield inverse transformation is performed. Equation (1) belongs to the first-kind Fredholm integral equation and is solved by using the precise integration method. The specific process is as follows:

[0015] S221. First, a linear equation system is constructed as follows:

[0016] Ax = b (2);

[0017] Among them, A represents an n-order positive definite matrix, and b represents an n-dimensional real vector; let H = -A and r = b, and the transformation gives:

[0018] Hx + r = 0 (3);

[0019] S222. Secondly, establish a first-order differential equation as follows:

[0020]

[0021] The above first-order differential equation (4) can be regarded as the form of the transient heat conduction equation, while the steady-state heat conduction equation has the form of equation (3); the solution of equation (4) is as follows:

[0022]

[0023] Among them, H is a negative definite matrix and r is a constant vector;

[0024] S223. According to equation (5), when time t' → ∞, equation (4) approaches equation (3), and at this time exp(Ht') → 0, then the integral term in equation (5) approximates the solution of equation (3) as follows:

[0025]

[0026] Therefore, the solution of the linear equation system (2) is as follows:

[0027]

[0028] Based on the above process, the problem of solving an ill-conditioned linear equation system is transformed into a stable process of finding an integral;

[0029] S224. Solve equation (7), let the integration step size change by 2 k-1 ζ, then there is the following iterative expression:

[0030]

[0031] According to the recurrence formula of the precise integration method, there is Ta k = 2Ta k-1 + Ta k-1 Ta k-1 , after k times of cycling, exp(-2 k ζA) = I + Ta k ; combining the above formulas, we get:

[0032]

[0033] Among them, I represents the identity matrix, and T k represents the value of the matrix exponential function.

[0034] Preferably, in step S3, based on the multi-component virtual wave field, the second-order Born approximation method is used to obtain the velocity perturbation of the electrical interface. The specific process is as follows:

[0035] S31. Construct the equation satisfied by the transient electromagnetic diffusion field and the virtual wave field as follows:

[0036]

[0037] S32. The second-order Born approximation algorithm is based on the frequency-domain wave equation, and the complex transformation is performed on equation (10)(b) as follows:

[0038]

[0039] where v(r) represents the wave speed of the virtual wave field, and its magnitude is

[0040] S33. The velocity v(r) and the wave field u(r,r s ,ω) in formula (11) are respectively decomposed into two parts as follows:

[0041]

[0042] where v0(r) represents the background wave speed, α(r) represents the velocity perturbation, and u i (r,r s ,ω) represents the background wave field, and u s (r,r s ,ω) represents the scattered wave field.

[0043] Preferably, in step S4, Green's theorem is used, and after derivation, the relationship expression between the scattered wave field and the velocity perturbation is established to achieve the purpose of imaging the underground electrical interface. The specific process is as follows:

[0044] S41. The relationship expression between the scattered wave field u s (r,r s ,ω) and the velocity perturbation α(r) is as follows:

[0045] u s (r g ,r s ,k) = ∫k 2 α(r)G(r,r g ,k)u(r,r s ,k)d 3 r (13);

[0046] where, Expanding formula (13) can obtain the scattering sequence as follows:

[0047]

[0048] Among them, the formula (14) has the following recurrence relation:

[0049] u n+1 (r g , r s , k) = ∫k 2 α(r')G(r g , r', k)u n (r', r s , k)d 3 r'(15);

[0050] S42. Take the first two terms of the above formula (14) to obtain the expression of the second-order Born approximation as follows:

[0051]

[0052] S43. Solve the formula (16) to obtain the velocity perturbation of the underground electrical interface, and realize the imaging of the underground electrical interface.

[0053] Therefore, the present invention adopts the above-mentioned virtual wavefield imaging method based on transient electromagnetic multi-components. Under the condition of the transient electromagnetic diffusion field excited by an electrical source, the vertical component of the magnetic induction intensity and the horizontal component of the electric field are received simultaneously. The wavefield inverse transformation is performed on the two components respectively by using the precise integration method, and the multi-component pseudo-seismic imaging is performed by using the second-order Born approximation algorithm to determine the position and shape of the underground geological interface. Compared with the traditional single-component imaging method, the present invention obtains more comprehensive geological information and improves the ability to accurately and quickly interpret electromagnetic data.

[0054] Next, through the drawings and embodiments, the technical solution of the present invention will be further described in detail. Description of the Drawings

[0055] Figure 1 It is a complex three-dimensional geological model diagram in the embodiment of the present invention;

[0056] Figure 2 It is a multi-trace map of the vertical component of the magnetic induction intensity of the complex three-dimensional model; among them, (a) offset = 300m; (b) offset = 800m;

[0057] Figure 3 It is a multi-trace map of the horizontal component of the electric field of the complex three-dimensional model; among them, (a) offset = 300m; (b) offset = 800m;

[0058] Figure 4It is the virtual wave field map of the vertical component of the magnetic induction intensity of a complex three-dimensional model; among them, (a) offset = 300 m; (b) offset = 800 m;

[0059] Figure 5 It is the virtual wave field map of the horizontal component of the electric field of a complex three-dimensional model; among them, (a) offset = 300 m; (b) offset = 800 m;

[0060] Figure 6 It is the imaging result of the vertical component of the magnetic induction intensity of a complex three-dimensional model; among them, (a) offset = 300 m; (b) offset = 800 m;

[0061] Figure 7 It is the imaging result map of the horizontal component of the electric field of a complex three-dimensional model; among them, (a) offset = 300 m; (b) offset = 800 m;

[0062] Figure 8 It is the flow chart of a virtual wave field imaging method based on transient electromagnetic multi-components of the present invention. Specific implementation manners

[0063] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0064] As Figure 8 shown, a virtual wave field imaging method based on transient electromagnetic multi-components of the present invention includes the following steps:

[0065] S1. Based on the existing open-source code of transient electromagnetic one-dimensional forward modeling, obtain the horizontal component of the electric field and the vertical component of the magnetic induction intensity respectively, obtain the electromagnetic field response, and analyze the signal intensity of the two components under a homogeneous half-space and their sensitivities to resistivity and offset.

[0066] S2. Based on the relationship between the diffusion field and the virtual wave field, use the precise integration method to solve the wave field inverse transform.

[0067] S21. Establish the relationship formula between the transient electromagnetic diffusion field and the virtual wave field as follows:

[0068]

[0069] where f(r, t) represents the electromagnetic field component, t represents time, with the unit of s; U(r, τ) represents the virtual wave field, τ represents the virtual time, and its unit is

[0070] S22. Based on the above relationship formula between the transient electromagnetic diffusion field and the virtual wave field, perform the wave field inverse transform.

[0071] The process of obtaining the virtual wave field from the known transient electromagnetic diffusion field is called wave field inverse transformation. Equation (1) belongs to the first kind of Fredholm integral equation and is solved by the precise integration method. The specific process is as follows:

[0072] S221. First, construct a linear equation system as follows:

[0073] Ax = b (2);

[0074] where A represents an n-order positive definite matrix, and b represents an n-dimensional real vector. Denote H = -A, r = b, and transform to get:

[0075] Hx + r = 0 (3);

[0076] S222. Second, establish a first-order differential equation as follows:

[0077]

[0078] The above first-order differential equation (4) can be regarded as the form of the transient heat conduction equation, while the steady-state heat conduction equation has the form of equation (3). Given the solution of equation (4) as follows:

[0079]

[0080] where H is a negative definite matrix and r is a constant vector.

[0081] S223. According to equation (5), when time t' → ∞, equation (4) approaches equation (3), and at this time exp(Ht') → 0. Therefore, the integral term in equation (5) approximates the solution of equation (3) as follows:

[0082]

[0083] Therefore, the solution of the linear equation system (2) is as follows:

[0084]

[0085] According to the above analysis, the problem of solving an ill-conditioned linear equation system can be transformed into a stable process of solving an integral.

[0086] S224. Next, solve equation (7). Let the integration step size change with 2 k-1 ζ, then there is the following iterative expression:

[0087]

[0088] According to the recurrence formula of the precise integration method, there is Ta k = 2Ta k-1 + Ta k-1 Tak-1 , after k cycles, we can obtain exp(-2 k ζA) = I + Ta k ; Combining the above formulas, we get:

[0089]

[0090] where I represents the identity matrix, and T k represents the value of the matrix exponential function.

[0091] According to the above content, the ill-posed problem of wavefield inverse transformation can be converted into a stable process of solving integrals by using the precise integration method, realizing the transformation from the transient electromagnetic multi-component diffusion field to the virtual wavefield.

[0092] S3. Based on the multi-component virtual wavefield, use the second-order Born approximation method to obtain the velocity perturbation of the electrical interface.

[0093] Refer to the second-order Born approximation algorithm in seismic exploration to image the position and shape of the underground electrical interface. The specific process is as follows:

[0094] S31. Construct the equation satisfied by the transient electromagnetic diffusion field and the virtual wavefield, as follows:

[0095]

[0096] S32. The second-order Born approximation algorithm is based on the frequency-domain wave equation and performs a complex transformation on equation (10)(b), as follows:

[0097]

[0098] where v(r) represents the wave speed of the virtual wavefield, and its magnitude is

[0099] S33. Decompose the velocity v(r) and the wavefield u(r,r s ,ω) in formula (11) into two parts, as follows:

[0100]

[0101] where v0(r) represents the background wave speed, α(r) represents the velocity perturbation, and u i (r,r s ,ω) represents the background wavefield, and u s (r,r s ,ω) represents the scattered wavefield.

[0102] S4. Apply Green's theorem. After a series of derivations, establish the relationship expression between the scattered wave field and the velocity perturbation, and achieve the purpose of imaging the underground electrical interface.

[0103] S41. The relationship expression between the scattered wave field u s (r, r s , ω) and the velocity perturbation α(r) is as follows:

[0104] u s (r g , r s , k) = ∫k 2 α(r)G(r, r g , k)u(r, r s , k)d 3 r (13);

[0105] Where, Expanding formula (13) can obtain the scattering sequence as follows:

[0106]

[0107] Among them, formula (14) has the following recurrence relation:

[0108] u n+1 (r g , r s , k) = ∫k 2 α(r')G(r g , r', k)u n (r', r s , k)d 3 r' (15);

[0109] S42. Take the first two terms of the above formula (14), and the expression of the second-order Born approximation can be obtained as follows:

[0110]

[0111] S43. Solve formula (16) to obtain the velocity perturbation of the underground electrical interface, and the purpose of imaging the underground electrical interface can be achieved.

[0112] Example

[0113] This example uses as Figure 1The complex three-dimensional geological model shown has the following model parameter settings: In a homogeneous half-space medium, there are two anomalous bodies with different burial depths, different scales, and different resistivities. The resistivity of the homogeneous half-space is 100 Ω·m; the resistivity of the first anomalous body is 1 Ω·m, with a scale of 800 m × 100 m × 10 m and a burial depth of 80 m; the resistivity of the second anomalous body is 1000 Ω·m, with a scale of 800 m × 120 m × 20 m and a burial depth of 130 m. The parameters of the transceiver device are as follows: The electrical source is arranged along the Y-axis, with a length of 500 m, and the coordinates of the two end points are (0 m, -250 m, 0 m) and (0 m, 250 m, 0 m) respectively. The transmitting current is 1 A, and the time range is [10 -5 s, 10 -1 s]; Two survey lines are parallel to the source, both with a length of 200 m. The offset of one survey line is 300 m, and the coordinates of the two end points are (300 m, -100 m, 0 m) and (300 m, 100 m, 0 m). The offset of the other survey line is 800 m, and the coordinates of the two end points are (800 m, -100 m, 0 m) and (800 m, 100 m, 0 m).

[0114] As Figure 2 and Figure 3 shown, they respectively represent the multi-trace maps of the vertical component of the magnetic induction intensity and the horizontal component of the electric field of the complex three-dimensional model. By comparing Figure 2 and Figure 3 it can be seen that the numerical value of the electromagnetic field decreases with the increase of the offset; near Y = 0 m, the early signal "sags" downward and the late signal "bulges" upward, which is caused by the existence of a shallow low-resistivity block and a deep high-resistivity block; however, the diffusion field data of both components cannot significantly highlight the position and morphological characteristics of the anomalous body.

[0115] As Figure 4 and Figure 5 shown, they respectively represent the virtual wave field maps of the vertical component of the magnetic induction intensity and the horizontal component of the electric field of the complex three-dimensional model. By comparing Figure 4 and Figure 5 it can be seen that the vertical component of the magnetic induction intensity reflects the shallow low-resistivity block significantly when the offset is 300 m; the horizontal component of the electric field is more sensitive to the deep high-resistivity block when the offset is 800 m.

[0116] As Figure 6 and Figure 7 shown, they respectively represent the imaging results of the vertical component of the magnetic induction intensity and the horizontal component of the electric field of the complex three-dimensional model. By comparing Figure 6 and Figure 7It can be seen that when the offset is 300 m, the vertical component of the magnetic induction intensity shows the most obvious reflection on the shallow low-resistivity anomaly body; when the offset increases to 800 m, the reflection on the deep high-resistivity block is the least prominent. On the contrary, when the offset is 800 m, the horizontal component of the electric field shows the most obvious reflection on the deep high-resistivity body.

[0117] Therefore, the present invention adopts the above-mentioned virtual wavefield imaging method based on transient electromagnetic multi-components. Under the condition of the transient electromagnetic diffusion field excited by an electric source, the vertical component of the magnetic induction intensity and the horizontal component of the electric field are received simultaneously. The wavefield inverse transformation is performed on the two components respectively by using the precise integration method, and the multi-component pseudo-seismic imaging is carried out by using the second-order Born approximation algorithm to determine the position and shape of the underground geological interface. Compared with the traditional single-component imaging method, the present invention obtains more comprehensive geological information and improves the ability to accurately and quickly interpret electromagnetic data.

[0118] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A virtual wave field imaging method based on transient electromagnetic multi-component, characterized in that: The following steps are involved: S1. Based on the existing transient electromagnetic one-dimensional forward modeling open source code, the horizontal component of the electric field and the vertical component of the magnetic induction intensity are obtained respectively, the electromagnetic field response is obtained, and the signal strength of the two components in a uniform half space and their sensitivity to resistivity and offset are analyzed; S2. Based on the precise integration method, the multi-component transient electromagnetic diffusion field is converted into a virtual wave field; S3. Based on the multi-component virtual wave field, the second-order Born approximation method is used to obtain the velocity perturbation of the electrical interface and obtain the interface information; S4. Using Green's theorem, after deduction, the relationship expression between the scattered wave field and the velocity disturbance is established to achieve underground electrical interface imaging.

2. The method for virtual wave field imaging based on transient electromagnetic multi-component according to claim 1, characterized in that: In step S2, a relationship between the transient electromagnetic diffusion field and the virtual wave field is established as follows: Among them, f(r,t) represents the electromagnetic field component, t represents time, and its unit is s; U(r,τ) represents the virtual wave field, τ represents the virtual time, and its unit is 3. The method for virtual wave field imaging based on transient electromagnetic multi-component according to claim 2, characterized in that: Based on the above relationship between transient electromagnetic diffusion field and virtual wave field, the wave field inverse transformation is performed. Equation (1) belongs to the first kind of Fredholm integral equation and is solved by the precise integration method. The specific process is as follows: S221. First, construct a linear equation system as follows: Ax=b(2); Where A represents an n-order positive definite matrix, and b represents an n-dimensional real vector; let H = -A, r = b, and the transformation is: Hx+r=0 (3); S222. Secondly, establish a first-order differential equation as follows: The first-order differential equation (4) can be regarded as the form of transient heat conduction equation, while the steady-state heat conduction equation has the form of equation (3); the solution of equation (4) is as follows: Among them, H is a negative definite matrix, r is a constant vector; S223. According to equation (5), when time t'→∞, equation (4) approaches equation (3), and at this time exp(Ht')→0, then the integral term in equation (5) approaches the solution of equation (3), as shown below: Therefore, the solution of the linear equation system (2) is as follows: Based on the above process, the problem of solving ill-conditioned linear equations is transformed into a stable process of finding integrals; S224, solve equation (7), set the integration step size to 2 k-1 ζ changes, then the iterative expression is as follows: According to the recursive formula of the precise integration method, Ta k =2Ta k-1 +Ta k-1 Ta k-1 After k cycles, we get exp(-2 k ζA)=I+Ta k ; Combining the above formulas, we get: Where I represents the identity matrix, T k Represents the value of the matrix exponential function.

4. The method for virtual wave field imaging based on transient electromagnetic multi-component according to claim 1, characterized in that: In step S3, based on the multi-component virtual wave field, the velocity perturbation of the electrical interface is obtained by using the second-order Born approximation method. The specific process is as follows: S31. Construct the equations satisfied by the transient electromagnetic diffusion field and the virtual wave field as follows: S32, the second-order Born approximation algorithm is based on the frequency domain wave equation, and the complex transformation of (b) in equation (10) is as follows: Among them, v(r) represents the wave velocity of the virtual wave field, and its magnitude is S33, replace the velocity v(r) and wave field u(r,r in formula (11) s ,ω) are decomposed into two parts as follows: Among them, v0(r) represents the background wave velocity, α(r) represents the velocity disturbance, and u i (r,r s ,ω) represents the background wave field, u s (r,r s ,ω) represents the scattered wave field.

5. The method for virtual wave field imaging based on transient electromagnetic multi-component according to claim 1, characterized in that: In step S4, Green's theorem is used to establish the relationship between the scattered wave field and the velocity disturbance through derivation to achieve underground electrical interface imaging. The specific process is as follows: S41, scattered wave field u s (r,r s The relationship between the velocity disturbance α(r) and the velocity disturbance ω is as follows: u s (r g ,r s ,k)=∫k 2 α(r)G(r,r g ,k)u(r,r s ,k)d 3 r (13); in, Expanding formula (13) can obtain the scattering sequence as follows: Among them, formula (14) has the following recursive relationship: u n+1 (r g ,r s ,k)=∫k 2 α(r')G(r g ,r',k)u n (r',r s ,k)d 3 r' (15); S42. Take the first two terms of equation (14) to obtain the expression of the second-order Born approximation, as shown below: S43. Solve formula (16) to obtain the velocity disturbance of the underground electrical interface, thereby realizing imaging of the underground electrical interface.

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