A method for calculating the multi-component electromagnetic wave logging response in triaxial anisotropic formations

Abstract

The invention discloses a method for calculating the multi-component electromagnetic wave logging response of a triaxial anisotropic formation, which relates to the technical field of petroleum exploration and development, including: inputting data; establishing a homogeneous triaxial anisotropic formation, calculating the tensor background magnetic field response P at the receiving antenna, j ; Obtain the magnetic field responses P1~P corresponding to all layers N ; Establish a simplified equivalent uniaxial anisotropic model M j ; Obtain equivalent uniaxial anisotropic models M1~M9; Use the uniaxial anisotropic model, combined with the Hertz potential function method, improved amplitude propagation coefficient algorithm and fast Hankel transform technology, to calculate the magnetic field tensor secondary field response S1~S N ; The uniform triaxial anisotropic medium response is superimposed with the secondary field response to obtain the total magnetic field response H j =P j +S j ; After the multi-component magnetic field response of the formation coordinate system is transformed, the magnetic field response of the instrument coordinate system is obtained, and then converted into tensor apparent conductivity. The method of the present invention avoids matrix operations and double infinite domain integration, and while ensuring the calculation accuracy, the forward modeling speed can be increased by more than 10 times.

Description

Technical Field

[0001] The invention relates to the technical field of petroleum exploration and development, belongs to the category of electric logging methods, and in particular to a method for calculating multi-component electromagnetic wave logging responses of triaxial anisotropic formations. Background Art

[0002] Multi-component electromagnetic wave logging has many advantages, such as rich measurement information, sensitivity to formation electrical properties and inclination, and strong interface detection capabilities. It plays an important role in cable well anisotropic resistivity detection and geological guidance while drilling. Affected by the combined influence of inclination, layer thickness and anisotropic resistivity, the response of this type of data is extremely complex, and the qualitative and quantitative evaluation of the data needs to rely on rapid forward and inversion. Affected by sedimentary grain sequence, microfracture development and layer thickness, resistivity anisotropy is generally developed in the formation, especially triaxial anisotropy is common in shale reservoirs. The existence of triaxial anisotropy increases the complexity of logging interpretation on the one hand, and makes calculation more difficult on the other.

[0003] At present, the forward modeling of multi-component electromagnetic wave logging in layered triaxial anisotropic formations mainly relies on three-dimensional numerical algorithms and one-dimensional pseudo-analytical algorithms. However, numerical algorithms have slow calculation speed and difficult to ensure accuracy, and are rarely used in multi-component induction logging data processing. Compared with uniaxial anisotropic formations, the pseudo-analytical algorithm for triaxial anisotropic formations involves double infinite domain integration and amplitude propagation matrix recursion, resulting in slow calculation speed and large memory usage.

[0004] Therefore, it is urgent to develop an equivalent calculation method for multi-component induction logging response to significantly improve the calculation speed of triaxial anisotropic formations to meet the needs of real-time data processing. Summary of the invention

[0005] In order to solve the above technical problems, the present invention discloses a method for calculating the multi-component electromagnetic wave logging response of a triaxial anisotropic formation. By constructing an equivalent anisotropic model, the difficulty of forward modeling is reduced and the calculation speed is improved, in order to lay a foundation for the real-time processing of such logging data.

[0006] To achieve the above object, the present invention adopts the following technical solutions:

[0007] A method for calculating multi-component electromagnetic wave logging response of triaxial anisotropic formations comprises the following steps:

[0008] s1. Input the horizontal layered triaxial anisotropic formation model, multi-component electromagnetic wave logging instrument parameters and sampling point locations; the model has N layers, and the conductivity in the x, y and z directions in the jth layer is σ x,j , σ y,j and σ z,j Indicates; instrument parameters include transmission frequency f and source distance L;

[0009] s2. For the jth stratum, a homogeneous triaxial anisotropic stratum is established, and the tensor background magnetic field response P at the receiving antenna is quickly calculated by combining the instrument parameters. j ;

[0010] s3. Execute step s2 for all strata in sequence to obtain the tensor background magnetic field responses P1 to P2 of uniform triaxial anisotropic strata corresponding to all layers. N ;

[0011] s4. For the i-th detection mode, using the multi-solution of the magnetic field in the homogeneous medium, a simplified equivalent uniaxial anisotropy model M is established j ;

[0012] s5. For the 9 detection modes, execute step s4 in sequence to obtain equivalent uniaxial anisotropic models M1 to M9;

[0013] s6. Using the uniaxial anisotropic model obtained in step s5, combined with the Hertz potential function method, the improved amplitude propagation coefficient algorithm and the fast Hankel transform technology, the magnetic field tensor secondary field response S1~S of the equivalent model is quickly calculated. N ; Secondary field response S j is the best approximation to the jth detection mode response of the original model;

[0014] s7. The uniform triaxial anisotropic medium response and the secondary field response are superimposed to obtain the total multi-component magnetic field response H of the layered triaxial anisotropic formation. j =P j +S j ;

[0015] s8. After coordinate transformation of the multi-component magnetic field response in the formation coordinate system, the magnetic field response in the instrument coordinate system is obtained, which is then converted into tensor apparent conductivity.

[0016] Optionally, in step s2, the tensor background magnetic field response P j The calculation method specifically includes:

[0017] s2.1 For the jth stratum, a homogeneous triaxial anisotropic stratum is established; if the conductivity along the x and y directions is consistent, the tensor background magnetic field response P is obtained by using the analytical formula of the magnetic field excited by the uniaxial anisotropic medium magnetic dipole source j ; Otherwise, execute step s2.2;

[0018] s2.2 Project the distance between the transmitting and receiving points in the three coordinate axis directions to obtain the two directions v and w with the smallest projection length. Perform double Fourier transform along the v and w directions to analytically calculate the spectral domain magnetic field at the receiving antenna of the three-axis anisotropic formation.

[0019] s2.3 Construct a uniaxial anisotropic formation, with the vertical and horizontal conductivity set to σ z,j and sqrt(σ x,j *σ y,j ), and then analytically calculate the uniaxial anisotropic formation spectral domain magnetic field

[0020] s2.4 Eliminating the contribution of the uniaxial anisotropic field in the spectral domain The double Fourier transform is converted to the polar coordinate system, including definite integrals and semi-infinite integrals. Linear interpolation and direct integration are used for definite integrals, and sine-cosine filter integration is used for semi-infinite integrals. The spatial domain response P is quickly calculated. j2 ;

[0021] s2.5 Calculation of the uniaxial anisotropic medium magnetic field space domain analytical solution P j1 , P j1 and P j2 The tensor background magnetic field response P of the receiving coil in the uniform triaxial anisotropic formation is obtained by adding j =P j1 +P j2 .

[0022] Optionally, in step s5, the specific construction method of the equivalent uniaxial anisotropic models M1 to M9 includes:

[0023] s5.1 For the i-th detection mode, establish a horizontal layered uniaxial anisotropic formation model M i ;

[0024] s5.2 For the jth layer, determine whether the conductivity in the x and y directions of the layer is equal; if they are equal, the conductivity of the jth layer in the equivalent uniaxial anisotropic model is set to σ x,j , otherwise, execute step s5.3;

[0025] s5.3 Take the jth layer for the uniform medium response P j The i-th detection mode response p j,i , the initial horizontal conductivity σ jh0 Set to sqrt(σ x,j *σ y,j ); Using the analytical solution of the magnetic field of a uniform uniaxial anisotropic medium and the gradient descent algorithm, the horizontal conductivity value is continuously updated until the uniaxial anisotropic model response is consistent with p j,i The error between them satisfies the precision error, and finally the equivalent horizontal conductivity σ of the jth layer is obtained jh ;

[0026] s5.4 From the 1st layer to the Nth layer, execute steps s5.2 and s5.3 in sequence to obtain the horizontal conductivity σ of all equivalent uniaxial anisotropic formation models in sequence j1~σ jΝ , thus obtaining the equivalent uniaxial anisotropic model M for the i-th detection mode i ;

[0027] s5.5 For the 1st, 2nd, 3rd, 5th, 6th and 9th detection modes, execute steps s5.2 to s5.4 in sequence to obtain the corresponding equivalent uniaxial anisotropic models M1, M2, M3, M5, M6 and M9; using the symmetry of each detection mode, obtain M4, M7 and M8, where M4=M2, M7=M3, M8=M6.

[0028] Optionally, in step s6, the equivalent model magnetic field tensor secondary field responses S1 to S N The specific calculation methods include:

[0029] s6.1 Equivalent Model M i , using the Hertz potential function method, the calculation problem of the magnetic field excited by the magnetic dipole in the space domain is converted into the calculation of the spectral domain field and the Sommerfeld integral; at positions infinitely close above and below the emission point, double virtual boundaries are introduced to obtain the continuity equation of the spectral domain field at the formation interface and the emission point;

[0030] s6.2 Recursively deduce from the first layer to the stratum interface below the source, and obtain the relationship between the amplitude of the upward wave at the bottom interface of each layer and the amplitude of the downward wave at the top interface; recursively deduce from the Nth layer to the stratum interface above the source, and obtain the relationship between the amplitude of the downward wave at the top interface of each layer and the amplitude of the upward wave at the bottom interface; with the help of the continuity condition at the source point, solve the amplitude of the upward and downward waves at the source point;

[0031] s6.3 Recursively infer from the source layer to the stratum where the receiving point is located to obtain the amplitude of the up and down waves in the stratum where the receiving point is located; use the fast Hankel transform technology to convert the spectral domain magnetic field response into the spatial domain magnetic field response S i ;

[0032] s6.4 Execute steps s6.1 to s6.3 for the nine detection modes in turn to obtain the secondary field responses S1 to S2 of the equivalent models of all detection modes. N .

[0033] The beneficial effect of the present invention is that the present invention separates the primary field and the secondary field of the multi-component electromagnetic wave logging of the triaxial anisotropic formation, and adopts different methods to accelerate, which greatly improves the calculation efficiency. The primary field adopts a strict calculation method, combined with strategies such as coordinate transformation and approximation elimination, and has the characteristics of fast speed and high precision. In comparison, the solution of the secondary field adopts an approximation algorithm, and the core is to construct an equivalent uniaxial anisotropic model. Utilizing the multi-solution of the uniform triaxial anisotropic formation magnetic field, combined with the uniaxial anisotropic medium magnetic field analytical expression and gradient optimization inversion, an equivalent layered uniaxial anisotropic formation model is constructed, and then the secondary magnetic field excited by the magnetic dipole source of the equivalent model is quickly calculated. Compared with the traditional algorithm, the method of the present invention avoids matrix operations and double infinite domain integration, and while ensuring the calculation accuracy, the forward modeling speed can be increased by more than 10 times. The method of the present invention not only lays the foundation for the rapid processing of data, but also provides a new idea for the extraction of formation parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a flow chart of the method for calculating the multi-component electromagnetic wave logging response of triaxial anisotropic formations in the present invention;

[0035] Figure 2 Schematic diagram and parameters of the multi-component electromagnetic wave logging instrument in the present invention;

[0036] Figure 3 It is a five-layer triaxial anisotropic formation model in the embodiment of the present invention;

[0037] Figure 4 is the equivalent uniaxial anisotropy model corresponding to each detection mode in the embodiment of the present invention;

[0038] Figure 5 For the present invention Figure 3 Comparison of the calculation results of the spectral domain secondary field by the fast calculation method and the traditional method in the embodiment shown;

[0039] Figure 6 For the present invention Figure 3 The total magnetic field response calculated by each detection mode in the formation coordinate system in the embodiment shown;

[0040] Figure 7 For the present invention Figure 3 The total magnetic field response calculated for each detection mode in the instrument coordinate system in the illustrated embodiment;

[0041] Figure 8 For the present invention Figure 3 The apparent conductivity calculated for each detection mode in the illustrated embodiment. DETAILED DESCRIPTION

[0042] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, rather than all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention. Therefore, the following detailed description of the embodiments of the present invention provided in the drawings is not intended to limit the scope of the invention claimed for protection, but merely represents the selected embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0043] A method for calculating the multi-component electromagnetic wave logging response of triaxial anisotropic formations, such as Figure 1 As shown, the following steps are included:

[0044] s1. Input the horizontal layered triaxial anisotropic formation model, multi-component electromagnetic wave logging instrument parameters and sampling point locations; among them, the multi-component electromagnetic wave logging instrument structure and parameters are as follows Figure 2 As shown in Figure 2, the horizontal layered triaxial anisotropic strata model is as follows: Figure 3 As shown in the figure, in this example, the horizontal layered triaxial anisotropic stratum model has 5 layers, and the conductivity in the x, y and z directions in the jth layer is represented by σ x,j , σ y,j and σ z,j Indicates; the instrument parameters include the transmission frequency f = 20kHz and the source distance L = 1m;

[0045] s2. Taking the first layer as an example, a homogeneous triaxial anisotropic layer is established for the first layer, and the tensor background magnetic field response P1 at the receiving antenna is quickly calculated in combination with the instrument parameters;

[0046] The tensor background magnetic field response P1 calculation method specifically includes:

[0047] S2.1 For the first stratum, a homogeneous triaxial anisotropic stratum is established. If the conductivity along the x and y directions is consistent, the tensor background magnetic field response P1 is obtained using the analytical formula of the magnetic field excited by the uniaxial anisotropic medium magnetic dipole source; otherwise, step S2.2 is executed, and Figure 3 It can be seen that the conductivity in the x and y directions is inconsistent, so step s2.2 is executed;

[0048] s2.2 According to the source distance and the well inclination angle, the projection of the distance between the transmitting point and the receiving point in the three coordinate axis directions is calculated. Figure 2 The projections of the instrument in three directions are L x =0.87m, Ly =0.0m, L z =0.5m; obtain the two directions y and z with the smallest projection length, perform double Fourier transform along the y and z directions, and analytically calculate the spectral domain magnetic field at the receiving antenna of the triaxial anisotropic formation

[0049] s2.3 Construct a uniaxial anisotropic formation with vertical and horizontal conductivity set to σ z,1 =0.025S / m and sqrt(σ x,1 *σ y,1 )=0.224S / m, and then the uniaxial anisotropic formation spectral domain magnetic field is calculated analytically

[0050] s2.4 Eliminating the contribution of the uniaxial anisotropic field in the spectral domain The double Fourier transform is converted to the polar coordinate system, including the definite integral and the semi-infinite integral. Linear interpolation and direct integration are used for the definite integral to reduce the number of calculation points. For the semi-infinite integral, sine and cosine filter integration is used to quickly calculate the spatial domain response:

[0051]

[0052] S2.5 The analytical solution for calculating the magnetic field of uniaxial anisotropic medium in the spatial domain is:

[0053] P j1 and P j2 The tensor background magnetic field response at the receiving coil of the uniform triaxial anisotropic formation is obtained by adding:

[0054]

[0055] s3. Execute step s2 for all strata in sequence to obtain the tensor background magnetic field responses P1 to P2 of uniform triaxial anisotropic strata corresponding to all layers. N ;

[0056] s4. For the i-th detection mode, using the multi-solution of the magnetic field in the homogeneous medium, a simplified equivalent uniaxial anisotropy model M is established j ;

[0057] s5. For the 9 detection modes, execute step s4 in sequence to obtain equivalent uniaxial anisotropic models M1 to M9;

[0058] The specific construction method of the equivalent uniaxial anisotropic models M1 to M9 includes:

[0059] s5.1 For the first detection mode, a horizontal layered uniaxial anisotropic formation model M1 is established. The formation interface position of model M1 is consistent with the original triaxial anisotropic model, and the vertical conductivity of each layer is set to the conductivity in the z direction of the original model;

[0060] s5.2 For the first layer, determine whether the conductivity in the x and y directions of the layer is equal; if they are equal, the conductivity of the first layer in the equivalent uniaxial anisotropic model is set to σ x,j , otherwise, execute step s5.3. Figure 3 It can be seen that the conductivity in the x and y directions of layer 1 is not equal, so step s5.3 is executed;

[0061] s5.3 Take the first detection mode response p of the first layer for the uniform medium response P1 1,1 =-0.0764+0.0014i, the initial horizontal conductivity σ 1h0 Set to sqrt(σ x,1 *σ y,1 )=0.224S / m. Using the analytical solution of the magnetic field of a uniform uniaxial anisotropic medium and the gradient descent algorithm, the horizontal conductivity value is continuously updated until the uniaxial anisotropic model response is consistent with p 1,1 The error between them satisfies the precision error (in this case, the precision error is set to 1e-7), and finally the equivalent horizontal conductivity σ of the first detection mode for the first layer is obtained 1,1h =0.114S / m;

[0062] S5.4 From the 1st layer to the 5th layer, execute steps S5.2 and S5.3 in sequence to obtain the horizontal conductivity σ of all equivalent uniaxial anisotropic formation models in sequence. 1,1 ~σ 1,5 =[0.114, 1, 0.011, 1, 0.354] S / m, thereby obtaining the equivalent uniaxial anisotropic model M1 for the first detection mode;

[0063] s5.5 For the 1st, 2nd, 3rd, 5th, 6th and 9th detection modes, execute steps s5.2 to s5.4 in sequence to obtain the corresponding equivalent uniaxial anisotropic models M1, M2, M3, M5, M6 and M9. Using the symmetry of each detection mode, M4, M7 and M8 are obtained, that is, M4=M2, M7=M3, M8=M6. Since the 2nd and 6th detection modes cannot detect signals in biaxial anisotropic media, there are no equivalent uniaxial anisotropic models M2, M4, M6 and M8. The horizontal resistivity of each layer of the equivalent uniaxial anisotropic models M3, M5 and M9 is σ respectively. 3,1 ~σ 3,5 =[0.162,1,0.016,1,0.274]S / m,σ 5,1 ~σ5,5 =[0.291,1,0.030,1,0.113]S / m and σ 9,1 ~σ 9,5 =[0.390,1,0.036,1,0.118]S / m. The equivalent uniaxial anisotropic models M1 to M9 corresponding to each detection mode are as follows: Figure 4 shown.

[0064] s6. Using the uniaxial anisotropy model obtained in step s5, combined with the Hertz potential function method, the improved amplitude propagation coefficient algorithm and the fast Hankel transform technology, the magnetic field tensor secondary field response S1~S9 of the equivalent model is quickly calculated; the secondary field response S j is the best approximation to the jth detection mode response of the original model;

[0065] Equivalent model magnetic field tensor secondary field response S1~S N The specific calculation methods include:

[0066] s6.1 For the equivalent model M1, the Hertz potential function method is used to convert the calculation problem of the magnetic field excited by the magnetic dipole in the space domain into the calculation of the spectral field and the Sommerfeld integral; a double virtual boundary is introduced at the position infinitely close above and below the emission point to obtain the continuity equation of the spectral field at the formation interface and the emission point;

[0067] s6.2 Recursively deduce from the first layer to the stratum interface below the source, and obtain the relationship between the amplitude of the upward wave at the bottom interface of each layer and the amplitude of the downward wave at the top interface; recursively deduce from the fifth layer to the stratum interface above the source, and obtain the relationship between the amplitude of the downward wave at the top interface of each layer and the amplitude of the upward wave at the bottom interface; with the help of the continuity condition at the source point, solve the amplitude of the upward and downward waves at the source point;

[0068] s6.3 Recursively infer from the source layer to the stratum where the receiving point is located to obtain the amplitude of the up and down waves in the stratum where the receiving point is located; use the fast Hankel transform technology to convert the spectral domain magnetic field response into the spatial domain magnetic field response S1;

[0069] s6.4 Execute steps s6.1 to s6.3 for the nine detection modes in turn to obtain the secondary field responses S1 to S9 of the equivalent models of all detection modes. Similarly, the secondary field responses S2, S4, S6 and S8 are all zero, and the imaginary parts of the secondary field responses S1, S3, S5, S7 and S9 are as follows: Figure 5 To verify the accuracy of the method of the present invention, Figure 5 The scattered points in represent the calculation results of the strict forward algorithm, and the solid line represents the simulation results of the fast calculation method proposed by the present invention. It can be seen that the calculation results of the two methods basically overlap with each other, verifying the accuracy of the method of the present invention.

[0070] s7. The uniform triaxial anisotropic medium response and the secondary field response are superimposed to obtain the total multi-component magnetic field response H of the layered triaxial anisotropic formation. j =P j +S j ; The imaginary parts of the total multi-component magnetic field response H1, H3, H5, H7 and H9 of the layered triaxial anisotropic strata are as follows: Figure 6 As shown in the figure, the H1 and H9 responses calculated in the formation coordinate system are relatively smooth at the interface without horns. The H3, H5, and H7 responses all have horns of varying magnitudes at the interface, and the H3 and H5 responses are symmetrical in shape.

[0071] s8. After the multi-component magnetic field response of the formation coordinate system is transformed, the magnetic field response of the instrument coordinate system is obtained, wherein the conversion formula from the formation coordinate system to the instrument coordinate system is:

[0072] In the formula, is the total magnetic field response in the instrument coordinate system after conversion, α is the well inclination angle, and β is the azimuth angle. The total magnetic field response of each detection mode in the instrument coordinate system is as follows: Figure 7 After obtaining the total magnetic field response in the instrument coordinate system, the instrument coefficient is further converted into tensor apparent conductivity. The specific conversion formula is: In the formula, ω is the angular frequency, μ is the vacuum permeability, A T and A R are the areas of the transmitting and receiving coils, respectively, T and N R are the turns of the transmitting and receiving coils respectively. K is the instrument coefficient. The instrument coefficient expression of each detection mode is: In this embodiment, the area and number of turns of the transmitting and receiving coils are both assumed to be 1, and the apparent conductivity of each detection mode in the layered triaxial anisotropic formation is obtained, such as Figure 8 shown.

[0073] Of course, the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by technicians in this technical field within the essential scope of the present invention should also fall within the protection scope of the present invention.

Claims

1. A method for calculating the multi-component electromagnetic wave logging response of a triaxial anisotropic formation, characterized in that: The steps include: s1. Input the horizontal layered triaxial anisotropic formation model, multi-component electromagnetic wave logging instrument parameters and sampling point locations; s2. For the jth formation, a homogeneous triaxial anisotropic formation is established, and the tensor background magnetic field response P at the receiving antenna is calculated based on the instrument parameters. j ; s3. Execute step s2 for all strata in sequence to obtain the tensor background magnetic field responses P1 to P2 of uniform triaxial anisotropic strata corresponding to all layers. N ; s4. For the i-th detection mode, using the multi-solution of the magnetic field in the homogeneous medium, a simplified equivalent uniaxial anisotropy model M is established j ; s5. For the 9 detection modes, execute step s4 in sequence to obtain equivalent uniaxial anisotropic models M1 to M9; s6. Using the uniaxial anisotropy model obtained in step s5, combined with the Hertz potential function method, the improved amplitude propagation coefficient algorithm and the fast Hankel transform technology, calculate the magnetic field tensor secondary field response S1~S of the equivalent model N ; s7. The uniform triaxial anisotropic medium response and the secondary field response are superimposed to obtain the total multi-component magnetic field response H of the layered triaxial anisotropic formation. j =P j +S j ; s8. After coordinate transformation of the multi-component magnetic field response of the formation coordinate system, the magnetic field response of the instrument coordinate system is obtained, and then converted into tensor apparent conductivity; In step s2, the tensor background magnetic field response P j The calculation method specifically includes: s2.1 For the jth stratum, a homogeneous triaxial anisotropic stratum is established; if the conductivity along the x and y directions is consistent, the tensor background magnetic field response P is obtained by using the analytical formula of the magnetic field excited by the uniaxial anisotropic medium magnetic dipole source j ; Otherwise, execute step s2.2; s2.2 Project the distance between the transmitting and receiving points in the three coordinate axis directions to obtain the two directions v and w with the smallest projection length. Perform double Fourier transform along the v and w directions to analytically calculate the spectral domain magnetic field at the receiving antenna of the three-axis anisotropic formation. s2.3 Construct a uniaxial anisotropic formation, with the vertical and horizontal conductivity set to σ z,j and sqrt(σ x,j *σ y,j ), and then analytically calculate the uniaxial anisotropic formation spectral domain magnetic field s2.4 Eliminating the contribution of the uniaxial anisotropic field in the spectral domain The double Fourier transform is converted to the polar coordinate system, including definite integrals and semi-infinite integrals. Linear interpolation and direct integration are used for definite integrals, and sine-cosine filter integration is used for semi-infinite integrals. The spatial domain response P is quickly calculated. j2 ; s2.5 Calculation of the uniaxial anisotropic medium magnetic field space domain analytical solution P j1 , P j1 and P j2 The background tensor background magnetic field response P at the receiving coil of the uniform triaxial anisotropic formation is obtained by adding j =P j1 +P j2 ; In step s5, the specific construction method of the equivalent uniaxial anisotropic models M1 to M9 includes: s5.1 For the i-th detection mode, establish a horizontal layered uniaxial anisotropic formation model M i ; s5.2 For the jth layer, determine whether the conductivity in the x and y directions of the layer is equal; if they are equal, the conductivity of the jth layer in the equivalent uniaxial anisotropic model is set to σ x,j , otherwise, execute step s5.3; s5.3 Take the jth layer for the uniform medium response P j The i-th detection mode response p j,i , the initial horizontal conductivity σ jh0 Set to sqrt(σ x,j *σ y,j ) ; Using the analytical solution of the magnetic field of a uniform uniaxial anisotropic medium, combined with the gradient descent algorithm, the horizontal conductivity value is updated until the uniaxial anisotropic model response is consistent with p j,i The error between them satisfies the precision error, and the equivalent horizontal conductivity σ of the jth layer is obtained. jh ; s5.4 From the 1st layer to the Nth layer, execute steps s5.2 and s5.3 in sequence to obtain the horizontal conductivity σ of all equivalent uniaxial anisotropic formation models in sequence j1 ~σ jΝ , the equivalent uniaxial anisotropic model M for the i-th detection mode is obtained i ; s5.5 For the 1st, 2nd, 3rd, 5th, 6th and 9th detection modes, perform steps s5.2 to s5.4 in sequence to obtain the corresponding equivalent uniaxial anisotropic models M1, M2, M3, M5, M6 and M9; using the symmetry of each detection mode, obtain M4, M7 and M8, where M4 = M2, M7 = M3, M8 = M6; In step s6, the equivalent model magnetic field tensor secondary field responses S1 to S N The specific calculation methods include: s6.1 Equivalent Model M i , using the Hertz potential function method, the calculation problem of the magnetic field excited by the magnetic dipole in the space domain is converted into the calculation of the spectral domain field and the Sommerfeld integral; at positions infinitely close above and below the emission point, double virtual boundaries are introduced to obtain the continuity equation of the spectral domain field at the formation interface and the emission point; s6.2 Recursively deduce from the first layer to the stratum interface below the source, and obtain the relationship between the amplitude of the upward wave at the bottom interface of each layer and the amplitude of the downward wave at the top interface; recursively deduce from the Nth layer to the stratum interface above the source, and obtain the relationship between the amplitude of the downward wave at the top interface of each layer and the amplitude of the upward wave at the bottom interface; with the help of the continuity condition at the source point, solve the amplitude of the upward and downward waves at the source point; s6.3 Recursively infer from the source layer to the stratum where the receiving point is located to obtain the amplitude of the up and down waves in the stratum where the receiving point is located; use the fast Hankel transform technology to convert the spectral domain magnetic field response into the spatial domain magnetic field response S i ; s6.4 Execute steps s6.1 to s6.3 for the nine detection modes in turn to obtain the secondary field responses S1 to S2 of the equivalent models of all detection modes. N .

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