Complex structure stratum while-drilling azimuth electromagnetic wave logging parameterization inversion method

Abstract

The invention discloses a complex structure stratum while-drilling azimuth electromagnetic wave logging parameterization inversion method, and belongs to the field of oil exploration and development. The method comprises the following steps: s1, modeling a complex geologic structure, constructing a 2D complex geologic model, and parameterizing the 2D complex geologic model; s2, analyzing response characteristics of the 2D complex geological model according to the 2D complex geological model established in the s1, and carrying out influence factor and sensitivity analysis; s3, obtaining observation data according to response characteristics of s2, and constructing an objective function; and s4, in combination with s2 and s3, performing inversion on the parameterized 2D complex geological model by using a PT-MCMC inversion method to realize fine reconstruction of the complex stratum. According to the method, fine reconstruction of the complex stratum is achieved, good inversion precision is achieved, and the characterization capacity and the calculation efficiency are both considered. The method provides support for real-time geosteering, reservoir evaluation, layer interface prediction and the like of oil and gas fields.

Description

Technical Field

[0001] The present invention relates to the field of petroleum exploration and development, in particular to active geosteering of horizontal wells and reservoir parameter identification, and more particularly to a parametric inversion method for azimuthal electromagnetic wave logging while drilling of complex structure formations. Background Art

[0002] Azimuthal electromagnetic logging while drilling (AWD) is widely used in reservoir exploration and development. It provides real-time information about the formation surrounding the wellbore, playing a crucial role in downhole geosteering and reservoir fluid identification. However, its measurement information is affected by factors such as formation thickness and resistivity, making it inaccurate. Inversion techniques are required to reconstruct information such as formation interfaces and resistivity.

[0003] Based on the difference between the dimensions of the formation model and the forward algorithm, inversion methods are divided into: 1D inversion, 2D inversion, 2.5D inversion, and 3D inversion. To quickly achieve geosteering and post-drilling reservoir interpretation, dimensionality reduction strategies such as sliding windows are often used to simplify the geological model into a 1D layered model. However, as the detection range increases, the simple 1D model cannot represent the heterogeneous changes in the formation, and 2D or 3D inversion must be used to finely reconstruct complex geological reservoirs. However, 3D and 2D inversion technologies are still immature, and the excessive number of parameters to be inverted results in poor inversion accuracy for 3D and 2D inversion. In addition, electromagnetic logging while drilling in complex formations also suffers from problems such as low simulation efficiency, which greatly limits the application of high-dimensional inversion methods. Summary of the Invention

[0004] Based on the above technical problems, the present invention proposes a parametric inversion method for azimuthal electromagnetic wave logging while drilling in complex structure formations.

[0005] The technical solution adopted by the present invention is:

[0006] A parametric inversion method for azimuthal electromagnetic wave logging while drilling in complex structural formations, comprising the following steps:

[0007] s1. Model complex geological structures, construct 2D complex geological models, and parameterize the 2D complex geological models;

[0008] s2. Analyze the response characteristics of the 2D complex geological model established in s1, and conduct influencing factors and sensitivity analysis;

[0009] s3. Obtain observation data based on the response characteristics of s2 and construct the objective function;

[0010] s4. Combining s2 and s3, the PT-MCMC inversion method is used to invert the parameterized 2D complex geological model to achieve a fine reconstruction of the complex strata.

[0011] In the above step s1: the constructed 2D complex geological model includes a fault model, a fold model and an unconformity model.

[0012] Preferably, the steps of parameterizing the fault model are as follows:

[0013] s1.1.1. Convert the 3D fault model into a 2D fault model based on its structural characteristics, analyze the parameters that determine the basic morphology and electrical characteristics of the fault, and parameterize the fault model into fault throw, fault dip, and resistivity.

[0014] s1.1.2. The fault throw reflects the relative displacement between the upper and lower strata of the fault and controls the degree of stratum movement. It is represented by the parameter d.

[0015] s1.1.3. The fault dip can control the fault geometry and affect the horizontal asymmetry of the resistivity, significantly affecting the logging response characteristics. This is represented by the parameter θ.

[0016] s1.1.4. For resistivity, since fault movement results in a discontinuous distribution in the lateral direction, the resistivity of each layer on both sides of the fault needs to be parameterized and expressed as resistivity R.

[0017] s1.1.5. Parameterize the fault model using fault throw, fault dip, and resistivity parameters for subsequent model inversion.

[0018] Preferably, the steps of parameterizing the wrinkle model are as follows:

[0019] s1.2.1. Convert the 3D wrinkle model into a 2D wrinkle model based on its structural characteristics and analyze and determine the wrinkle parameters;

[0020] For a simple wrinkle model, approximate the core of the wrinkle as a triangle. Using the three-point method, the coordinates of these three points control the shape of the entire core and characterize the changing trend of the core of the entire wrinkle model.

[0021] For more complex wrinkle models, a five-point method is used to characterize the core morphology in more detail using the coordinates of five points.

[0022] s1.2.4. Finally, use spline interpolation to refine the entire wrinkle core;

[0023] s1.2.5. After determining the core's morphology and direction, parameterize the electrical properties of each portion of the formation and express them in terms of resistivity R.

[0024] s1.2.6. Parameterize the fold model using the three-point method and parameters such as resistivity for subsequent model inversion.

[0025] Preferably, the steps of parameterizing the unconformity model are as follows:

[0026] s1.3.1. Convert the 3D unconformity structural model into a 2D unconformity structural model based on its structural characteristics, and analyze and determine the unconformity structural morphological parameters;

[0027] s1.3.2. Taking the angular unconformity as an example, first determine the location of the unconformity surface, and then directly determine the length and position of the unconformity surface through the coordinates of two points;

[0028] s1.3.3. Use angles to characterize the changing trends of overlying and underlying strata. Angular unconformities only require determining the dip angle of the underlying strata, denoted by θ.

[0029] s1.3.4. After determining the shape and location of the unconformity, parameterize the electrical properties of each part of the formation and express them in terms of resistivity R.

[0030] s1.3.5. Finally, determine the thickness of each stratum and parameterize the unconformity model using the length of the unconformity surface, the dip of the underlying stratum, and the resistivity parameters of each part of the stratum for subsequent model inversion.

[0031] Preferably, step s4 includes the following steps:

[0032] s4.1. Determine the initial model for PT-MCMC sampling and determine the length and temperature of the sampling chain, and set the number of iterations;

[0033] s4.2. Select initial values ​​and perform multi-chain parallel non-interaction sampling. Use the MCMC method to sample each Markov chain, and each time choose whether to accept the next state according to the acceptance rate function α;

[0034] After this iteration, the temperature exchange parameter ζ is used to determine whether to perform inter-chain interaction.

[0035] Preferably, step s4.1 specifically includes the following steps:

[0036] S4.1.1. Based on the 2D complex geological model analysis in S2 and the objective function constructed in S3, construct K Markov chains with increasing temperatures. The solution of each Markov chain l at different temperatures satisfies the posterior distribution of the different temperatures.

[0037] s4.1.2. Introducing the temperature parameter T into the likelihood function l Control the sampling step size:

[0038]

[0039] Where, T l is the temperature parameter of each chain, T minis the chain with the lowest defined temperature, T max is the chain with the highest defined temperature.

[0040] Preferably, step s4.2 specifically includes the following steps:

[0041] s4.2.1. Take the initial value selected according to the set initial model as m (0) state;

[0042] s4.2.2. Determine the posterior distribution using the prior distribution and the likelihood function;

[0043] s4.2.3. Sample from the posterior distribution. The probability distribution of the solution m at future times depends only on the solution m at the current time k+1 ; k ;

[0044] s4.2.4. Introduce the acceptance rate function α, and the expression is as follows:

[0045]

[0046] In the formula, x and y are formation models at any time, d is the formation measurement data, Π(x, y) is the transition kernel function, indicating the transition from model x to model y. Correspondingly, Π(y, x) indicates the transition from model y to model x; assuming that the transition kernel function follows a Gaussian distribution, then Π(x, y) = Π(y, x), and the acceptance rate function is further simplified to:

[0047]

[0048] s4.2.5. Calculate a(x, y) using the above formula and compare it with the random number μ that follows a uniform distribution. If μ < a(x, y), then accept the model solution m k+1 , otherwise retain the model solution m k , and enter the next iteration.

[0049] Preferably, step s4.3 specifically includes the following steps:

[0050] s4.3.1. After the previous sampling ends, generate a random number ρ that follows a uniform distribution;

[0051] s4.3.2. When ρ is greater than the preset temperature exchange parameter ζ, there is no interaction between Markov chains with different temperatures, and repeat s4.2.4~s4.2.5;

[0052] s4.3.3. Otherwise, determine whether there is a state interaction between Markov chains with different temperatures according to the state interaction function defined by the following formula;

[0053]

[0054] Where, represents the solution of the lth Markov chain at the nth sampling moment, represents the solution of the l+1th Markov chain at the nth sampling moment;

[0055] s4.3.4.If Then the Markov chains interact with each other in state, otherwise they do not interact with each other in state;

[0056] s4.3.5. Repeat steps s4.3.1 to s4.3.4 until the loop termination condition is met, give the maximum a posteriori probability solution, and perform statistical analysis on the inversion parameters.

[0057] Preferably, step s4 further includes the following steps:

[0058] s4.4. Repeat s4.2 to s4.3 until the number of iterations meets the set value, and the sampling ends. The results of each iteration of each parameter are collected.

[0059] s4.5. Collect the final reconstruction results of the inversion parameters for different complex formation settings;

[0060] s4.6. After collecting the reconstruction results at different vertical depths, visualize them.

[0061] The beneficial technical effects of the present invention are as follows:

[0062] This paper proposes a parametric inversion method for azimuthal electromagnetic logging while drilling (AWD) in complex formations. This method first establishes complex formation models—fault, fold, and unconformity models—and parameterizes these models. The logging responses of these complex formation models, as well as the factors and sensitivities influencing these responses, are then analyzed. Finally, the PT-MCMC inversion method is used to rapidly invert these parameterized complex formation models, achieving detailed reconstruction of the complex formations. This method achieves high inversion accuracy while balancing characterization capabilities and computational efficiency. This method supports real-time geosteering, reservoir evaluation, and layer boundary prediction in oil and gas fields. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 This is a flow chart of the parametric inversion method for azimuthal electromagnetic wave logging while drilling in complex structural formations according to the present invention;

[0064] Figure 2 Schematic diagram of the complex stratum model established for the present invention; wherein (a) is a fault model, (b) is a fold model, and (c) is an unconformity surface model;

[0065] Figure 3Schematic diagram of the parameterization of the model established in the present invention; wherein (a) is a parameterized fault model, (b) is a parameterized fold model, and (c) is a parameterized unconformity surface model;

[0066] Figure 4 The well logging response results of the fault model of the present invention are shown in FIG. 1 , wherein (a) is the apparent resistivity curve and (b) is the azimuth signal curve.

[0067] Figure 5 This is the visualization result of the inversion fault model of the present invention; wherein, (a) is the fault model, and (b) is the inversion result of the fault model. DETAILED DESCRIPTION

[0068] The information measured by azimuthal electromagnetic logging while drilling is affected by the logging environment, such as layer thickness, surrounding rock, and well deviation, making the logging response relatively complex and requiring inversion. The following difficulties exist in the rapid inversion of complex structural formation models: (1) There are too many high-dimensional inversion parameters, limited measurement information, and the inversion may have multiple solutions; (2) During the drilling process, due to the lack of sufficient known information, the initial value of the inversion is difficult to determine, which further increases the difficulty of inversion; (3) 3D forward modeling methods suitable for complex formation structures are time-consuming and require high hardware performance. Therefore, choosing an inversion method with high efficiency and fine model reconstruction is crucial for the prediction and reconstruction of complex structural formation models.

[0069] Based on this, the present invention proposes a parameterized inversion method for azimuthal electromagnetic logging while drilling (AWED) of complex structural formations. The method uses a 2.5D half-spectral domain simulation method to simulate the complex formation model, and then uses the PT-MCMC inversion method to invert and reconstruct the complex formation model. The present invention specifically includes the following steps: s1. Modeling the complex geological structure, constructing a 2D complex geological model, and parameterizing the 2D complex geological model; s2. Analyzing the response characteristics of the 2D complex geological model established in s1, and performing influencing factor and sensitivity analysis; s3. Obtaining observation data based on the response characteristics of s2 and constructing an objective function; s4. Combining s2 and s3, inverting the parameterized 2D complex geological model using the PT-MCMC inversion method to achieve a detailed reconstruction of the complex formation. The present invention parameterizes the complex formation model and uses the PT-MCMC inversion method, ensuring both inversion efficiency and reconstruction effect, thereby facilitating geosteering in AWED.

[0070] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0071] like Figure 1 As shown, the parametric inversion method of azimuthal electromagnetic wave logging while drilling for complex structural formations includes the following steps:

[0072] s1. Modeling of complex geological structures, such as Figure 2 As shown, a 2D complex geological model is constructed and parameterized.

[0073] like Figure 3 As shown in (a), for the fault model:

[0074] s1.1.1. Convert the 3D fault model into a 2D fault model based on its structural characteristics, analyze the parameters that determine the basic morphology and electrical characteristics of the fault, and parameterize the fault model into fault throw, fault dip, and resistivity.

[0075] s1.1.2. The fault throw can reflect the relative displacement between the upper and lower layers of the fault and control the degree of stratum movement, which is expressed by the parameter d.

[0076] s1.1.3. The dip angle of the fault can control the geometry of the fault and affect the horizontal asymmetry of the resistivity, which has a significant impact on the logging response characteristics and is represented by the parameter θ.

[0077] s1.1.4. As for resistivity, since the fault movement causes discontinuous distribution in the lateral direction, it is necessary to parameterize the resistivity of each layer on both sides of the fault and express it as resistivity R.

[0078] s1.1.5. Parameterize the fault model using fault throw, fault dip, and resistivity parameters for subsequent model inversion.

[0079] like Figure 3 As shown in (b), for the wrinkle model:

[0080] s1.2.1. Convert the 3D wrinkle model into a 2D wrinkle model based on its structural characteristics, and analyze and determine the wrinkle parameters.

[0081] s1.2.2. For a simple wrinkle model, the core of the wrinkle is approximated as a triangle. Using the three-point method, the coordinates of these three points control the shape of the entire core and characterize the changing trend of the core of the entire wrinkle model.

[0082] For more complex wrinkle models, the five-point method is used to use the coordinates of five points to characterize the core morphology in more detail.

[0083] s1.2.4. Finally, spline interpolation is used to refine the entire wrinkle core.

[0084] s1.2.5. After determining the shape and direction of the core, parameterize the electrical properties of each part of the formation and express them in terms of resistivity R.

[0085] s1.2.6. Parameterize the fold model using the three-point method and parameters such as resistivity for subsequent model inversion.

[0086] like Figure 3 As shown in (c), for the unconformity model:

[0087] s1.3.1. Convert the 3D unconformity structural model into a 2D unconformity structural model based on its structural characteristics, and analyze and determine the unconformity structural morphological parameters.

[0088] s1.3.2. Taking the angular unconformity as an example, first determine the position of the unconformity surface, and then directly determine the length and position of the unconformity surface through the coordinates of two points.

[0089] s1.3.3. The changing trends of the upper and lower strata are characterized by angles. For angular unconformity, it is only necessary to determine the dip angle of the underlying strata, which is represented by θ.

[0090] s1.3.4. After determining the shape and location of the unconformity, parameterize the electrical properties of each part of the formation and express them in terms of resistivity R.

[0091] s1.3.5. Finally, determine the thickness of each stratum and parameterize the unconformity model using parameters such as the length of the unconformity surface, the dip of the underlying stratum, and the resistivity of each part of the stratum to facilitate subsequent model inversion.

[0092] s2. Such as Figure 4 As shown in Figure 1, the response characteristics of the 2D complex geological model established by s1 are analyzed, and the influencing factors and sensitivity analysis are carried out.

[0093] s3. Obtain observation data based on the response characteristics of s2 and construct the objective function.

[0094] S4. Combining S2 and S3, the PT-MCMC inversion method is used to invert the parameterized 2D complex geological model to achieve a fine reconstruction of the complex strata. Specifically, the following steps are included:

[0095] s4.1. Determine the initial model for PT-MCMC sampling and determine the length and temperature of the sampling chain, and set the number of iterations.

[0096] Based on the analysis of the 2D complex geological model in s2 and the objective function constructed in s3, construct K Markov chains with increasing temperatures. The solution of each Markov chain l at different temperatures satisfies the posterior distribution of the different temperatures.

[0097] s4.1.2. Introducing the temperature parameter T into the likelihood function l Control the sampling step size:

[0098]

[0099] Where, T l is the temperature parameter of each chain, T minThe chain with the lowest defined temperature, T max is the chain with the highest defined temperature.

[0100] S4.2. Select the initial value and perform multi-chain parallel non-interactive sampling. Use the MCMC method to sample each Markov chain, and each time, select whether to accept the next state according to the acceptance rate function α.

[0101] S4.2.1. Take the initial value selected according to the set initial model as m (0) state.

[0102] S4.2.2. Determine the posterior distribution using the prior distribution and the likelihood function.

[0103] S4.2.3. Sample from the posterior distribution. The probability distribution of the solution m at the future time only depends on the solution m at the current time k+1 k . S4.2.4. Introduce the acceptance rate function α, and the expression is as follows:

[0104]

[0105] In the formula, x and y are formation models at any time, d is the formation measurement data, and Π(x, y) is the transition kernel function, representing the transition from model x to model y. Assume that the transition kernel function follows a Gaussian distribution, then Π(x, y) = Π(y, x), and the acceptance rate function is further simplified to:

[0106]

[0107] S4.2.5. Calculate a(x, y) using the above formula and compare it with the random number μ that follows a uniform distribution. If μ < a(x, y), then accept the model solution m k+1 , otherwise retain the model solution m k , and enter the next iteration.

[0108] S4.3. After this iteration ends, determine whether to perform inter-chain interaction through the temperature exchange parameter ζ.

[0109] S4.3.1. After the previous sampling ends, generate a random number ρ that follows a uniform distribution.

[0110] S4.3.2. When ρ is greater than the preset temperature exchange parameter ζ, there is no interaction between adjacent Markov chains with different temperatures, and repeat S4.2.4 - S4.2.5.

[0111] S4.3.3. Otherwise, determine whether to perform state interaction between adjacent Markov chains with different temperatures according to the state interaction function defined by the following formula;

[0112] ​

[0113] Where, represents the solution of the lth Markov chain at the nth sampling moment, represents the solution of the l+1th Markov chain at the nth sampling time.

[0114] s4.3.4.If The Markov chains interact with each other in state, otherwise they do not interact with each other in state.

[0115] s4.3.5. Repeat steps s4.3.1 to s4.3.4 until the loop termination condition is met, give the maximum a posteriori probability solution, and perform statistical analysis on the inversion parameters.

[0116] s4.4. Repeat s4.2 to s4.3 until the number of iterations meets the set value, and the sampling ends. The results of each iteration of each parameter are collected.

[0117] s4.5. Collect the final reconstruction results of the inversion parameters set for different complex formations.

[0118] s4.6. Figure 5 As shown in Figure 1, after the reconstruction results of different vertical depths are collected, they are visualized.

[0119] Parts not described in the above methods can be achieved by adopting or drawing on existing technologies.

[0120] The above-described embodiments are merely descriptions of preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Without departing from the spirit of the present invention, various modifications and improvements to the technical solutions of the present invention made by ordinary technicians in this field should fall within the scope of protection determined by the claims of the present invention.

Claims

1. A parametric inversion method for azimuthal electromagnetic logging while drilling in complex formations, characterized by The following steps are involved: s1. Model complex geological structures, construct 2D complex geological models, and parameterize the 2D complex geological models; s2. Analyze the response characteristics of the 2D complex geological model established in s1, and conduct influencing factors and sensitivity analysis; s3. Obtain observation data based on the response characteristics of s2 and construct the objective function; s4. Combining s2 and s3, the PT-MCMC inversion method is used to invert the parameterized 2D complex geological model to achieve a fine reconstruction of the complex strata.

2. The parametric inversion method for azimuthal electromagnetic logging while drilling in complex structure formations according to claim 1, characterized in that: In step s1: the constructed 2D complex geological model includes a fault model, a fold model and an unconformity model.

3. The parametric inversion method for azimuthal electromagnetic logging while drilling in complex structure formations according to claim 2, characterized in that: The steps to parameterize the fault model are as follows: s1.1.

1. Convert the 3D fault model into a 2D fault model based on its structural characteristics, analyze the parameters that determine the basic morphology and electrical characteristics of the fault, and parameterize the fault model into fault throw, fault dip, and resistivity. s1.1.

2. The fault throw reflects the relative displacement between the upper and lower strata of the fault and controls the degree of stratum movement. It is represented by the parameter d. s1.1.

3. The fault dip can control the fault geometry and affect the horizontal asymmetry of the resistivity, significantly affecting the logging response characteristics. This is represented by the parameter θ. s1.1.

4. For resistivity, since fault movement results in a discontinuous distribution in the lateral direction, the resistivity of each layer on both sides of the fault needs to be parameterized and expressed as resistivity R. s1.1.

5. Parameterize the fault model using fault throw, fault dip, and resistivity parameters for subsequent model inversion.

4. The parametric inversion method for azimuthal electromagnetic logging while drilling in complex structure formations according to claim 3, characterized in that: The steps to parameterize the wrinkle model are as follows: s1.2.

1. Convert the 3D wrinkle model into a 2D wrinkle model based on its structural characteristics and analyze and determine the wrinkle parameters; For a simple wrinkle model, approximate the core of the wrinkle as a triangle. Using the three-point method, the coordinates of these three points control the shape of the entire core and characterize the changing trend of the core of the entire wrinkle model. For more complex wrinkle models, a five-point method is used, using the coordinates of five points to more fully characterize the core morphology. Finally, spline interpolation is used to refine the entire wrinkle core. s1.2.

5. After determining the core's morphology and direction, parameterize the electrical properties of each portion of the formation and express them in terms of resistivity R. s1.2.

6. Parameterize the fold model using the three-point method and resistivity parameters for subsequent model inversion.

5. The parametric inversion method for azimuthal electromagnetic logging while drilling in complex structure formations according to claim 4, characterized in that: The steps to parameterize the unconformity model are as follows: s1.3.

1. Convert the 3D unconformity structural model into a 2D unconformity structural model based on its structural characteristics, and analyze and determine the unconformity structural morphological parameters; s1.3.

2. Taking the angular unconformity as an example, first determine the location of the unconformity surface, and then directly determine the length and position of the unconformity surface through the coordinates of two points; s1.3.

3. Use angles to characterize the changing trends of overlying and underlying strata. Angular unconformities only require determining the dip angle of the underlying strata, denoted by θ. s1.3.

4. After determining the shape and location of the unconformity, parameterize the electrical properties of each part of the formation and express them in terms of resistivity R. s1.3.

5. Finally, determine the thickness of each stratum and parameterize the unconformity model using the length of the unconformity surface, the dip of the underlying stratum, and the resistivity parameters of each part of the stratum for subsequent model inversion.

6. The parametric inversion method for azimuthal electromagnetic logging while drilling in complex structure formations according to claim 5, characterized in that: Step s4 includes the following steps: s4.

1. Determine the initial model for PT-MCMC sampling and determine the length and temperature of the sampling chain, and set the number of iterations; s4.

2. Select initial values ​​and perform multi-chain parallel non-interaction sampling. Use the MCMC method to sample each Markov chain, and each time choose whether to accept the next state according to the acceptance rate function α; s4.

3. After this iteration, the temperature exchange parameter ζ is used to determine whether to conduct inter-chain interaction.

7. The parametric inversion method for azimuthal electromagnetic logging while drilling in complex structure formations according to claim 6, characterized in that: Step s4.1 specifically includes the following steps: S4.1.

1. Based on the 2D complex geological model analysis in S2 and the objective function constructed in S3, construct K Markov chains with increasing temperatures. The solution of each Markov chain l at different temperatures satisfies the posterior distribution of the different temperatures. s4.1.

2. Introducing the temperature parameter T into the likelihood function l Control the sampling step size: Where, T l is the temperature parameter of each chain, T min The lowest temperature chain is defined as T max The chain with the highest temperature is defined.

8. The parametric inversion method for azimuthal electromagnetic logging while drilling in complex structure formations according to claim 7, characterized in that: Step s4.2 specifically includes the following steps: s4.2.

1. The initial value selected according to the initial model is used as m (0) state; s4.2.

2. Determine the posterior distribution using the prior distribution and the likelihood function; s4.2.

3. Sampling from the posterior distribution, solving m at future moments k+1 The probability distribution of m depends only on the solution m at the current moment k ; s4.2.

4. Introduce the receiving rate function α, which is expressed as follows: Where x and y are the formation models at any time, d is the formation measurement data, and Π(x, y) is the transfer kernel function, which represents the transfer from model x to model y. Assuming that the transfer kernel function obeys Gaussian distribution, then Π(x, y) = Π(y, x), and the acceptance rate function is further simplified to: s4.2.

5. Calculate a(x, y) using the above formula, and compare it with the random number μ that follows a uniform distribution. If μ < a(x, y), then accept the model solution m k+1 , otherwise retain the model solution m k , and enter the next iteration.

9. The parametric inversion method for azimuthal electromagnetic logging while drilling in complex structure formations according to claim 8, characterized in that: Step s4.3 specifically includes the following steps: s4.3.

1. After the last sampling is completed, generate a random number ρ that follows a uniform distribution; s4.3.

2. When ρ is greater than the preset temperature exchange parameter ζ, adjacent Markov chains with different temperatures do not interact, and steps 4.2.4 to 4.2.5 are repeated. Conversely, the state interaction function defined in the following formula is used to determine whether adjacent Markov chains with different temperatures interact with each other. Where, represents the solution of the lth Markov chain at the nth sampling moment, represents the solution of the l+1th Markov chain at the nth sampling moment; s4.3.4.If Then the Markov chains interact with each other in state, otherwise they do not interact with each other in state; s4.3.

5. Repeat steps s4.3.1 to s4.3.4 until the loop termination condition is met, give the maximum a posteriori probability solution, and perform statistical analysis on the inversion parameters.

10. The parametric inversion method for azimuthal electromagnetic logging while drilling in complex structure formations according to claim 9, characterized in that: Step s4 also includes the following steps: S4.

4. Repeat S4.2 to S4.3 until the number of iterations meets the set value, and the sampling ends. The results of each iteration of each parameter are collected. S4.

5. The final reconstruction results of the inversion parameters set for different complex formations are collected. s4.

6. After collecting the reconstruction results at different vertical depths, visualize them.

Images