A method for electromagnetic wave resistivity logging while drilling inversion based on quasi-newton method

Abstract

The application provides a method for electromagnetic wave resistivity logging while drilling inversion based on quasi-Newton method, and relates to the technical field of oil and gas exploration and development, which comprises the following steps: collecting measured response data of isotropic or anisotropic target formation, constructing a three-layer TI medium formation model, and determining the parameters to be inverted; performing global optimization by using genetic algorithm, and outputting the optimal result as an initial value; constructing a quasi-Newton inversion model containing a regularization term, dynamically updating the Jacobian matrix by using Broyden updating rule, introducing a diagonal adaptive damping matrix to replace the fixed damping factor, and adaptively adjusting the damping strength according to the relative increment of the parameters; inputting the initial value into the improved model for iterative operation until the termination condition is met. The application is free from dependence on artificial experience, avoids local extremum convergence, improves inversion accuracy, reduces the number of iterations, improves calculation efficiency, accurately inverts key parameters, meets the requirements of real-time geosteering engineering, and improves the efficiency of oil and gas exploration and development.

Description

Technical Field

[0001] This invention belongs to the field of oil and gas exploration and development technology, specifically relating to a drilling electromagnetic resistivity logging inversion method based on the quasi-Newton method. Background Technology

[0002] Oil and gas exploration and development is accelerating its expansion into complex areas such as deep earth, deep water, unconventional environments, old oilfields, and new energy sources. The burial depth of oil and gas reservoirs continues to increase, and the formation structure and fluid characteristics are becoming increasingly complex. While drilling azimuth electromagnetic resistivity logging technology is rapidly developing, the information transmission capacity of this type of logging instrument is extremely limited. It is necessary to extract key geological information such as formation resistivity (both horizontal and vertical), formation boundary locations, and anisotropy from a limited combination of signals.

[0003] In existing technologies, inversion algorithms are divided into stochastic and gradient-based algorithms. Stochastic algorithms (such as simulated annealing and genetic algorithms) have good global optimization capabilities and layer adaptability, but they require extensive sampling of the model space. In multi-layer model inversion, the large number of parameters limits their practical application. Gradient-based algorithms have fewer iterations and faster inversion speed, and are widely used in well logging data processing. However, they rely on the selection of initial values, are prone to convergence to local extrema, and require the calculation of complex Jacobian matrices in each iteration, resulting in a heavy computational burden and making it difficult to meet the requirements of real-time inversion.

[0004] Although the quasi-Newton method can approximate the new matrix by using the Jacobian matrix and gradient information from the previous iteration, reducing the amount of computation, it still faces two major challenges: first, it is highly dependent on the initial value of the iteration and needs to be selected precisely; second, the fixed damping factor cannot adaptively adjust the convergence speed, making it difficult to balance convergence efficiency and stability, and may cause out-of-bounds problems when approaching the minimum point.

[0005] Therefore, there is an urgent need for a drilling electromagnetic resistivity logging inversion method that relies on reliable initial values ​​to avoid local extrema, adaptively adjusts damping strength to balance inversion speed and stability, adapts to multi-layered anisotropic formations, accurately inverts key parameters, and meets the needs of real-time geological guidance engineering. Summary of the Invention

[0006] In view of this, in order to solve the above problems, this invention provides a drilling electromagnetic resistivity logging inversion method based on the quasi-Newton method. The method uses a genetic algorithm to select initial values ​​and uses the better results obtained by the genetic algorithm as the initial values ​​for subsequent inversions. An adaptive damping matrix is ​​introduced into the quasi-Newton method to adaptively adjust the damping strength according to different parameters, thereby realizing the resistivity and interface distance inversion of an anisotropic three-layer formation model.

[0007] The methods include:

[0008] S1. Acquire measured response data of the target formation using a drilling electromagnetic wave logging instrument, wherein the target formation includes isotropic formations and anisotropic formations;

[0009] S2. Based on the geological scene corresponding to the measured response data, construct a three-dimensional model of the target stratum and obtain the geological parameters as parameters to be inverted;

[0010] S3. Initial values ​​for the parameters to be inverted are selected using a genetic algorithm. The process involves initializing the population, obtaining fitness values, selecting individuals, exchanging gene fragments from parents, and performing mutation operations to iterate and evolve the population. When the number of iterations exceeds the set maximum number of iterations, the m forward simulation values ​​with the highest fitness are output as the initial values ​​for inversion.

[0011] S4. Construct a quasi-Newton inversion model with constraint terms, and update the Jacobian matrix using the Broyden update method; replace the fixed damping factor in the quasi-Newton inversion model with an adaptive damping matrix, and adaptively adjust the damping strength according to different parameters to obtain an improved quasi-Newton inversion model.

[0012] S5. Input the initial values ​​of the inversion into the improved quasi-Newton inversion model, iteratively execute the inversion calculation until the preset termination condition is met, and obtain the inversion result.

[0013] Optionally, in step S2:

[0014] The three-dimensional model is a three-layer TI medium stratigraphic model, including an isotropic stratigraphic model and an anisotropic stratigraphic model;

[0015] In the isotropic stratigraphic model, the electrical conductivity of the first and third layers is 1 S·m. -1 The conductivity of the second layer is 0.5 S·m. -1 ;

[0016] In the anisotropic stratigraphic model, the horizontal and vertical electrical conductivity of the first layer is 1 S·m. -1 The second layer has a horizontal conductivity of 0.5 S·m. -1 The vertical conductivity of the second layer is 0.2 S·m. -1 The third layer has a horizontal conductivity of 2 S·m. -1 The vertical conductivity of the third layer is 1 S·m -1 .

[0017] Optionally, in step S2:

[0018] The formation parameters include the electrical conductivity of isotropic formations or the horizontal and vertical electrical conductivity of anisotropic formations, the distance of the instrument from the upper boundary, and the distance of the instrument from the lower boundary.

[0019] Optionally, in step S3, the model parameters of the genetic algorithm are set as follows:

[0020] The population size is 500, the maximum number of iterations is 100, the crossover probability is 0.8, the mutation probability is 0.05, and the tournament size is 3.

[0021] Optionally, step S3 includes:

[0022] S31. Initialize the population; the optimization problem is:

[0023] ;

[0024] in, min For minimization operation, f(x) The objective function represents the optimization problem. x Represents a formation parameter vector. S Indicates the feasible region of the parameter. Let be an n-dimensional real space, where n is the number of stratigraphic parameters to be inverted. Indicates the first j Lower limit constraint values ​​for each formation parameter, x j Represents the formation parameter vector x The j One portion, u j Indicates the first j Upper limit constraint value for each stratigraphic parameter;

[0025] S32. Uniformly randomize within the parameter space to obtain the sampled values:

[0026] ;

[0027] in, This is the initial population size value. It is the spatial dimension, i.e., the number of initial values ​​that need to be determined;

[0028] S33. In each generation, calculate the fitness value for each individual, where the fitness function is:

[0029] ;

[0030] S34. Select superior individuals for mating pool based on fitness, for each position in the population. Random selection Each individual index is used to select the highest fitness value, and this selection is repeated until the highest fitness value is found. There are 1 parent generation, where the probability of each individual being selected is:

[0031] ;

[0032] in Ranking of individual fitness;

[0033] S35. Randomly select a cut point and exchange gene segments from the parent generation to generate two offspring using the following formula:

[0034] ;

[0035] ;

[0036] in, and For two offspring individuals, and There are two parent individuals. c The intersection point is randomly selected. L The total length of the genes in the parent individual.

[0037] S36. Each individual is evaluated using the following formula with probability. Perform mutation operation:

[0038] ;

[0039] in, This represents a random number that follows a continuous uniform distribution on the interval [0,1].

[0040] S37. Repeat steps S31-S36 to iterate. When the number of iterations exceeds the set maximum number of iterations, output the m forward simulation values ​​with the highest fitness at this time as the initial values ​​for inversion.

[0041] Optionally, the construction of the quasi-Newton inversion model containing constraint terms in step S4, and the updating of the Jacobian matrix using the Broyden update method, includes:

[0042] S41. Set the constraint term as a regularization term, and its formula is:

[0043] ;

[0044] in, Let Jacobian matrix be the value at the k-th iteration. for The transpose of the matrix, Let I be the square of the regularization coefficient, and I be the identity matrix. This is the formation parameter update vector for the k-th iteration. Let be the observed response vector for the k-th iteration;

[0045] S42. Introduce a damping factor into the regularization formula. The parameter update amount is obtained:

[0046] ;

[0047] S43. Order Let this be the step size vector at the k-th iteration. For the change of a function, the quasi-Newton equations satisfy the following formula:

[0048] ;

[0049] S44. Update the rank-1 matrix:

[0050] ;

[0051] in, and It is an undetermined vector;

[0052] S45. Substituting the rank-one matrix into the quasi-Newton equation yields the following formula:

[0053] ;

[0054] S46. According to the principle of minimum change, let We obtain the following equation:

[0055] ;

[0056] S47. Substitute the equation from step S46 into the rank-1 matrix from step S44, and... The direction-corrected Jacobian matrix is ​​obtained as follows:

[0057] .

[0058] Optionally, step S4, which involves replacing the fixed damping factor in the quasi-Newton inversion model with an adaptive damping matrix and adaptively adjusting the damping strength according to different parameters, to obtain an improved quasi-Newton inversion model, includes:

[0059] S48. Define the adaptive damping matrix as... :

[0060] ;

[0061] in, It is the number of parameters to be inverted;

[0062] The matrix elements are:

[0063] ;

[0064] S49. Replace the original damping coefficients with the adaptive damping matrix to obtain:

[0065] .

[0066] Optionally, in step S5:

[0067] The inversion calculation aims to minimize the difference between the measured response data and the forward simulation values. The objective function formula is:

[0068] ;

[0069] in, It is a regularization term. It is the regularization coefficient. , For horizontal conductivity, Vertical conductivity, and These represent the distances from the instrument to the upper boundary and the instrument to the lower boundary, respectively. This refers to the measured response data from the logging-while-drilling instrument. These are forward simulation values.

[0070] As can be seen from the above technical solutions, the present invention has the following advantages:

[0071] This paper employs a genetic algorithm for global optimization, using multiple rounds of optimization to obtain high-quality initial inputs and iterating using a quasi-Newton method. Leveraging the powerful global search capability of the genetic algorithm, it eliminates reliance on manual experience, ensuring that the initial values ​​closely approximate the true solution. This avoids inversion failures caused by local extrema from the outset, guaranteeing the reliability of the inversion results. The Jacobian matrix is ​​updated using the Broyden condition, requiring only one calculation in the initial inversion stage. Subsequent iterations use the rank-one matrix for correction, reducing unnecessary computation. Combined with the optimization of the number of iterations, this improves the inversion speed and adapts to the limited information transmission capabilities of logging instruments. A diagonal adaptive damping matrix is ​​introduced, dynamically adjusting the damping strength based on the relative increment ratio of the parameters to be inverted. Parameters deviating significantly from their true values ​​are damped more to ensure stability, while parameters close to their true values ​​are damped less or even eliminated to accelerate convergence. This overcomes the rigidity of fixed damping factors, achieving an optimal balance between convergence speed and stability. This invention can effectively adapt to three-layer anisotropic formation models, and the inversion accuracy is significantly improved compared with the traditional quasi-Newton method. It meets the engineering requirements of geological steering for interface positioning accuracy, and can efficiently analyze formation information from limited logging signals, providing data support for real-time wellbore trajectory adjustment and reservoir drilling rate improvement. Attached Figure Description

[0072] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0073] Figure 1 This is a schematic diagram of the process of the drilling electromagnetic resistivity logging inversion method based on the quasi-Newton method of the present invention.

[0074] Figure 2 This is a schematic diagram of the three-layer isotropic stratigraphic model of the present invention;

[0075] Figure 3 This is a schematic diagram of the three-layer anisotropic stratigraphic model of the present invention;

[0076] Figure 4 This is a schematic diagram of the genetic algorithm flow of the present invention;

[0077] Figure 5 This is a schematic diagram of the isotropic initial value selection results of the present invention, wherein, Figure 5 (a) in the figure represents the fitness evolution curve. Figure 5 (b) in the figure represents the evolution curve of the optimal parameters;

[0078] Figure 6 This is a schematic diagram showing the selection results of the anisotropic initial value in this invention, wherein, Figure 6 (a) in the figure represents the fitness evolution curve. Figure 6 (b) in the figure represents the evolution curve of the optimal parameters;

[0079] Figure 7 This is a schematic diagram of the isotropic inversion results of the fixed damping method of the present invention;

[0080] Figure 8 This is a schematic diagram of the fixed-damping anisotropic inversion results of the present invention, wherein, Figure 8 In the figure, (a) represents the horizontal conductivity. Figure 8 In the figure, (b) represents the vertical conductivity;

[0081] Figure 9 This is a schematic diagram of the isotropic inversion results of the adaptive damping in this invention;

[0082] Figure 10 This is a schematic diagram of the adaptive damping anisotropy inversion results of the present invention, wherein, Figure 10 In the figure, (a) represents the horizontal conductivity. Figure 10 In the figure, (b) represents the vertical conductivity;

[0083] Figure 11 This is a schematic diagram of the inversion results of the fixed damping boundary distance according to the present invention, wherein, Figure 11In this context, (a) represents the distance to the upper boundary. Figure 11 In this context, (b) represents the distance to the lower boundary;

[0084] Figure 12 This is a schematic diagram of the adaptive damping boundary distance inversion result of the present invention, wherein, Figure 12 In this context, (a) represents the distance to the upper boundary. Figure 12 In the diagram, (b) represents the distance to the lower boundary. Detailed Implementation

[0085] The various embodiments of the present invention will be described more fully in the detailed steps of the drilling electromagnetic resistivity logging inversion method based on the quasi-Newton method described below. The present invention may have various embodiments, and adjustments and modifications may be made therein. However, it should be understood that there is no intention to limit the various embodiments of the present invention to the specific embodiments disclosed herein, but rather the present invention should be understood to cover all adjustments, equivalents, and / or alternatives falling within the spirit and scope of the various embodiments of the present invention.

[0086] It should be understood that, when used in this specification, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components, and / or collections thereof. The terms "comprising," "including," "having," and variations thereof all mean "including but not limited to," unless otherwise specifically emphasized.

[0087] The terms "one embodiment" or "some embodiments" used in this invention mean that one or more embodiments of the invention include the specific features, structures, or characteristics described in that embodiment. Therefore, the terms "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of the invention do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized.

[0088] To facilitate a clear description of the technical solution of this invention, the terms "first" and "second" are used to distinguish identical or similar items with essentially the same function and effect. Those skilled in the art will understand that the terms "first" and "second" do not limit the quantity or execution order, and that "first" and "second" are not necessarily different.

[0089] To make the objectives, features, and advantages of this invention more apparent and understandable, specific embodiments and accompanying drawings will be used to clearly and completely describe the technical solutions protected by this invention. Obviously, the embodiments described below are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0090] Please see Figure 1 The diagram illustrates a drilling electromagnetic resistivity logging inversion method based on the quasi-Newton method. The method includes:

[0091] S1. Acquire measured response data of the target formation using a drilling electromagnetic wave logging instrument, wherein the target formation includes isotropic formations and anisotropic formations;

[0092] S2. Based on the geological scene corresponding to the measured response data, construct a three-dimensional model of the target stratum and obtain the geological parameters as parameters to be inverted;

[0093] S3. Initial values ​​for the parameters to be inverted are selected using a genetic algorithm. The process involves initializing the population, obtaining fitness values, selecting individuals, exchanging gene fragments from parents, and performing mutation operations to iterate and evolve the population. When the number of iterations exceeds the set maximum number of iterations, the m forward simulation values ​​with the highest fitness are output as the initial values ​​for inversion.

[0094] S4. Construct a quasi-Newton inversion model with constraint terms, and update the Jacobian matrix using the Broyden update method; replace the fixed damping factor in the quasi-Newton inversion model with an adaptive damping matrix, and adaptively adjust the damping strength according to different parameters to obtain an improved quasi-Newton inversion model.

[0095] S5. Input the initial values ​​of the inversion into the improved quasi-Newton inversion model, iteratively execute the inversion calculation until the preset termination condition is met, and obtain the inversion result.

[0096] As a refinement and extension of the specific implementation of the above embodiments, in order to fully illustrate the specific implementation process of this embodiment, another drilling electromagnetic resistivity logging inversion method based on the quasi-Newton method is provided, which includes the following steps:

[0097] S1. Acquire measured response data of the target formation using a drilling electromagnetic wave logging instrument, wherein the target formation includes isotropic formations and anisotropic formations;

[0098] S2. Based on the stratigraphic scene corresponding to the measured response data, construct a 3D model of the target stratigraphy and obtain stratigraphic parameters as parameters to be inverted; In step S2:

[0099] The three-dimensional model is a three-layer TI medium stratigraphic model, including an isotropic stratigraphic model and an anisotropic stratigraphic model;

[0100] like Figure 2 As shown, in the isotropic stratigraphic model, the electrical conductivity of the first and third layers is 1 S·m. -1 The conductivity of the second layer is 0.5 S·m. -1 ;

[0101] like Figure 3 As shown, in the anisotropic stratigraphic model, the horizontal and vertical electrical conductivity of the first layer is 1 S·m. -1 The second layer has a horizontal conductivity of 0.5 S·m. -1 The vertical conductivity of the second layer is 0.2 S·m. -1 The third layer has a horizontal conductivity of 2 S·m. -1 The vertical conductivity of the third layer is 1 S·m -1 .

[0102] In step S2:

[0103] The formation parameters include the electrical conductivity of isotropic formations or the horizontal and vertical electrical conductivity of anisotropic formations, the distance of the instrument from the upper boundary, and the distance of the instrument from the lower boundary.

[0104] S3. Initial values ​​for the parameters to be inverted are selected using a genetic algorithm. The process involves initializing the population, obtaining fitness values, selecting individuals, exchanging gene fragments from parents, and performing mutation operations to iterate and evolve the population. When the number of iterations exceeds the set maximum number of iterations, the m forward simulation values ​​with the highest fitness are output as the initial values ​​for inversion.

[0105] In some embodiments, in step S3, the model parameters of the genetic algorithm are set as follows:

[0106] The population size is 500, the maximum number of iterations is 100, the crossover probability is 0.8, the mutation probability is 0.05, and the tournament size is 3.

[0107] Step S3 includes:

[0108] S31. Initialize the population; the optimization problem is:

[0109] ;

[0110] in, min For minimization operation, f(x) The objective function represents the optimization problem. x Represents a formation parameter vector. S Indicates the feasible region of the parameter. Let be an n-dimensional real space, where n is the number of stratigraphic parameters to be inverted. Indicates the first j Lower limit constraint values ​​for each formation parameter, x j Represents the formation parameter vector x The j One portion, u j Indicates the first j Upper limit constraint value for each stratigraphic parameter;

[0111] S32. Uniformly randomize within the parameter space to obtain the sampled values:

[0112] ;

[0113] in, This is the initial population size value. It is the spatial dimension, i.e., the number of initial values ​​that need to be determined;

[0114] S33. In each generation, calculate the fitness value for each individual, where the fitness function is:

[0115] ;

[0116] S34. Select superior individuals for mating pool based on fitness, for each position in the population. Random selection Each individual index is used to select the highest fitness value, and this selection is repeated until the highest fitness value is found. There are 1 parent generation, where the probability of each individual being selected is:

[0117] ;

[0118] in Ranking of individual fitness;

[0119] S35. Randomly select a cut point and exchange gene segments from the parent generation to generate two offspring using the following formula:

[0120] ;

[0121] ;

[0122] in, and For two offspring individuals, and There are two parent individuals. c The intersection point is randomly selected. L The total length of the genes in the parent individual.

[0123] S36. Each individual is evaluated using the following formula with probability. Perform mutation operation:

[0124] ;

[0125] in, This represents a random number that follows a continuous uniform distribution on the interval [0,1].

[0126] S37. Repeat steps S31-S36 to iterate. When the number of iterations exceeds the set maximum number of iterations, output the m forward simulation values ​​with the highest fitness at this time as the initial values ​​for inversion.

[0127] It should be noted that, as Figure 4 As shown, the basic process of a genetic algorithm includes steps such as population initialization, fitness evaluation, selection, crossover, and mutation. At the start of the algorithm, an initial population of several individuals is randomly generated, each representing a potential solution to the problem, typically represented using binary, real number, or symbolic encoding. Subsequently, the algorithm enters an iterative evolutionary process, with each generation generating a new population through selection, crossover, and mutation, until the termination condition is met.

[0128] S4. Construct a quasi-Newton inversion model with constraint terms, and update the Jacobian matrix using the Broyden update method; replace the fixed damping factor in the quasi-Newton inversion model with an adaptive damping matrix, and adaptively adjust the damping strength according to different parameters to obtain an improved quasi-Newton inversion model.

[0129] Step S4, which involves constructing a quasi-Newton inversion model with constraint terms and updating the Jacobian matrix using the Broyden update method, includes:

[0130] S41. Set the constraint term as a regularization term, and its formula is:

[0131] ;

[0132] in, Let Jacobian matrix be the value at the k-th iteration. for The transpose of the matrix, Let I be the square of the regularization coefficient, and I be the identity matrix. This is the formation parameter update vector for the k-th iteration. Let be the observed response vector for the k-th iteration;

[0133] S42. Introduce a damping factor into the regularization formula. The parameter update amount is obtained:

[0134] ;

[0135] S43. Order Let this be the step size vector at the k-th iteration. For the change of a function, the quasi-Newton equations satisfy the following formula:

[0136] ;

[0137] S44. Update the rank-1 matrix:

[0138] ;

[0139] in, and It is an undetermined vector;

[0140] S45. Substituting the rank-one matrix into the quasi-Newton equation yields the following formula:

[0141] ;

[0142] S46. According to the principle of minimum change, let We obtain the following equation:

[0143] ;

[0144] S47. Substitute the equation from step S46 into the rank-1 matrix from step S44, and... The direction-corrected Jacobian matrix is ​​obtained as follows:

[0145] .

[0146] Step S4 involves replacing the fixed damping factor in the quasi-Newton inversion model with an adaptive damping matrix, and adaptively adjusting the damping strength according to different parameters to obtain the improved quasi-Newton inversion model, which includes:

[0147] S48. Define the adaptive damping matrix as... :

[0148] ;

[0149] in, It is the number of parameters to be inverted;

[0150] The matrix elements are:

[0151] ;

[0152] S49. Replace the original damping coefficients with the adaptive damping matrix to obtain:

[0153] .

[0154] It should be noted that the damping matrix is ​​defined... The purpose is to address the challenges of high-dimensional inversion problems involving multiple parameters, such as well logging, which have been observed in previous inversion practices. The degree of deviation between each element in the calculation and the true value is generally different, especially for the initial value and the first few iterations. Introducing a damping factor alone is often insufficient. In the calculated... Generally, only elements with large absolute values ​​will have a significant impact on the stability of the next iteration; therefore, it is necessary to... Each element provides different damping effects based on its different size.

[0155] S5. Input the initial values ​​of the inversion into the improved quasi-Newton inversion model, iteratively execute the inversion calculation until the preset termination condition is met, and obtain the inversion result.

[0156] In step S5:

[0157] The inversion calculation aims to minimize the difference between the measured response data and the forward simulation values. The objective function formula is:

[0158] ;

[0159] in, It is a regularization term. It is the regularization coefficient. , For horizontal conductivity, Vertical conductivity, and These represent the distances from the instrument to the upper boundary and the instrument to the lower boundary, respectively. This refers to the measured response data from the logging-while-drilling instrument. These are forward simulation values.

[0160] In some embodiments, since the results of the genetic algorithm differ each time, the obtained formation signal is optimized ten times using the genetic algorithm to obtain ten initial values ​​of the formation model that are approximately similar but not identical. These ten initial values ​​are then used as the initial values ​​for the quasi-Newton method iterative inversion. The model parameters of the quasi-Newton algorithm are set to an initial damping coefficient of 0 and 5, and a regularization parameter of 0.1. Finally, the inversion results of different formation models are compared.

[0161] The initial value obtained through a genetic algorithm for a certain inversion is as follows: Figure 5 and Figure 6 As shown, Figure 5 This is a schematic diagram illustrating the selection results for isotropic initial values, where... Figure 5 (a) in the figure represents the fitness evolution curve. Figure 5(b) in the figure represents the evolution curve of the optimal parameters; Figure 6 This is a schematic diagram illustrating the selection results of initial values ​​for anisotropy, where... Figure 6 (a) in the figure represents the fitness evolution curve. Figure 6 (b) in the table represents the evolution curve of the optimal parameters; Table 1 shows the root mean square error between the isotropic and anisotropic stratigraphic models and the actual values.

[0162] Table 1. Relative Error of Initial Value Selection in Genetic Algorithm

[0163]

[0164] Using the initial values ​​of the model selected by the genetic algorithm, resistivity and boundary distance were inverted in isotropic and anisotropic strata using both the traditional quasi-Newton method and the improved quasi-Newton method. The results are as follows. Figure 7 , Figure 8 , Figure 9 , Figure 10 , Figure 11 , Figure 12 As shown; Figure 7 A schematic diagram of the inversion results for isotropic fixed damping; Figure 8 This is a schematic diagram of the inversion results for fixed-damping anisotropy, where, Figure 8 In the figure, (a) represents the horizontal conductivity. Figure 8 In the figure, (b) represents the vertical conductivity; Figure 9 This is a schematic diagram of the isotropic inversion results for adaptive damping. Figure 10 This is a schematic diagram of the adaptive damping anisotropy inversion results. Figure 10 In the figure, (a) represents the horizontal conductivity. Figure 10 In the figure, (b) represents the vertical conductivity; Figure 11 This is a schematic diagram of the inversion results with fixed damping boundary distance, where, Figure 11 In this context, (a) represents the distance to the upper boundary. Figure 11 In this context, (b) represents the distance to the lower boundary; Figure 12 This is a schematic diagram of the adaptive damping boundary distance inversion results, where, Figure 12 In this context, (a) represents the distance to the upper boundary. Figure 12 In the diagram, (b) represents the distance to the lower boundary.

[0165] Meanwhile, the comparison of the resistivity and boundary distance inversion results is shown in Tables 2 and 3:

[0166] Table 2. Isotropic Inversion Results

[0167]

[0168] Table 3 Anisotropic Inversion Results

[0169]

[0170] It should be noted that the adaptive quasi-Newton method dynamically adjusts the local damping strength according to different iteration points of different inversion values, effectively balancing the contradiction between convergence speed and stability in multi-parameter inversion, and improving the accuracy of both resistivity inversion and boundary distance inversion. Applying a genetic algorithm to the initial value selection of the logging-while-drilling inversion problem, the adaptive global optimization of the genetic algorithm can quickly and accurately find suitable initial values. Compared with the traditional quasi-Newton method, the adaptive damped quasi-Newton method improves the accuracy of each parameter inversion, especially in anisotropic formations and boundary distance inversion. Compared with the fixed-damped quasi-Newton method, the adaptive damped quasi-Newton method reduces the number of iterations and improves the inversion speed.

[0171] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0172] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A drilling electromagnetic resistivity logging inversion method based on the quasi-Newton method, characterized in that, The method includes: S1. Acquire measured response data of the target formation using a drilling electromagnetic wave logging instrument, wherein the target formation includes isotropic formations and anisotropic formations; S2. Based on the geological scene corresponding to the measured response data, construct a three-dimensional model of the target stratum and obtain the geological parameters as parameters to be inverted; S3. Initial values ​​for the parameters to be inverted are selected using a genetic algorithm. The process involves initializing the population, obtaining fitness values, selecting individuals, exchanging gene fragments from parents, and performing mutation operations to iterate and evolve the population. When the number of iterations exceeds the set maximum number of iterations, the m forward simulation values ​​with the highest fitness are output as the initial values ​​for inversion. S4. Construct a quasi-Newton inversion model with constraint terms, and update the Jacobian matrix using the Broyden update method; replace the fixed damping factor in the quasi-Newton inversion model with an adaptive damping matrix, and adaptively adjust the damping strength according to different parameters to obtain an improved quasi-Newton inversion model. S5. Input the initial values ​​of the inversion into the improved quasi-Newton inversion model, iteratively execute the inversion calculation until the preset termination condition is met, and obtain the inversion result; Step S4 involves replacing the fixed damping factor in the quasi-Newton inversion model with an adaptive damping matrix, and adaptively adjusting the damping strength according to different parameters to obtain the improved quasi-Newton inversion model, which includes: S48. Define the adaptive damping matrix as... : ； in, It is the number of parameters to be inverted; The matrix elements are: ； S49. Replace the original damping coefficients with the adaptive damping matrix to obtain: ; In step S5: The inversion calculation aims to minimize the difference between the measured response data and the forward simulation values. The objective function formula is: ； in, It is a regularization term. It is the regularization coefficient. , For horizontal conductivity, Vertical conductivity, and These represent the distances from the instrument to the upper boundary and the instrument to the lower boundary, respectively. This refers to the measured response data from the logging-while-drilling instrument. These are forward simulation values.

2. The drilling electromagnetic resistivity logging inversion method based on the quasi-Newton method according to claim 1, characterized in that, In step S2: The three-dimensional model is a three-layer TI medium stratigraphic model, including an isotropic stratigraphic model and an anisotropic stratigraphic model; In the isotropic stratigraphic model, the electrical conductivity of the first and third layers is 1 S·m. -1 The conductivity of the second layer is 0.5 S·m. -1 ; In the anisotropic stratigraphic model, the horizontal and vertical electrical conductivity of the first layer is 1 S·m. -1 The second layer has a horizontal conductivity of 0.5 S·m. -1 The vertical conductivity of the second layer is 0.2 S·m. -1 The third layer has a horizontal conductivity of 2 S·m. -1 The vertical conductivity of the third layer is 1 S·m -1 .

3. The drilling electromagnetic resistivity logging inversion method based on the quasi-Newton method according to claim 1, characterized in that, In step S2: The formation parameters include the electrical conductivity of isotropic formations or the horizontal and vertical electrical conductivity of anisotropic formations, the distance of the instrument from the upper boundary, and the distance of the instrument from the lower boundary.

4. The drilling electromagnetic resistivity logging inversion method based on the quasi-Newton method according to claim 1, characterized in that, In step S3, the model parameters of the genetic algorithm are set as follows: The population size is 500, the maximum number of iterations is 100, the crossover probability is 0.8, the mutation probability is 0.05, and the tournament size is 3.

5. The drilling electromagnetic resistivity logging inversion method based on the quasi-Newton method according to claim 1, characterized in that, Step S3 includes: S31. Initialize the population; the optimization problem is: ； in, min For minimization operation, f(x) The objective function represents the optimization problem. x Represents a formation parameter vector. S Indicates the feasible region of the parameter. Let be an n-dimensional real space, where n is the number of stratigraphic parameters to be inverted. Indicates the first j Lower limit constraint values ​​for each formation parameter, x j Represents the formation parameter vector x The j One portion, u j Indicates the first j Upper limit constraint value for each stratigraphic parameter; S32. Uniformly randomize within the parameter space to obtain the sampled values: ； in, This is the initial population size value. It is the spatial dimension, i.e., the number of initial values ​​that need to be determined; S33. In each generation, calculate the fitness value for each individual, where the fitness function is: ； S34. Select superior individuals for mating pool based on fitness, for each position in the population. Random selection Each individual index is used to select the highest fitness value, and this selection is repeated until the highest fitness value is found. There are 1 parent generation, where the probability of each individual being selected is: ； in Ranking of individual fitness; S35. Randomly select a cut point and exchange gene segments from the parent generation to generate two offspring using the following formula: ； ； in, and For two offspring individuals, and There are two parent individuals. c The intersection point is randomly selected. L The total length of the genes in the parent individual; S36. Each individual is evaluated using the following formula with probability. Perform mutation operation: ； in, This represents a random number that follows a continuous uniform distribution on the interval [0,1]. S37. Repeat steps S31-S36 to iterate. When the number of iterations exceeds the set maximum number of iterations, output the m forward simulation values ​​with the highest fitness at this time as the initial values ​​for inversion.

6. The drilling electromagnetic resistivity logging inversion method based on the quasi-Newton method according to claim 1, characterized in that, Step S4, which involves constructing a quasi-Newton inversion model with constraint terms and updating the Jacobian matrix using the Broyden update method, includes: S41. Set the constraint term as a regularization term, and its formula is: ； in, Let Jacobian matrix be the value at the k-th iteration. for The transpose of the matrix, Let I be the square of the regularization coefficient, and I be the identity matrix. This is the formation parameter update vector for the k-th iteration. Let be the observed response vector for the k-th iteration; S42. Introduce a damping factor into the regularization formula. The parameter update amount is obtained: ； S43. Order Let this be the step size vector at the k-th iteration. For the change of a function, the quasi-Newton equations satisfy the following formula: ； S44. Update the rank-1 matrix: ； in, and It is an undetermined vector; S45. Substituting the rank-one matrix into the quasi-Newton equation yields the following formula: ； S46. According to the principle of minimum change, let We obtain the following equation: ； S47. Substitute the equation from step S46 into the rank-1 matrix from step S44, and... The direction-corrected Jacobian matrix is ​​obtained as follows: 。

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