While-drilling electromagnetic wave resistivity logging inversion method based on quasi-Newton method

Abstract

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

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of oil and gas exploration and development, and particularly relates to a while-drilling electromagnetic wave resistivity logging inversion method based on a quasi-Newton method. BACKGROUND

[0002] Oil and gas exploration and development is accelerating towards complex fields such as deep land, deep water, unconventional, old oil fields and new energy, the burial depth of oil and gas reservoirs continues to increase, and the structure of the formation and the characteristics of the formation fluid are increasingly complex. With the rapid development of while-drilling azimuthal electromagnetic wave resistivity logging technology, however, the information transmission capability of such logging instruments is extremely limited, and key geological information such as formation transverse and longitudinal resistivity, formation boundary position and anisotropy needs to be inverted from a limited combination of signals.

[0003] In the prior art, inversion algorithms are divided into random and gradient classes. Random algorithms (such as simulated annealing algorithm, genetic algorithm, etc.) have good global optimization ability and layer adaptation ability, but require a large number of model space samples, and in multi-layer model inversion, due to the large number of parameters, practical application is limited; gradient algorithms have fewer iterations, fast inversion speed, and are widely used in logging data processing, but depend on initial value selection, are prone to converge to local extreme values, and require complex Jacobian matrix calculations for each iteration, which is computationally intensive and difficult to meet real-time inversion requirements.

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

[0005] Therefore, there is an urgent need for a while-drilling electromagnetic wave resistivity logging inversion method that relies on reliable initial value selection to avoid local extreme values, adaptively adjusts the damping strength to balance inversion speed and stability, adapts to multi-layer anisotropic formations, accurately inverts key parameters, and meets the real-time geosteering engineering requirements. SUMMARY

[0006] Therefore, in order to solve the above problems, the present application provides a while-drilling electromagnetic wave resistivity logging inversion method based on a quasi-Newton method, which uses a genetic algorithm to select initial values, uses the better results inverted by the genetic algorithm as the initial values for subsequent inversion, and introduces an adaptive damping matrix in the quasi-Newton method to adaptively adjust the damping strength according to different parameters, thereby realizing resistivity and interface distance inversion of anisotropic three-layer formation models.

[0007] The method comprises:

[0008] S1. collecting measured response data of a target formation by a logging-while-drilling electromagnetic wave logging instrument, the target formation including isotropic formation and anisotropic formation; S2. constructing a three-dimensional model of the target formation based on a formation scene corresponding to the measured response data, and obtaining formation parameters as to-be-inverted parameters; S3. selecting initial values of the to-be-inverted parameters by a genetic algorithm, and iteratively evolving by initializing a population, obtaining a fitness value, selecting individuals, exchanging gene fragments of parents, and mutation operation, when the iteration exceeds a set maximum iteration number, outputting m forward simulation values with the highest fitness as initial values of inversion; S4. constructing a quasi-Newton inversion model containing a constraint term, updating a Jacobian matrix by a Broyden update method; replacing a fixed damping factor in the quasi-Newton inversion model with an adaptive damping matrix, and adaptively adjusting damping strength according to different parameters to obtain an improved quasi-Newton inversion model; S5. inputting the initial values of the inversion into the improved quasi-Newton inversion model, and iteratively performing inversion calculation until a preset termination condition is met, and obtaining an inversion result.

[0009] Optionally, in step S2: the three-dimensional model is a three-layer TI medium formation model, including an isotropic formation model and an anisotropic formation model; in the isotropic formation model, the electrical conductivity of the first layer and the third layer is 1 S·m -1 , and the electrical conductivity of the second layer is 0.5 S·m -1 ; in the anisotropic formation model, the horizontal electrical conductivity and the vertical electrical conductivity of the first layer are 1 S·m -1 ; the horizontal electrical conductivity of the second layer is 0.5 S·m -1 , and the vertical electrical conductivity of the second layer is 0.2 S·m -1 ; the horizontal electrical conductivity of the third layer is 2 S·m -1 , and the vertical electrical conductivity of the third layer is 1 S·m -1 .

[0010] Optionally, in step S2: the formation parameters include the electrical conductivity of the isotropic formation or the horizontal electrical conductivity and the vertical electrical conductivity of the anisotropic formation, the distance of the instrument from the upper boundary, and the distance of the instrument from the lower boundary.

[0011] Optionally, in step S3, the model parameters of the genetic algorithm are set as: the population size is 500, the maximum iteration number is 100, the crossover probability is 0.8, the mutation probability is 0.05, and the tournament size is 3.

[0012] Optionally, 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.

[0013] 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].

[0014] 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.

[0015] 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: 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 correction Jacobian matrix is obtained: .

[0016] Optionally, in step S4, the fixed damping factor in the quasi-Newton inversion model is replaced by an adaptive damping matrix, and the damping strength is adaptively adjusted according to different parameters to obtain an improved quasi-Newton inversion model, including: S48. The adaptive damping matrix is defined as : ; Wherein, is the number of parameters to be inverted; The matrix element of is: ; S49. The adaptive damping matrix is replaced by the original damping coefficient to obtain: .

[0017] Optionally, in step S5: The inversion calculation aims to minimize the difference between the measured response data and the forward simulation value, and the objective function formula is: ; Wherein, is a regularization term, is a regularization coefficient, , is the horizontal conductivity, is the vertical conductivity, and are the distance of the upper boundary of the instrument distance and the distance of the lower boundary of the instrument distance respectively, is the measured response data of the logging-while-drilling instrument, is the forward simulation value.

[0018] From the above technical solutions, the present application has the following advantages: The genetic algorithm is adopted to globally optimize, high-quality initial values are obtained through multiple rounds of optimization to input the quasi-Newton method iteration, the powerful global search capability of the genetic algorithm is used to get rid of the dependence on artificial experience, the initial value is ensured to be close to the true solution, the inversion failure caused by the local extreme value is avoided from the source, and the reliability of the inversion result is ensured; the Broyden condition is used to update the Jacobian matrix, the Jacobian matrix needs to be calculated only once in the initial stage of inversion, and the new matrix can be obtained through rank-one matrix correction in the subsequent iteration, so that the invalid calculation amount is reduced, the iteration number is optimized, the inversion speed is improved, and the limited information transmission capacity of the logging instrument is adapted; the diagonal adaptive damping matrix is introduced, the damping strength is dynamically adjusted according to the relative increment of the to-be-inverted parameter, the damping of the parameter deviating from the true value is enhanced to ensure stability, the damping of the parameter close to the true value is weakened or even cancelled to speed up convergence, the rigid defect of the fixed damping factor is solved, and the optimal balance between convergence speed and stability is realized. The present application can effectively adapt to the three-layer anisotropic formation model, the inversion precision is significantly improved compared with the traditional quasi-Newton method, the engineering requirements of interface positioning precision for geosteering are met, and the formation information can be efficiently analyzed from the limited logging signal, thereby providing data support for real-time adjustment of well trajectory and improvement of reservoir drilling rate. BRIEF DESCRIPTION OF DRAWINGS

[0019] In order to more clearly illustrate the technical solutions of the present application, the drawings required to be used in the description will be briefly introduced below. Obviously, the drawings in the following description are only some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creating laborious work.

[0020] Figure 1 It is a flowchart of the present application based on the quasi-Newton method of the while-drilling electromagnetic wave resistivity logging inversion method. Figure 2 It is a three-layer isotropic formation model schematic diagram of the present application. Figure 3 It is a three-layer anisotropic formation model schematic diagram of the present application. Figure 4 It is a genetic algorithm flowchart of the present application. Figure 5 It is an isotropic initial value selection result schematic diagram of the present application, wherein, Figure 5 (a) in the above (a) is the fitness evolution curve, Figure 5 (b) in the above (b) is the optimal parameter evolution curve. Figure 6 It is an anisotropic initial value selection result schematic diagram of the present application, wherein, Figure 6 (a) in the above (a) is the fitness evolution curve, Figure 6 (b) in the above (b) is the optimal parameter evolution curve. Figure 7Fig. 2 is a schematic diagram of fixed-damping isotropic inversion results of the present application; Figure 8 Fig. 3 is a schematic diagram of fixed-damping anisotropic inversion results of the present application, wherein, Figure 8 (a) in Fig. 3 is the horizontal conductivity, Figure 8 (b) in Fig. 3 is the vertical conductivity; Figure 9 Fig. 4 is a schematic diagram of adaptive-damping isotropic inversion results of the present application; Figure 10 Fig. 5 is a schematic diagram of adaptive-damping anisotropic inversion results of the present application, wherein, Figure 10 (a) in Fig. 5 is the horizontal conductivity, Figure 10 (b) in Fig. 5 is the vertical conductivity; Figure 11 Fig. 6 is a schematic diagram of fixed-damping boundary distance inversion results of the present application, wherein, Figure 11 (a) in Fig. 6 is the upper boundary distance, Figure 11 (b) in Fig. 6 is the lower boundary distance; Figure 12 Fig. 7 is a schematic diagram of adaptive-damping boundary distance inversion results of the present application, wherein, Figure 12 (a) in Fig. 7 is the upper boundary distance, Figure 12 (b) in Fig. 7 is the lower boundary distance. DETAILED DESCRIPTION

[0021] Various embodiments of the present application will be more fully understood from the following detailed description taken in conjunction with the accompanying drawings, in which:

[0022] It should be understood that the terms "comprises", "comprising", "includes", "including", "has", "having" and their derivatives, as used herein, indicate "including but not limited to". The term "consisting of" is intended to mean "including and limited to". The term "consisting essentially of" is intended to mean "including at least the recited elements but not excluding others". The term "exemplary" is used herein to mean "serving as an example, instance, or illustration". Any implementation described herein as exemplary is not necessarily to be construed as preferred or advantageous over other implementations. Unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the relevant art and the present disclosure, and will not be interpreted in an overly literal sense unless expressly so defined herein.

[0023] The phrase "one embodiment" or "some embodiments" appearing in the present disclosure are used to describe a specific feature, structure, or characteristic in one or more embodiments of the application. Thus, the appearances of the phrase "in one embodiment" or "in some embodiments" in various places in the specification are not necessarily all referring to the same embodiment, but can refer to one or more but not all embodiments unless otherwise indicated.

[0024] In order to clearly describe the technical solutions of the present application, the terms "first", "second", etc. are used to distinguish the same or similar items with basically the same function and role. Those skilled in the art can understand that the terms "first", "second", etc. do not limit the quantity and execution order, and the terms "first", "second", etc. also do not necessarily mean different.

[0025] In order to make the purposes, features, and advantages of the present application more obvious and easy to understand, the technical solutions protected by the present application will be described in detail below with specific embodiments and drawings. Obviously, the embodiments described below are only some of the embodiments of the present application, not all. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0026] Please refer to Figure 1 The method shown in the figure is an electromagnetic wave resistivity logging inversion method based on the quasi-Newton method, which comprises: S1. Collecting measured response data of a target formation by a while-drilling electromagnetic wave logging instrument, the target formation including isotropic and anisotropic formations; S2. Constructing a three-dimensional model of the target formation based on the formation scene corresponding to the measured response data, and obtaining formation parameters as inversion parameters to be inverted; S3. Selecting initial values for the inversion parameters to be inverted by a genetic algorithm, and iterating evolution through initialization of a population, obtaining of fitness values, selection of individuals, exchange of parent gene fragments, and mutation operations, and outputting m forward simulation values with the highest fitness as initial values for inversion when the iteration exceeds the set maximum iteration times; S4. Constructing a quasi-Newton inversion model containing a constraint term, updating the Jacobian matrix by the Broyden update method, 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; S5. Inputting the initial values for inversion into the improved quasi-Newton inversion model, and iteratively performing inversion calculation until a preset termination condition is met to obtain an inversion result.

[0027] As a refinement and extension of the above embodiment, in order to fully describe the specific implementation process in the embodiment, another electromagnetic wave resistivity logging while drilling inversion method based on the quasi-Newton method is provided, which comprises the following steps: S1. Collecting the measured response data of the target formation by the logging while drilling electromagnetic wave logging instrument, the target formation including isotropic formation and anisotropic formation; S2. Based on the formation scene corresponding to the measured response data, a three-dimensional model of the target formation is constructed, and the formation parameters are obtained as the to-be-inverted parameters; in step S2: The three-dimensional model is a three-layer TI medium formation model, including an isotropic formation model and an anisotropic formation model; As shown in Figure 2 In the isotropic formation model, the conductivities of the first layer and the third layer are 1 S·m -1 , and the conductivity of the second layer is 0.5 S·m -1 ; As shown in Figure 3 In the anisotropic formation model, the horizontal conductivity and the vertical conductivity of the first layer are 1 S·m -1 ; the horizontal conductivity of the second layer is 0.5 S·m -1 , and the vertical conductivity of the second layer is 0.2 S·m -1 ; the horizontal conductivity of the third layer is 2 S·m -1 , and the vertical conductivity of the third layer is 1 S·m -1 .

[0028] In step S2: The formation parameters include the conductivity of the isotropic formation or the horizontal conductivity and the vertical conductivity of the anisotropic formation, the distance of the instrument from the upper boundary, and the distance of the instrument from the lower boundary.

[0029] S3. Selecting initial values for the to-be-inverted parameters by a genetic algorithm, and iterating evolution through initialization of a population, acquisition of fitness values, selection of individuals, exchange of parent gene fragments, and mutation operations, and when the iteration exceeds the set maximum iteration number, outputting m forward simulation values with the highest fitness as initial values for inversion; In some embodiments, in step S3, the model parameters of the genetic algorithm are set as: The population size is 500, the maximum iteration number is 100, the crossover probability is 0.8, the mutation probability is 0.05, and the tournament size is 3.

[0030] Step S3 comprises: S31. Initializing the population, and the optimization problem is: ; Wherein,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.

[0031] S36. Each individual is evaluated using the following formula with probability. Perform mutation operation: ; wherein, denotes a random number obeying a continuous uniform distribution on the interval [0, 1].

[0032] S37. Repeating steps S31-S36, iterations are performed, and when the iterations exceed a set maximum iteration round, the m forward modeling values with the highest fitness at this time are output as initial values of the inversion.

[0033] It should be noted that, as Figure 4 shown, the basic flow of the genetic algorithm includes steps such as initialization of the population, fitness evaluation, selection operation, crossover operation, and mutation operation. At the beginning of the algorithm, an initial population consisting of several individuals is randomly generated, each individual representing a potential solution to the problem, usually represented by binary, real or symbolic encoding. Subsequently, the algorithm enters the iterative evolution process, and each generation of population generates a new generation of population through selection, crossover and mutation until the termination condition is met.

[0034] S4. Constructing a quasi-Newton inversion model containing a constraint term, updating the Jacobian matrix by the Broyden update method; 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; The step S4 of constructing a quasi-Newton inversion model containing a constraint term, updating the Jacobian matrix by the Broyden update method comprises: S41. Setting the constraint term as a regularization term, and the formula is: ; wherein, is the Jacobian matrix at the kth iteration, is the transpose matrix of , is the square of the regularization coefficient, I is the unit matrix, is the stratum parameter update vector at the kth iteration, is the observation response vector at the kth iteration; S42. Introducing a damping factor into the regularization formula, and obtaining the parameter update amount: ; S43. Let be the step length vector at the kth iteration, be the function change amount, and the quasi-Newton equation satisfies the following formula: ; S44. Updating the rank-one matrix: ;​ wherein, and are to-be-oriented vectors; S45. Substitute the rank-one matrix into the quasi-Newton equation to obtain the following formula: ; S46. According to the principle of minimum change, let , to obtain the equation: ; S47. Substitute the equation in step S46 into the rank-one matrix in step S44, and correct the Jacobian matrix in the direction to obtain: .

[0035] In step S4, the fixed damping factor in the quasi-Newton inversion model is replaced by an adaptive damping matrix, and the damping strength is adaptively adjusted according to different parameters, to obtain an improved quasi-Newton inversion model, which includes: S48. Define the adaptive damping matrix as : ; wherein, is the number of to-be-inverted parameters; The matrix element of ; S49. Replace the original damping coefficient with the adaptive damping matrix to obtain: .

[0036] It should be noted that the purpose of defining the damping matrix is that in the past inversion practice, it is found that the high-dimensional inversion problem of multi-parameter inversion such as logging is generally different in the deviation degree of each element in from the true value, especially the initial value and the first few iterations, and the effect of introducing a damping factor is often not ideal. In the calculated , only the elements with large absolute values will have a greater impact on the stability of the next iteration, so different damping effects need to be given to each element of according to their different sizes.

[0037] S5. Input the initial value of the inversion into the improved quasi-Newton inversion model, and iteratively perform inversion calculation until a preset termination condition is met, to obtain an inversion result.

[0038] In step S5: The inversion calculation aims to minimize the difference between the measured response data and the forward simulation value, and the objective function formula is: ; Wherein, is a regularization term, is a regularization coefficient, , is the horizontal conductivity, is the vertical conductivity, and are the distance of the upper boundary of the instrument distance and the distance of the lower boundary of the instrument distance respectively, is the measured response data of the logging-while-drilling instrument, is the forward simulation value.

[0039] In some embodiments, since the result of genetic algorithm is different each time, ten genetic algorithm optimization is performed on the obtained formation signal, ten approximate but different formation model initial values are obtained, and the ten initial value results are set as the initial values of the quasi-Newton method iteration inversion. The model parameter of the quasi-Newton algorithm is set as the initial damping coefficient 0.5, and the regularization parameter is 0.1. Finally, the inversion results of different formation models are compared.

[0040] An inversion initial value obtained by genetic algorithm is shown in Figure 5 and Figure 6 , Figure 5 is an isotropic initial value selection result diagram, wherein, Figure 5 (a) in (a) is the fitness evolution curve, Figure 5 (b) in (b) is the optimal parameter evolution curve; Figure 6 is an anisotropic initial value selection result diagram, wherein, Figure 6 (a) in (a) is the fitness evolution curve, Figure 6 (b) in (b) is the optimal parameter evolution curve; Table 1 is the root mean square error of the isotropic formation model and the anisotropic formation model and the actual value.

[0041] Table 1 Relative error of genetic algorithm initial value selection

[0042] Using the model initial value selected by the genetic algorithm, the resistivity and boundary distance are inverted under the isotropic formation and the anisotropic formation by using the traditional quasi-Newton method and the improved quasi-Newton method respectively, and the results are shown in Figure 7 , Figure 8 , Figure 9 , Figure 10 , Figure 11 , Figure 12 ; Figure 7 is a fixed damping isotropic inversion result diagram; Figure 8Fig. 2 is a schematic diagram of fixed damping anisotropy inversion results, wherein, Figure 8 (a) in Fig. 2 is a horizontal conductivity, Figure 8 (b) in Fig. 2 is a vertical conductivity; Figure 9 Fig. 3 is a schematic diagram of adaptive damping isotropy inversion results; Figure 10 Fig. 4 is a schematic diagram of adaptive damping anisotropy inversion results, Figure 10 (a) in Fig. 4 is a horizontal conductivity, Figure 10 (b) in Fig. 4 is a vertical conductivity; Figure 11 Fig. 5 is a schematic diagram of fixed damping boundary distance inversion results, wherein, Figure 11 (a) in Fig. 5 is an upper boundary distance, Figure 11 (b) in Fig. 5 is a lower boundary distance; Figure 12 Fig. 6 is a schematic diagram of adaptive damping boundary distance inversion results, wherein, Figure 12 (a) in Fig. 6 is an upper boundary distance, Figure 12 (b) in Fig. 6 is a lower boundary distance.

[0043] Meanwhile, the comparison of resistivity and boundary distance inversion results is shown in Table 2 and Table 3: Table 2 Isotropy inversion results

[0044] Table 3 Anisotropy inversion results

[0045] 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 balances the contradiction between convergence speed and stability in multi-parameter inversion, and improves the accuracy of resistivity inversion and boundary distance inversion. The genetic algorithm is used for initial value selection of the logging while drilling inversion problem, and the adaptive global optimization of the genetic algorithm can quickly and accurately find the appropriate inversion initial value. Compared with the traditional quasi-Newton method, the quasi-Newton method with adaptive damping improves the accuracy of each parameter inversion, especially in anisotropic formation and boundary distance inversion. Compared with the fixed damping quasi-Newton method, the adaptive damping quasi-Newton method reduces the number of iterations and improves the inversion speed.

[0046] It should be understood that the size of the serial number of each step in the above embodiment does not mean the order of execution, and the execution order of each process should be determined according to its function and inherent logic, and should not constitute any limitation on the implementation process of the embodiment of the present application.

[0047] The foregoing description of the disclosed embodiments enables a person skilled in the art to make or use the application. Modifications of these embodiments will occur to persons of skill in the art, and that the appended claims are intended to cover all such modifications that do not depart from the true spirit and scope of the application. Therefore, the application is not limited to the embodiments shown but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method of electromagnetic wave resistivity logging while drilling inversion based on quasi-Newton method, characterized in that, The method comprises: S1. Collecting measured response data of a target formation by a logging-while-drilling electromagnetic wave logging instrument, the target formation comprising isotropic formations and anisotropic formations; S2. Constructing a three-dimensional model of the target formation based on a formation scene corresponding to the measured response data, and obtaining formation parameters as to-be-inverted parameters; S3. Selecting initial values of the to-be-inverted parameters by a genetic algorithm, and iteratively evolving by initializing a population, obtaining a fitness value, selecting individuals, exchanging gene fragments of parents, and mutation operation, and outputting m forward simulation values with the highest fitness as initial values of inversion when the iteration exceeds a set maximum iteration number; S4. Constructing a quasi-Newton inversion model containing a constraint term, updating a Jacobian matrix by a Broyden update method, replacing a fixed damping factor in the quasi-Newton inversion model with an adaptive damping matrix, and adaptively adjusting damping strength according to different parameters to obtain an improved quasi-Newton inversion model; S5. Inputting the initial values of inversion into the improved quasi-Newton inversion model, and iteratively performing inversion calculation until a preset termination condition is met to obtain an inversion result.

2. The quasi-Newton method based inversion method for electromagnetic wave resistivity logging while drilling according to claim 1, wherein, In step S2: The three-dimensional model is a three-layer TI medium formation model, comprising an isotropic formation model and an anisotropic formation model; The conductivity of the first and third layers in the isotropic formation model is 1 S-m -1 , and 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 quasi-Newton method based inversion method for electromagnetic wave resistivity logging while drilling according to claim 1, wherein, In step S2: The formation parameters comprise conductivity of the isotropic formation or horizontal conductivity and vertical conductivity of the anisotropic formation, distance of the instrument from an upper boundary, and distance of the instrument from a lower boundary.

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

5. The quasi-Newton method based inversion method for electromagnetic wave resistivity logging while drilling according to claim 1, wherein, Step S3 comprises: S31. Initializing the population, and the optimization problem is: ； wherein, min to minimize the operation, f(x) denotes an objective function of the optimization problem, x denotes a formation parameter vector, S denotes a parameter feasible region, is an n-dimensional real number space, where n is the number of formation parameters to be inverted, denotes a lower bound constraint value of the j th formation parameter, x j denotes the x th component of the formation parameter vector j u j denotes an upper bound constraint value of the j th formation parameter;​ S32. Uniformly and randomly sampling in the parameter space to obtain values generated by sampling: ； wherein, is the initial population size value, is the spatial dimension, i.e. the number of initial values to be determined; S33. In each generation, calculating a fitness value of each individual, wherein the fitness function is: ； S34. Select elite individuals into the mating pool based on fitness, for each position in the population randomly select individual indices; select the highest fitness value among them, repeat the selection until parents are selected, where the probability of each individual being selected is: ； wherein a ranking of individual fitnesses; S35. Randomly selecting a cut point, and exchanging gene fragments of parents to generate two offspring by the following formula: ； ； wherein, and are two offspring individuals, and are two parent individuals, c is a randomly selected crossover point position, L is the total length of the genes of the parent individuals; S36. Perform the probability of each individual by the following formula Perform the mutation operation: ； wherein, denotes a random number subject to a continuous uniform distribution on the interval [0, 1]; S37. Repeating steps S31-S36 for iteration, and outputting m forward simulation values with the highest fitness at this time as initial values of inversion when the iteration exceeds a set maximum iteration number.

6. The quasi-Newton method based inversion method for electromagnetic wave resistivity logging while drilling according to claim 1, wherein, In step S4, the quasi-Newton inversion model containing a constraint term is constructed, and the Jacobian matrix is updated by the Broyden update method, comprising: S41. Setting the constraint term as a regularization term, and the formula is: ； wherein is the Jacobian matrix at the kth iteration, is the transpose of is the square of the regularization coefficient, I is the identity matrix, is the formation parameter update vector at the kth iteration, is the observed response vector at the kth iteration;​ S42. Introducing a damping factor in the regularization formula , resulting in a parameter update ； S43. Let is the step vector at the kth iteration, is the function variation, the quasi-Newton equation satisfies the following formula: ； S44. Updating the rank-one matrix: ； wherein and are pending vectors; S45. Substituting the rank-one matrix into the quasi-Newton equation to obtain the following formula: ； S46. According to the principle of minimum change, let resulting in the equation: ； S47. Substitute the equation in step S46 into the rank-one matrix in step S44, to get the direction correction Jacobian matrix, to get: 。 7. The quasi-Newton method based inversion method for electromagnetic wave resistivity logging while drilling according to claim 6, wherein, In step S4, the fixed damping factor in the quasi-Newton inversion model is replaced with an adaptive damping matrix, and damping strength is adaptively adjusted according to different parameters to obtain an improved quasi-Newton inversion model, comprising: S48. Define the adaptive damping matrix as : ； wherein, is the number of parameters to be inverted; The matrix elements of the matrix are: ； S49. Replacing the original damping coefficient with the adaptive damping matrix to obtain: 。 8. The quasi-Newton method based inversion method for electromagnetic wave resistivity logging while drilling according to claim 1, wherein, In step S5: The inversion calculation aims to minimize differences between the measured response data and the forward simulation values, and the objective function formula is: ； wherein, is a regularization term, is a regularization coefficient, , is a horizontal conductivity, is a vertical conductivity, and are the distance of the instrument from the upper boundary and the distance of the instrument from the lower boundary, respectively, is the measured response data of the logging-while-drilling instrument, is the forward modeling value.

Images