A data processing method for a while-drilling electromagnetic wave logging instrument
Patent Information
- Application Number
- CN202611099458.6
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-23
- Publication Date
- 2026-10-23
AI Technical Summary
此时有限差分法需要大量重复正演计算，导致计算时间急剧增加，难以满足实时解释与地质导向需求
[0042]针对多发射多接收随钻电磁波测井仪器建立可微正演求导框架，实现正演与求导一体化计算。利用自动微分技术自动获得梯度、雅可比矩阵及海森矩阵，无需采用有限差分扰动方法，大幅减少正演计算次数。有效消除有限差分步长选择带来的截断误差和舍入误差，提高导数计算精度。支持一阶导数、二阶导数及海森向量积的统一求取，适用于Gauss-Newton、Levenberg-Marquardt、Trust Region Reflective等多种梯度优化算法。特别适用于多发射、多接收、多频率、多分量电磁波测井仪器形成的大规模观测数据场景，可显著提高实时反演效率。
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Abstract
Description
Technical Field
[0001] This invention relates to the field of logging while drilling (LWD), and specifically to a data processing method for LWD instruments. Background Technology
[0002] As oil and gas exploration and development gradually expands into deeper, ultra-deeper formations and areas with complex geological structures, electromagnetic logging while drilling (EMWL) technology has attracted widespread attention due to its advanced detection capabilities. EMWL instruments transmit electromagnetic fields and receive formation response signals to detect and identify electrical parameters of the formation ahead of and around the wellhead.
[0003] In recent years, to improve detection range, vertical resolution, and geological guidance capabilities, new-generation electromagnetic logging-while-drilling (EMWWD) instruments have gradually adopted multi-transmitter antenna, multi-receiver antenna, multi-frequency, and multi-component joint measurement modes. Compared to traditional single-transmitter, single-receiver EMWD systems, the scale of observation data from EMWD instruments increases exponentially. For example, when an instrument simultaneously includes multiple transmitting antennas, multiple receiving antennas, and multiple operating frequencies, it can generate hundreds to thousands of observations, resulting in a significant increase in the data dimensionality during the inversion process.
[0004] Currently, electromagnetic inversion typically employs gradient optimization algorithms such as the Gauss-Newton method, the Levenberg-Marquardt method, the Trust Region Reflective method, and quasi-Newton methods. All of these algorithms require calculating the first derivative of the objective function with respect to the model parameters, the Jacobian matrix, and the Hessian matrix.
[0005] In existing technologies, derivative calculations primarily employ the finite difference method. The basic idea is to perturb each model parameter individually and calculate the response difference before and after the parameter changes by repeatedly calling the forward modeling procedure, thereby approximating the gradient information. For a model containing N inversion parameters, calculating the Jacobian matrix using the finite difference method typically requires N+1 forward modeling calculations; calculating the Hessian matrix requires O(N²) forward modeling calculations.
[0006] For multi-transmitter, multi-receiver electromagnetic logging instruments, inversion parameters typically include horizontal conductivity, vertical conductivity, layer thickness, interface location, and structural parameters of multiple formations, with the number of parameters reaching dozens or even hundreds. In this case, the finite difference method requires a large number of repeated forward modeling calculations, leading to a sharp increase in computation time and making it difficult to meet the needs of real-time interpretation and geological guidance.
[0007] Furthermore, the finite difference method also suffers from problems such as difficulty in selecting the perturbation step size, large numerical errors, limited gradient accuracy, and poor parallel scalability. When the parameter scales differ significantly, the finite difference method is prone to truncation and rounding errors, which affect the stability and accuracy of the inversion results.
[0008] Therefore, there is an urgent need for an automatic method to obtain the first and second derivatives, which can directly and automatically acquire high-precision derivative information from the electromagnetic forward model, in order to improve the efficiency of inversion calculation of electromagnetic logging data while drilling. Summary of the Invention
[0009] The purpose of this invention is to address the above-mentioned shortcomings by proposing a data processing method for drilling electromagnetic wave logging instruments. This method involves constructing a differentiable forward modeling calculation model for drilling electromagnetic waves, introducing automatic differentiation technology into the inversion process of drilling electromagnetic logging, and realizing the automatic construction and rapid calculation of the objective function gradient, Jacobian matrix, and Hessian matrix.
[0010] The present invention specifically adopts the following technical solution:
[0011] A data processing method for logging-while-drilling (LWD) electromagnetic wave instruments includes the following steps:
[0012] S1. Based on the structural parameters of the drilling electromagnetic wave logging instrument, the transmission and reception configuration, and the formation electrical parameters, a multi-transmission and multi-reception drilling electromagnetic wave logging forward model is established. The multi-transmission and multi-reception drilling electromagnetic wave logging forward model includes the excitation of the transmission source, electromagnetic field propagation, layered medium reflection and transmission, electromagnetic field reception response, and measurement data extraction, which are used to describe the nonlinear mapping relationship between formation parameters and measurement response.
[0013] S2, differentiable processing of each calculation module in the forward modeling process, unifies the model parameters, propagation constant calculation, reflection coefficient recursive calculation, electromagnetic field response calculation and observation data extraction process into a differentiable calculation graph, so that the entire electromagnetic forward modeling process meets the automatic differentiation requirements;
[0014] S3 constructs the objective function by combining the measured data with the forward response, and uses the automatic differentiation mechanism to backpropagate the objective function to automatically obtain the first derivative information of the objective function with respect to each inversion parameter, i.e., the gradient of the objective function;
[0015] S4 utilizes the vector-Jacobi product and Jacobi-vector product calculation mechanisms in automatic differentiation to automatically construct the Jacobi matrix of the measurement response with respect to formation parameters, enabling rapid calculation of the sensitivity matrix under multiple parameters and multiple observations.
[0016] Preferably, in the process of constructing the multi-transmitter, multi-receiver electromagnetic wave logging forward model:
[0017] First, a layered geoelectric model is constructed, and the number of layers n is initialized, and the layer interface positions z are defined. i(i=1,...,n-1), set the layer resistivity ρ, define the well inclination angle α, and derive the generalized reflection coefficient of each layer based on the structure of the drilling electromagnetic wave instrument, setting the coil direction, transmit / receive distance, and operating frequency. Then, derive the propagation term and construct the forward modeling algorithm F.
[0018]
[0019] Where m includes geoelectric model parameters and instrument parameters; d is the instrument observation response; and F(·) is the electromagnetic forward modeling operator.
[0020] Preferred,
[0021] In S3, the calculation of the first derivative relies on the differentiable forward modeling procedure built from the differentiable processing of the computation module in the previous step. For all parameters m, the instrument observation response vector d is obtained through forward propagation. During the forward propagation process, the computation graph automatically records the dependencies between each computation node and the calculation process of intermediate variables. Subsequently, the output response is backpropagated using an automatic differentiation mechanism, and the gradient information of the response with respect to the model parameters is automatically calculated according to the chain rule.
[0022]
[0023] That is, the first-order partial derivatives of the instrument response with respect to each model parameter are obtained. For the (i)th model parameter, the corresponding first-order derivative is expressed as:
[0024]
[0025] It reflects the degree of influence of small changes in model parameters on the instrument response. By automatically differentiating all parameters at the same time, the first derivative information of all parameters can be obtained at one time, which provides a basis for subsequent Jacobian matrix construction and gradient optimization inversion.
[0026] Preferably, after implementing the differentiability of the calculation module, the Jacobian matrix of the instrument response with respect to the model parameters is further constructed. Let the length of the electromagnetic foresight logging instrument observation response vector d be M, and the parameters to be inverted be [m1, m2, …, m N If the length of the response is N, then the Jacobian matrix of the response with respect to the model parameters can be defined as:
[0027]
[0028] The automatic differentiation framework is used to record the computational graph structure in the forward modeling process. The derivative relationship between each computation node is automatically calculated through the chain rule, and the elements of the Jacobian matrix are automatically constructed using vector-Jacobi product or Jacobian-vector product.
[0029] Preferably, after obtaining the gradient of the objective function, the Hessian matrix is constructed using second-order automatic differentiation to obtain the second derivative information of the objective function with respect to the model parameters;
[0030] The first derivative of the instrument response with respect to the model parameters is:
[0031]
[0032] Further automatic differentiation of the gradient vector yields the Hessian matrix:
[0033]
[0034] Its specific form is as follows:
[0035]
[0036] By utilizing the second-order backpropagation mechanism within the automatic differentiation framework, the Hessian matrix and Hessian vector product information are automatically obtained, providing efficient and stable second-order optimization computational capabilities for large-scale electromagnetic logging inversion.
[0037] Preferably, a two-dimensional layered stratigraphic model is constructed for testing. The model contains two anisotropic strata. The parameters to be inverted include the horizontal conductivity of the first layer, the vertical conductivity of the first layer, the horizontal conductivity of the second layer, the vertical conductivity of the second layer, and the layer thickness parameter, totaling five parameters:
[0038]
[0039] Response calculations are performed using a multi-transmitter, multi-receiver electromagnetic logging-while-drilling (MWD) instrument. The instrument contains multiple transmitting coils, multiple receiving coils, and multiple operating frequencies, forming a (M)-dimensional observation response vector.
[0040] .
[0041] The present invention has the following beneficial effects:
[0042] A differentiable forward modeling framework is established for multi-transmitter, multi-receiver electromagnetic wave logging instruments, enabling integrated forward modeling and differentiation calculations. Automatic differentiation technology is used to automatically obtain gradients, Jacobian matrices, and Hessian matrices, eliminating the need for finite difference perturbation methods and significantly reducing the number of forward modeling calculations. Truncation and rounding errors caused by finite difference step size selection are effectively eliminated, improving derivative calculation accuracy. Unified calculation of first-order derivatives, second-order derivatives, and Hessian vector products is supported, applicable to various gradient optimization algorithms such as Gauss-Newton, Levenberg-Marquardt, and Trust Region Reflective. It is particularly suitable for large-scale observation data scenarios generated by multi-transmitter, multi-receiver, multi-frequency, and multi-component electromagnetic wave logging instruments, significantly improving real-time inversion efficiency. Attached Figure Description
[0043] Figure 1 A flowchart of a data processing method for logging-while-drilling (LWD) electromagnetic wave instruments;
[0044] Figure 2 This is a structural diagram of a differentiable forward modeling computation graph;
[0045] Figure 3 This is a flowchart of the automatic differentiation process. Detailed Implementation
[0046] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and specific examples:
[0047] like Figure 1 As shown, a data processing method for drilling electromagnetic logging instruments includes the following steps:
[0048] S1. Based on the structural parameters of the drilling electromagnetic wave logging instrument, the transmission and reception configuration, and the formation electrical parameters, a forward model for multi-transmitter multi-receiver drilling electromagnetic wave logging is established. The forward model for multi-transmitter multi-receiver drilling electromagnetic wave logging includes excitation from the transmission source, electromagnetic field propagation, reflection and transmission of the layered medium, electromagnetic field reception response, and measurement data extraction, which is used to describe the nonlinear mapping relationship between formation parameters and measurement response.
[0049] S2 performs differentiable processing on each calculation module in the forward modeling process, and unifies the calculation of model parameters, propagation constants, recursive calculation of reflection coefficients, electromagnetic field response calculation, and observation data extraction process into a differentiable calculation diagram, so that the entire electromagnetic forward modeling process meets the requirements of automatic differentiation.
[0050] S3 constructs the objective function from the measured data and the forward response, and uses the automatic differentiation mechanism to perform backpropagation calculation on the objective function to automatically obtain the first derivative information of the objective function with respect to each inversion parameter, i.e., the gradient of the objective function.
[0051] S4 utilizes the vector-Jacobi product and Jacobi-vector product calculation mechanisms in automatic differentiation to automatically construct the Jacobi matrix of the measurement response with respect to formation parameters, enabling rapid calculation of the sensitivity matrix under multiple parameters and multiple observations.
[0052] like Figure 2 As shown, the construction process of the multi-transmitter, multi-receiver electromagnetic wave logging forward model during drilling is as follows:
[0053] Construct a layered geoelectric model, initialize the number of layers n, and define the layer interface location z. i (i=1,...,n-1), set the layer resistivity ρ, define the well inclination angle α, and derive the generalized reflection coefficient of each layer based on the structure of the drilling electromagnetic wave instrument, setting the coil direction, transmit / receive distance, and operating frequency. Then, derive the propagation term and construct the forward modeling algorithm F.
[0054]
[0055] Where m contains geoelectric model parameters and instrument parameters; d is the instrument observation response vector; and F(·) is the electromagnetic forward modeling operator.
[0056] like Figure 3 As shown, the calculation of the first derivative depends on the differentiable forward modeling program constructed in the previous step by differentiating the computation module. For all parameters m, the instrument observation response d is obtained through forward propagation. During the forward propagation process, the computation graph automatically records the dependencies between each computation node and the calculation process of intermediate variables. Subsequently, the output response is backpropagated using an automatic differentiation mechanism, and the gradient information of the response with respect to the model parameters is automatically calculated according to the chain rule.
[0057]
[0058] That is, the first-order partial derivatives of the instrument response with respect to each model parameter are obtained. For the (i)th model parameter, its corresponding first-order derivative is expressed as:
[0059]
[0060] It reflects the degree of influence of small changes in model parameters on the instrument response. By automatically differentiating all parameters at the same time, the first derivative information of all parameters can be obtained at one time, which provides a basis for subsequent Jacobian matrix construction and gradient optimization inversion.
[0061] like Figure 3 As shown, after implementing the differentiability of the computation module, the Jacobian matrix of the instrument response with respect to the model parameters is further constructed. Let the length of the electromagnetic foresight logging instrument observation response vector d be M, and the parameters to be inverted be [m1, m2, ..., m]. NIf the length of the response is N, then the Jacobian matrix of the response with respect to the model parameters can be defined as:
[0062]
[0063] The automatic differentiation framework is used to record the computational graph structure in the forward modeling process. The derivative relationship between each computation node is automatically calculated through the chain rule. The elements of the Jacobian matrix are automatically constructed using the vector-Jacobian product (VJP) or the Jacobian-vector product (JVP).
[0064] Compared to traditional finite difference methods that require applying perturbations to each model parameter and repeatedly performing forward modeling calculations, this invention can obtain the complete Jacobian matrix without explicitly constructing a perturbation model, thereby significantly reducing the computational cost in large-scale inversion problems and improving the efficiency of sensitivity analysis and gradient optimization inversion.
[0065] like Figure 3 As shown, after obtaining the gradient of the objective function, the Hessian matrix is constructed using second-order automatic differentiation to obtain the second derivative information of the objective function with respect to the model parameters.
[0066] The first derivative of the instrument response with respect to the model parameters is:
[0067]
[0068] Further automatic differentiation of the gradient vector yields the Hessian matrix:
[0069]
[0070] Its specific form is as follows:
[0071]
[0072] By utilizing the second-order backpropagation mechanism within the automatic differentiation framework, the Hessian matrix and Hessian vector product information are automatically obtained, providing efficient and stable second-order optimization computational capabilities for large-scale electromagnetic logging inversion.
[0073] A two-dimensional layered stratigraphic model was constructed for testing. The model contains two anisotropic strata. The parameters to be inverted include the horizontal conductivity of the first layer, the vertical conductivity of the first layer, the horizontal conductivity of the second layer, the vertical conductivity of the second layer, and the layer thickness parameter, totaling five parameters:
[0074]
[0075] Response calculations are performed using a multi-transmitter, multi-receiver electromagnetic logging-while-drilling (MWD) instrument. The instrument contains multiple transmitting coils, multiple receiving coils, and multiple operating frequencies, forming a (M)-dimensional observation response vector.
[0076] .
[0077] The logging-while-drilling (LWD) instrument used in this invention, taking a combination of one transmitting segment and three receiving segments as an example, has two z-direction antennas, one x-direction antenna, and one y-direction antenna in each segment. The instrument operates at six frequencies. Using the real part of the z-axis component of one segment as the observation response, the length of the response vector is M = 24.
[0078] The Jacobian matrix and Hessian matrix are calculated using the finite difference method and the automatic differentiation method proposed in this invention, respectively.
[0079] For the finite difference method, the Jacobian matrix calculation process requires perturbing each model parameter sequentially. Assuming there are N=5 model parameters, this would require 5 × 24 = 120 forward modeling calculations. Automatic differentiation, on the other hand, only requires a single forward modeling calculation to obtain all Jacobian matrices through gradient backpropagation.
[0080] This example first constructs a two-layer geoelectric model with horizontal conductivity of 0.01 and 1 S / m, and vertical conductivity of 0.001 and 0.5 S / m. The interface is located at -5m. The calculation time for both is shown in Table 1. As can be seen, the method proposed in this invention can reduce the calculation time to 1 / 24.
[0081] Table 1
[0082] method Finite difference method Automatic Differentiation Time elapsed (s) 2.1505 0.08891
[0083] The time required to obtain the Hessian matrix is shown in Table 2, and the calculation time has been reduced to 1 / 128.
[0084] Table 2
[0085] method Finite difference method Automatic Differentiation Time elapsed (s) 12.7411 0.09899
[0086] Of course, the above description is not intended to limit the present invention, and the present invention is not limited to the examples given above. Any changes, modifications, additions or substitutions made by those skilled in the art within the scope of the present invention should also fall within the protection scope of the present invention.
Claims
1. A data processing method for drilling electromagnetic logging instruments, characterized in that, Includes the following steps: S1. Based on the structural parameters of the drilling electromagnetic wave logging instrument, the transmission and reception configuration, and the formation electrical parameters, a multi-transmission and multi-reception drilling electromagnetic wave logging forward model is established. The multi-transmission and multi-reception drilling electromagnetic wave logging forward model includes the excitation of the transmission source, electromagnetic field propagation, layered medium reflection and transmission, electromagnetic field reception response, and measurement data extraction, which are used to describe the nonlinear mapping relationship between formation parameters and measurement response. S2, differentiable processing of each calculation module in the forward modeling process, unifies the model parameters, propagation constant calculation, reflection coefficient recursive calculation, electromagnetic field response calculation and observation data extraction process into a differentiable calculation graph, so that the entire electromagnetic forward modeling process meets the automatic differentiation requirements; S3 constructs the objective function by combining the measured data with the forward response, and uses the automatic differentiation mechanism to backpropagate the objective function to automatically obtain the first derivative information of the objective function with respect to each inversion parameter, i.e., the gradient of the objective function; S4 utilizes the vector-Jacobi product and Jacobi-vector product calculation mechanisms in automatic differentiation to automatically construct the Jacobi matrix of the measurement response with respect to formation parameters, enabling rapid calculation of the sensitivity matrix under multiple parameters and multiple observations.
2. The data processing method for electromagnetic logging-while-drilling instruments as described in claim 1, characterized in that, In the process of constructing the forward model for multi-transmitter, multi-receiver electromagnetic wave logging while drilling: First, a layered geoelectric model is constructed, and the number of layers n is initialized, and the layer interface positions z are defined. i (i=1,...,n-1), set the layer resistivity ρ, define the well inclination angle α, and derive the generalized reflection coefficient of each layer based on the structure of the drilling electromagnetic wave instrument, setting the coil direction, transmit / receive distance, and operating frequency. Then, derive the propagation term and construct the forward modeling algorithm F. Where m contains geoelectric model parameters and instrument parameters; d is the instrument observation response vector; and F(·) is the electromagnetic forward modeling operator.
3. The data processing method for electromagnetic logging-while-drilling instruments as described in claim 1, characterized in that, In S3, the calculation of the first derivative relies on the differentiable forward modeling procedure built from the differentiable processing of the computation module in the previous step. For all parameters m, the instrument observation response vector d is obtained through forward propagation. During the forward propagation process, the computation graph automatically records the dependencies between each computation node and the calculation process of intermediate variables. Subsequently, the output response is backpropagated using an automatic differentiation mechanism, and the gradient information of the response with respect to the model parameters is automatically calculated according to the chain rule. That is, the first-order partial derivatives of the instrument response with respect to each model parameter are obtained. For the (i)th model parameter, the corresponding first-order derivative is expressed as: It reflects the degree of influence of small changes in model parameters on the instrument response. By automatically differentiating all parameters at the same time, the first derivative information of all parameters can be obtained at one time, which provides a basis for subsequent Jacobian matrix construction and gradient optimization inversion.
4. The data processing method for electromagnetic logging-while-drilling instruments as described in claim 1, characterized in that, After implementing the differentiability of the computation module, the Jacobian matrix of the instrument response with respect to the model parameters is further constructed. Let the length of the electromagnetic foresight logging instrument observation response vector d be M, and the parameters to be inverted be [m1, m2, …, m]. N If the length of the response is N, then the Jacobian matrix of the response with respect to the model parameters can be defined as: The automatic differentiation framework is used to record the computational graph structure in the forward modeling process. The derivative relationship between each computation node is automatically calculated through the chain rule, and the elements of the Jacobian matrix are automatically constructed using vector-Jacobi product or Jacobian-vector product.
5. The data processing method for electromagnetic logging-while-drilling instruments as described in claim 1, characterized in that, After obtaining the gradient of the objective function, the Hessian matrix is constructed using second-order automatic differentiation to obtain the second derivative information of the objective function with respect to the model parameters; The first derivative of the instrument response with respect to the model parameters is: Further automatic differentiation of the gradient vector yields the Hessian matrix: Its specific form is as follows: By utilizing the second-order backpropagation mechanism within the automatic differentiation framework, the Hessian matrix and Hessian vector product information are automatically obtained, providing efficient and stable second-order optimization computational capabilities for large-scale electromagnetic logging inversion.
6. The data processing method for electromagnetic logging-while-drilling instruments as described in claim 1, characterized in that, A two-dimensional layered stratigraphic model was constructed for testing. The model contains two anisotropic strata. The parameters to be inverted include the horizontal conductivity of the first layer, the vertical conductivity of the first layer, the horizontal conductivity of the second layer, the vertical conductivity of the second layer, and the layer thickness parameter, totaling five parameters: Response calculations are performed using a multi-transmitter, multi-receiver electromagnetic logging-while-drilling (MWD) instrument. The instrument contains multiple transmitting coils, multiple receiving coils, and multiple operating frequencies, forming a (M)-dimensional observation response vector. 。