Multi-point joint inversion method of sliding window based on while-drilling azimuthal electromagnetic wave logging

Abstract

The application discloses a method for multi-point joint inversion of a sliding window-based azimuthal electromagnetic wave logging while drilling. The method constructs a sliding window, combines logging response data of a current depth point and a plurality of previous sampling points into an extended response matrix, performs multi-point joint inversion, and introduces a stratum spatial continuity constraint. In each iteration, a dynamic weight is adaptively assigned according to the residual size between the forward response of each sampling point in the window and the measured data; the quasi-Newton method and the Broyden rank-one update strategy are used to approximately update the Jacobian matrix, thereby reducing the calculation burden. The application effectively suppresses random noise through multi-point joint inversion, significantly reduces boundary distance inversion error, overcomes convergence difficulties when the initial value is poor through a dynamic weighting mechanism, prevents the inversion from falling into a local extremum, and simultaneously considers the calculation efficiency, thereby meeting the real-time requirement of logging while drilling and providing high-precision and high-reliability inversion results for geosteering.

Description

Technical Field

[0001] This invention belongs to the field of geophysical logging technology, specifically relating to an inversion method for azimuth electromagnetic wave logging while drilling, and in particular a multi-point joint inversion method for azimuth electromagnetic wave logging while drilling based on a sliding window. Background Technology

[0002] Azimuth-while-drilling (AWD) logging is one of the key measurement-while-drilling (MSW) technologies in the exploration and development of modern oil, gas, and unconventional oil and gas resources. This technology acquires the formation's response to electromagnetic fields in real time during drilling, and combines this with inversion algorithms to calculate the formation's true electrical parameters (such as horizontal conductivity, vertical conductivity, and the distance from the instrument to the formation boundary), providing crucial information for geological steering and reservoir evaluation. As exploration and development advances into complex areas such as deep earth, deep water, unconventional environments, old oilfields, and new energy sources, higher demands are placed on the performance of MWD technology. Among these, the efficiency and accuracy of inversion techniques directly determine the accuracy of geological steering and the safety of drilling.

[0003] Logging-while-drilling (LoWWL) inversion technology refers to the key technology that, during the drilling process, uses electromagnetic field signals acquired in real time by LoWWL instruments to deduce the true formation property parameters through mathematical and physical models and optimization algorithms. This technology is a crucial link in realizing the value of LoWWL and is directly related to the accuracy of geological steering. How to robustly, quickly, and accurately reconstruct the formation electrical structure from limited measurement signals is one of the core bottlenecks restricting the intelligent and real-time application of this technology. The increasing information demands of exploration work have led to the gradual emergence of traditional inversion algorithms facing the problem of low inversion efficiency, making it difficult to simultaneously meet the dual requirements of inversion speed and accuracy.

[0004] Currently, the inversion methods commonly used in the industry are mainly divided into two categories: single-point independent inversion and fixed sliding window multi-point joint inversion.

[0005] Single-point independent inversion independently derives formation model parameters for a given point using only a set of well log response data acquired at the current depth. While this method is direct and fast-responding, its inherent drawbacks include extremely limited formation information contained in single-point data and extreme sensitivity to measurement noise and wellbore environmental changes. In complex wellbore conditions or when the data is noisy, the inversion results are prone to random fluctuations, leading to inaccurate identification of formation parameters (especially interface locations) and severely impacting the reliability of geological steering decisions.

[0006] To overcome the limitations of single-point inversion, the industry has begun to introduce a sliding window multi-point joint inversion framework. This framework utilizes well logging data from the current depth point and multiple preceding sampling points for joint inversion, leveraging the spatial continuity of the formation. However, existing multi-point inversion schemes still face unresolved technical challenges in practical applications: within the sliding window, each sampling point is typically assigned the same weight (i.e., uniform weighting). When abrupt changes in geological conditions or poor initial value selection lead to significant discrepancies between the forward response and the measured data residuals of some sampling points within the window, the uniform weighting mechanism treats all sampling points equally. This results in those sampling points with poor fitting and large residuals contributing strong, erroneously oriented gradients to the objective function. This mechanism reinforces misfitting, causing the inversion update direction to be dominated by noise or anomalous residual points. This can lead to iterations getting trapped in local extrema or slow convergence, or even "step-like" jumps, and in severe cases, the inversion results may become completely invalid. Summary of the Invention

[0007] This invention aims to overcome the shortcomings of existing drilling azimuth electromagnetic wave logging inversion methods, such as the susceptibility of single-point inversion to noise interference and the susceptibility of traditional multi-point uniform weighted inversion to being misled by abnormal residual points. It provides a sliding window-based multi-point joint inversion method for drilling azimuth electromagnetic wave logging. The core of this method lies in the introduction of a dynamic weighting mechanism based on local fit goodness, breaking the limitations of "uniform weighting" in traditional multi-point inversion and significantly improving the robustness of the algorithm under complex formations and poor initial conditions. Combining the adaptive damped quasi-Newton method and the Broyden rank-one update strategy, this method significantly improves the accuracy of formation conductivity and boundary distance inversion while effectively overcoming the computational burden brought by multi-point data, thus balancing the stability and real-time performance of the inversion.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] A multi-point joint inversion method for azimuth electromagnetic wave logging while drilling based on a sliding window includes the following steps:

[0010] Step 1: Acquire the logging response data collected by the drilling azimuth electromagnetic logging instrument and construct a data structure of size [size missing]. The sliding window combines the logging response data of the current depth point and its preceding multiple sampling points into an extended response matrix. .

[0011] Step 2: Construct the initial stratigraphic model parameter vector based on prior stratigraphic information. The formation model parameters include the horizontal electrical conductivity of each layer. Vertical conductivity and the distance from the instrument to the upper and lower boundaries , .

[0012] Step 3: Enter the iterative inversion process, in the current formation model parameter vector Below, the forward response of each sampling point within the calculation window is calculated. And calculate the residual between the measured response and the forward response at each sampling point.

[0013] Step 4: Adaptively assign dynamic weights to each sampling point within the window based on the magnitude of the residual. The dynamic weights are negatively correlated with the residuals, and the dynamic weights decrease non-linearly and monotonically as the residuals increase.

[0014] Step 5: Utilize the dynamic weights Construct a weighted objective function and solve for the model parameter update amount. This is used to update the formation model parameter vector.

[0015] Step 6: Determine whether the iteration termination condition is met. If it is met, output the current formation model parameter vector as the inversion result; otherwise, return to step 3 to continue the iteration.

[0016] Furthermore, in step 4, dynamic weights are assigned. The specific method is as follows:

[0017] First, calculate the... L2 norm of the residual vector at each sampling point: .

[0018] Then, the residual norm of all sampling points within the window is normalized to obtain the normalized fitting error. .

[0019] Finally, the normalized fitting error is expressed using a negative exponential function. The mapping yields the dynamic weights assigned to each sampling point. The sum of all weights is 1.

[0020] Furthermore, in step 1, for the current depth point index... The actual size of the sliding window Determined adaptively based on rules.

[0021] when hour, That is, to utilize all existing sampling points.

[0022] when hour, That is, using the current point and its preceding points One sampling point.

[0023] Furthermore, the weighted objective function in step 5 is: The first term is the dynamically weighted data fitting term, and the second term is the Tikhonov regularization term. This is the regularization parameter.

[0024] Furthermore, in step 5, the model parameter update amount is calculated. The formula is: ,in, For Jacobian matrices, For adaptive damping matrix, For the residual vector, It is an identity matrix.

[0025] Furthermore, the adaptive damping matrix It is a diagonal matrix, and its diagonal elements The calculation formula is: ,in, The initial damping coefficient, It is the first The absolute change of each parameter It is the first The values ​​of the parameters.

[0026] Furthermore, the logging response data in step 1 includes at least the following signal combination: conventional conductivity signal. azimuth conductivity signal Geological signal amplitude ratio Phase difference The amplitude ratio of anisotropic signals Phase difference .

[0027] Furthermore, the iteration termination conditions in step 6 include: the change in the objective function is less than a preset threshold, the parameter update is less than a preset threshold, or the maximum number of iterations is reached.

[0028] Furthermore, in steps 3 and 5, the Broyden rank-one update strategy from the quasi-Newton method is used to approximately update the Jacobian matrix. .

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] 1. Improve inversion stability and anti-interference capability: By using a sliding window for multi-point joint inversion and introducing stratigraphic spatial continuity constraints, the influence of random noise on the inversion results is effectively suppressed, and the boundary distance inversion error is reduced by more than 60%.

[0031] 2. Overcoming convergence difficulties when initial values ​​are poor: A dynamic weighting strategy based on local goodness of fit is adopted. In each iteration, the weights are adaptively allocated according to the fitting residuals of each sampling point to suppress the bad guidance of abnormal residuals on the parameter update direction, so that the algorithm can still converge quickly when the initial values ​​deviate significantly from the true values.

[0032] 3. Considering computational efficiency: The Jacobian matrix is ​​updated approximately using the Broyden rank-one update strategy, avoiding the need to recalculate the sensitivity matrix in each iteration, which greatly reduces the computational burden caused by multi-point inversion and meets the real-time requirements of logging while drilling.

[0033] 4. Improved boundary identification accuracy: Multi-point joint inversion significantly reduces the inversion error of stratigraphic interface location, and the inversion profile is smoother and more continuous, providing a more reliable decision-making basis for geological guidance. Attached Figure Description

[0034] Figure 1 : Flowchart of the method described in this invention.

[0035] Figure 2 : A three-layer stratigraphic model diagram of this invention.

[0036] Figure 3 : A five-layer stratigraphic model diagram of this invention.

[0037] Figure 4 The conductivity inversion results of a single sampling point in this invention.

[0038] Figure 5 The results of the formation conductivity inversion at multiple sampling points in this invention.

[0039] Figure 6 The inversion results of the stratigraphic boundary distance at a single sampling point in this invention.

[0040] Figure 7 The inversion results of the stratigraphic boundary distance at multiple sampling points in this invention.

[0041] Figure 8 The results of the comparison between adaptive weighting and uniform weighting of horizontal and vertical conductivity in this invention.

[0042] Figure 9 The results of the comparison between adaptive weight and uniform weight of the distance from the instrument to the upper and lower boundaries in this invention.

[0043] Figure 10 The conductivity inversion results of the five-layer stratigraphic model of this invention.

[0044] Figure 11 The boundary distance inversion results of the five-layer stratigraphic model of this invention. Detailed Implementation

[0045] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the embodiments and specific features in the embodiments are detailed descriptions of the technical solution of the present application, rather than limitations thereof. In the absence of conflict, the embodiments and technical features in the embodiments can be combined with each other.

[0046] This invention provides a multi-point joint inversion method for azimuth electromagnetic wave logging based on a sliding window. The sliding window of this method adopts a local fitting weighting strategy, constructing an extended response matrix by combining the logging response data of the current depth point and its preceding multiple sampling points. This introduces a spatial continuity constraint of formation parameters along the well trajectory. In each iteration of the inversion process, the residual between the forward response and the measured data of each sampling point within the window is calculated. The weight is adaptively assigned to each sampling point according to the magnitude of the residual. The fitting term with a smaller residual is given a larger weight to enhance the guiding role of data points with better fitting quality in the objective function; the fitting term with a larger residual is given a smaller weight to suppress the interference of its erroneous gradient contribution on the inversion update direction.

[0047] like Figure 1 As shown, this invention presents a multi-point joint inversion method for azimuth electromagnetic wave logging based on a sliding window. First, an initial iterative formation model is constructed. Then, a quasi-Newton inversion method is used for iterative calculations. The Jacobian matrix is ​​updated using the Broyden update method to avoid redundant calculations. Finally, the data within the sliding window is used for inversion. The specific steps are as follows:

[0048] 1. Prepare logging data: Acquire the raw response signals collected by the azimuth electromagnetic logging instrument while drilling, and select conventional conductivity signals that are sensitive to formation parameters from them. azimuth conductivity signal Geological signal amplitude ratio Phase difference The amplitude ratio of anisotropic signals Phase difference This generates measured response data for inversion.

[0049] Meanwhile, following the multi-point joint inversion strategy, the preset size is... For a sliding window at the current depth point i, the actual window size is determined according to the window adaptation rule. .

[0050] The response data of the current depth point and its multiple preceding sampling points are combined into an extended response matrix. .

[0051] 2. Constructing the initial formation model: Based on prior formation information (such as adjacent well data and regional geological knowledge), set the parameter vector of the initial formation model. Including the horizontal conductivity of each layer Vertical conductivity and the distance from the instrument to the upper and lower boundaries , .

[0052] 3. Calculate the initial Jacobian matrix: with the current model parameters Next, calculate the forward response. The partial derivatives with respect to the model parameters yield the Jacobian matrix. For multi-point joint inversion, the Jacobian matrix is ​​expanded into Jacobian submatrices for each sampling point.

[0053] 4. Calculate the objective function: Calculate the weighted residuals between the current forward response and the measured data, and construct an objective function that includes dynamic weights. The dynamic weights are adaptively allocated based on the local fitting residuals of each sampling point within the window (smaller residuals have higher weights, and larger residuals have lower weights), and a Tikhonov regularization term is added to suppress ill-conditioned phenomena.

[0054] 5. Determine if the iteration termination condition is met: If the change in the objective function is less than the preset threshold, the parameter update is less than the preset threshold, or the maximum number of iterations is reached, then terminate the iteration, proceed to step 6, and output the inversion result; otherwise, proceed to step 7.

[0055] 6. Output inversion results: Output the current formation model parameter vector. The final inversion results include horizontal conductivity, vertical conductivity, and boundary distance curves at each depth point. These results can be used for geological steering and reservoir evaluation.

[0056] 7. Update the Jacobian matrix using the quasi-Newton method: Employ the Broyden rank-one update formula from the quasi-Newton method, using the Jacobian matrix from the previous iteration. Approximate calculation of the Jacobian matrix for the next iteration This update strategy avoids recalculating the exact Jacobian matrix in each iteration, significantly reducing the computational cost of multi-point inversion and improving the inversion speed.

[0057] 8. Update formation parameters: Solve for parameter update amounts using the damped quasi-Newton method. Introducing an adaptive damping matrix This is used to control the iteration step size and direction, preventing divergence or oscillation. The parameter update formula is: Then update the formation parameters: After updating, return to step 4, recalculate the objective function, and continue to the next iteration.

[0058] In this embodiment:

[0059] 1. Selection of formation parameter sensitive signals

[0060] Since the combination of signals uploaded to the surface during logging while drilling is limited, it is necessary to select a combination of signals that are sensitive to formation parameters and representative, as the data source for compressed uploading, to provide input for subsequent inversion algorithms. The definitions of each signal are as follows.

[0061] Conventional conductivity signal definition: , It is the well inclination angle.

[0062] Azimuth conductivity signal definition: , It is the well inclination angle.

[0063] Geological signal amplitude ratio Phase difference : , .

[0064] amplitude ratio of anisotropic signals Phase difference definition: , .

[0065] The above signal has nine eigenvalues ​​of voltage components, which are represented by a component matrix. express: In the formula, Dummy unit The instrument's operating angular frequency. For the formation magnetic permeability, For the area of ​​the receiving coil, These are the nine magnetic field components that were measured.

[0066] 2. Constructing a stratigraphic model

[0067] Establish as Figure 2 The three-layer stratigraphic model shown (all in TI medium) and Figure 3 The five-layer formation model is shown in Table 1. The parameters for the three-layer model are shown in Table 2, and the parameters for the five-layer model are shown in Table 2. The instrument drills downwards at a well inclination angle of 60°. The performance of the local fitting optimization dynamic weighting strategy for inverting conductivity and boundary distance is evaluated using the two formation models described above.

[0068] Table 1. Parameters of the Three Stratigraphic Layers

[0069]

[0070] Table 2. Parameters of Five Stratigraphic Layers

[0071]

[0072] 3. Quasi-Newton method

[0073] The inversion of logging-while-drilling data is essentially an optimization process. By continuously adjusting the parameter combination of the formation model, the difference between the theoretical logging response calculated by forward modeling and the actual logging data is minimized. This difference is usually defined as the objective function. ,in, For formation parameter vectors, , For horizontal conductivity, Vertical conductivity, and These represent the distances from the instrument to the upper and lower boundaries, respectively. This represents the response value of the logging-while-drilling instrument. These are the instrument's forward simulation values. Let be the objective function. The core of the inversion is to minimize the measured data. Compared with forward simulation values The differences.

[0074] In electromagnetic logging-while-drilling inversion, due to the large number of parameters to be inverted and the potential strong correlations between them, when the Jacobian matrix exhibits singularity or near-singularity, the unregularized least-squares solution amplifies data noise, leading to oscillations in the inverted formation parameters and inaccurate results. Furthermore, underdeterminism can result in infinitely many solutions, making it impossible to determine the true model. To address these issues, a constraint term (regularization term) is typically added to the objective function, transforming the original ill-conditioned problem into a well-conditioned optimization problem. This allows the algorithm to strike a balance between data fitting and the reasonableness of the solution, suppressing noise interference, eliminating singularities, and ultimately outputting a unique, stable, and reliable solution.

[0075] Add regularized target function: In the formula, the first term Represents the data fitting term, and represents the inversion and forward response. Compared with actual well logging data The difference between them, the second item For regularization terms, This is the regularization parameter.

[0076] Due to the forward function It is usually non-linear, making direct optimization difficult. Therefore, at the iteration point... For nonlinear functions Performing a first-order Taylor expansion and ignoring the second-order derivative terms, we obtain: In the formula, It is the Jacobian matrix, representing the forward response. For formation parameters Sensitivity, These are the formation parameters at the k-th iteration.

[0077] make and after unfolding Substituting into the objective function, we get: .

[0078] The original question has now been transformed into a question about The linear least squares problem aims to find the increment. Make the objective function Minimum. For simplicity, let... get: In the formula, This is the residual vector for the current iteration, representing the deviation between the actual logging data and the data obtained from the forward modeling. Take the derivative and set it to zero: In the formula, This is the transpose of the Jacobian matrix.

[0079] Simplifying, we get: .

[0080] Although Tikhonov regularization optimizes ill-posed problems at the system level by adding a model norm penalty term to the objective function, it is still necessary to effectively control the step size and direction of each iteration in the local iteration to prevent divergence or oscillations caused by strong model nonlinearity or poor initial values. Therefore, a damping factor also needs to be introduced. The damping term is introduced to affect the speed of iterative convergence and the accuracy of inversion. Finally, the parameter update amount is obtained. : In the formula, It is the identity matrix. It is an adaptive damping matrix, and satisfies: , diagonal elements in the formula This indicates that for each parameter in the iteration The applied damping effect, Using the initial damping coefficient, the constructed exponential function ensures the non-negativity of the damping value, thus guaranteeing the positive definiteness of the matrix; simultaneously, it achieves the effect of the relative rate of change of the parameters. The smoothness. It is the first The absolute change of each parameter It is the first The values ​​of the parameters.

[0081] 4. Multi-sampling point inversion method

[0082] To address the issues of lack of spatial constraints and high ambiguity in single-point inversion, a multi-sampling-point sliding window joint inversion method is introduced. This method leverages the spatial continuity of formation parameters along the well trajectory, incorporating well logging response data from the current depth point and multiple preceding sampling points into a unified optimization window for joint inversion. Within a finite sliding window, the formation parameter model is jointly estimated by simultaneously fitting the observation data from all sampling points within the window. This method essentially introduces strong spatial regularization constraints, effectively suppressing random noise and utilizing more data to increase constraints on model parameters, thereby improving the stability and accuracy of the inversion, particularly enhancing the ability to identify formation interface locations and suppress noise.

[0083] Let the window size be Therefore, the response adopted at this time is the current point and the previous point. A total of points The response at each point has a dimension of [dimensional value]. The response within the window is shown in the following formula: In the formula, To simulate the response matrix of actual well logging, ~ Sampling points The conventional conductivity signal logging response, ~ These represent the azimuth conductivity signals, respectively. Conventional conductivity signal The amplitude ratio of geological signals Phase difference The amplitude ratio of anisotropic signals Phase difference The response. Thus, the signal changes from a single response point to a... The signal combination of each response point, through Each point is used to jointly invert a stratigraphic model.

[0084] When the window starting point is close to the logging start position, there may be insufficient effective data points within the window. In this case, inversion can be performed based on existing sampling points. Specifically, when the instrument just begins logging (i.e., the initial stage of the well trajectory) or when processing depth points close to the measurement start position, if data is extracted forward strictly according to the preset window size, it will be impossible to obtain enough effective historical sampling points to fill the entire window, resulting in insufficient effective data points within the window. To ensure the continuity and stability of the inversion, a smaller but information-complete response window is constructed based on the limited number of available historical sampling points at the current point (i.e., all data from the first point to the current point) for inversion. This achieves logging as it goes, without waiting for the accumulation of sufficient historical data. In the initial stage where data is limited, it fully utilizes all acquired logging response information, enabling the algorithm to adaptively handle any data boundary conditions caused by the start or end of logging or data transmission interruptions, thus improving the practicality and reliability of the method. The specific window size value is shown in the formula: In the formula, This is the index of the current sampling point. For the first The actual size of each window This is the preset window size. When there are insufficient available sampling points... At that time, utilize all historical points, that is The logging response at each point; when the available sampling points are greater than or equal to When using the current point and its preceding points... Each sampling point serves as the response to the sliding window. In determining the included... After expanding the data window to include all sampling points, the objective function for inversion also needs to be transformed from fitting single-point data to simultaneously fitting the observed data of all sampling points within the window. At this point, the objective function becomes: .

[0085] In the multi-point joint inversion framework, since the input data expands from the response of one sampling point to a response matrix containing multiple sampling points, the corresponding forward response within this window also needs to increase to a size comparable to the actual well logging response window. The Jacobian matrix becomes: .

[0086] As can be seen from the formula, if the original Jacobian matrix has a data size of... Then the size of the Jacobian matrix for multi-point inversion is The size of the Jacobian matrix increases with the size of the sliding window. Each additional point requires an additional residual in the corresponding Jacobian matrix, which increases the computational cost. The quasi-Newton method can utilize Broyden's rank-one update to update the Jacobian matrix of the next iteration using the previous Jacobian matrix. This requires only a small amount of computation to obtain the new Jacobian matrix, reducing the computational cost of inversion and improving the speed of inversion.

[0087] 5. In-window weight adaptive allocation strategy

[0088] Electromagnetic waves attenuate and disperse as they propagate through strata. Sampling points farther apart within a window experience responses influenced by more complex strata paths and surrounding rock effects. Therefore, in a multi-point sliding window joint inversion framework, the responses of different sampling points within the window differ, and the reliability of the information about the current strata model carried by these responses also varies. Especially when encountering complex geological models such as those with strong heterogeneous media and thin interlayered layers, genetic algorithms may suffer from poor initial value selection due to complex geological conditions and poor fitting. When the initial inversion model is poorly selected, uniform weighting treats all sampling points equally, including those where initial value deviations cause a significant mismatch between the current forward response and measured data. This weighting method reinforces misfitting, causing the inversion update direction to be dominated by noise or anomalous residual points, easily leading to iteration getting trapped in local extrema or slow convergence.

[0089] To address this issue, a dynamic weighted strategy for local fit optimization is introduced within the sliding window. The core idea of ​​this strategy is to adaptively assign a weight to each sampling point in each iteration based on the residual between the measured response and the current forward model response. This mechanism can evaluate the reliability of each point in real time based on the local fit goodness of the current iteration: assigning higher weights to points with smaller residuals allows them to play a greater role in parameter updates; reducing the weights of points with larger residuals suppresses their negative impact. This allows the algorithm to gradually focus on reliable data through iteration, even with poor initial values, thereby enhancing the reliability of the inversion, accelerating convergence, and improving the ability to escape local extrema.

[0090] The specific implementation steps of the dynamic weighted strategy based on local fitting optimization are as follows. In the... In the nth iteration, for the sliding window For each sampling point, calculate the L2 norm of its residual vector: , The smaller the value, the better the fit. To prevent a large residual at any point from dominating the entire weight distribution, the fitting error for all points within the window is normalized: In the formula, For a tiny value, it is usually taken as To avoid errors in denominator calculation caused by the same fitting effect for all points, Indicates the first [number]th ... j The fitting error (residual L2 norm) of each sampling point. After normalization, the point corresponding to the best fit within the window. The point with the worst fit corresponds to .

[0091] Normalize the fitting error This is mapped to an initial weight through a negative exponential function transformation. The smaller the fitting error, the larger the mapped value. For the initial weights Normalization is performed to obtain the final dynamic weights assigned to each sampling point. To ensure that the sum of all weights is 1, the expression is: , It is the initial weight of the normalized fitting error for the j-th sampling point. Therefore, when the residual... The smaller (closer to 0), the higher the weight. The larger the residual (approaching the maximum value); when the residual The larger (approaching 1), the higher the weight. The smaller it is (closer to the minimum value).

[0092] The calculated dynamic weights This is incorporated into the multi-point joint inversion objective function. After introducing dynamic weights, the objective function becomes: .

[0093] This locally fitted dynamic weighting strategy, in each iteration, can adjust the model based on the current parameters. The residuals within the calculated window are used to recalculate and reassign weights. Points with smaller residuals indicate that the current model fits the measurement point well, and the data is more reliable, so they are given greater weights. Points with larger residuals may be more affected by initial value bias or noise, so their weights are reduced. Its core advantage lies in the algorithm's ability to intelligently focus on reliable data based on real-time goodness of fit during iterations. This allows it to guide the search direction even when initial values ​​are poor, avoiding erroneous update paths caused by uniform weighting.

[0094] Verification of the results of the multi-point adaptive inversion method for azimuth electromagnetic wave logging based on sliding window described in this invention:

[0095] 1. Comparison of inversion results of the three-layer model

[0096] For the inversion of three isotropic and anisotropic strata, we first uniformly selected normal initial values ​​to compare single-point inversions. To eliminate randomness, each inversion was performed ten times. The model parameters of the quasi-Newton algorithm were set with an initial damping coefficient of 0.5, a regularization parameter of 0.1, and a sliding window size of 10. One inversion result is shown below. Figures 4-7 As shown in Table 3, the average percentage root mean square error of the inversion is as follows.

[0097] Table 3 Comparison of Single-Point Inversion and Multi-Point Inversion

[0098]

[0099] To compare the impact of local fitting dynamic weighting strategies and uniform strategies on the inversion results, a set of initial values ​​significantly deviating from the true model (all conductivity parameters were initially set to 0.01 S / m) was set to simulate poor initial guesses that might be encountered in inversion practice. Under this condition, inversion was performed using both uniform weighting and dynamic weighting strategies, and the results were compared. Figures 8-9 As shown.

[0100] 2. Five-layer model inversion results

[0101] To evaluate the imaging capability and practicality of the proposed multi-sampling-point adaptive damped quasi-Newton inversion method under more complex and realistic geological conditions, this section applies the method to a five-layer stratigraphic model. This model aims to simulate complex stratigraphic sequences encountered during actual drilling, containing multiple electrical interfaces and anisotropic layers. Compared to the basic three-layer model, the five-layer model has a significantly increased number of parameters to be inverted, a significantly larger inversion parameter space, and stronger nonlinearity, requiring the inversion of more stratigraphic parameters. Therefore, it places higher demands on the robustness and resolution of the inversion algorithm.

[0102] Meanwhile, to better compare the multi-point adaptive damping quasi-Newton method and the single-point adaptive damping quasi-Newton method, both methods were used to invert a five-layer stratigraphic model. By comparing the differences between the two inversion methods in terms of parameter reconstruction accuracy, result smoothness, and convergence stability, the advantages of multi-point inversion can be objectively evaluated. The inversion results are as follows: Figures 10-11 As shown.

[0103] 3. Analysis of Inversion Results

[0104] Inversion experiments based on three-layer and five-layer stratigraphic models show that the dynamic weighting strategy proposed in this invention effectively solves the convergence problem of traditional multi-point inversion when the initial values ​​are poor. Figure 8 and Figure 9As shown, when faced with large initial deviations, traditional uniform weighting cannot distinguish residual quality, leading to the inversion trajectory being misled by outliers and exhibiting significant oscillations. In contrast, this method intelligently suppresses the negative impact of high residual points through dynamic weight allocation based on residuals, guiding the algorithm to quickly revert to the true values. Furthermore, Table 3 data shows that compared to single-point inversion, multi-point joint inversion with a sliding window reduces the stratigraphic boundary distance inversion error by more than 60%, significantly improving the spatial resolution and smoothness of the inversion profile. This verifies the superiority of this method in suppressing noise and enhancing spatial continuity constraints. Moreover, applying multi-point inversion to a five-layer model verifies its applicability in multi-layer models.

[0105] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A multi-point joint inversion method for azimuth electromagnetic wave logging while drilling based on a sliding window, characterized in that, Includes the following steps: Step 1: Acquire the logging response data collected by the drilling azimuth electromagnetic logging instrument and construct a data structure of size [size missing]. The sliding window combines the logging response data of the current depth point and its preceding multiple sampling points into an extended response matrix. ; Step 2: Construct the initial stratigraphic model parameter vector based on prior stratigraphic information. The formation model parameters include the horizontal electrical conductivity of each layer. Vertical conductivity and the distance from the instrument to the upper and lower boundaries , ; Step 3: Enter the iterative inversion process, in the current formation model parameter vector Below, the forward response of each sampling point within the calculation window is calculated. And calculate the residual between the measured response and the forward response at each sampling point; Step 4: Adaptively assign dynamic weights to each sampling point within the window based on the magnitude of the residual. The dynamic weights are negatively correlated with the residuals, and the dynamic weights decrease non-linearly and monotonically as the residuals increase. Step 5: Utilize the dynamic weights Construct a weighted objective function and solve for the model parameter update amount. To update the formation model parameter vector; Step 6: Determine whether the iteration termination condition is met. If it is met, output the current formation model parameter vector as the inversion result; otherwise, return to step 3 to continue the iteration.

2. The multi-point joint inversion method for azimuth electromagnetic wave logging based on a sliding window as described in claim 1, characterized in that, In step 4, dynamic weights are assigned. The specific method is as follows: First, calculate the... L2 norm of the residual vector at each sampling point: ; Then, the residual norm of all sampling points within the window is normalized to obtain the normalized fitting error. ; Finally, the normalized fitting error is expressed using a negative exponential function. The mapping yields the dynamic weights assigned to each sampling point. The sum of all weights is 1, where, It is the initial weight of the normalized fitting error for the i-th sampling point. It is the initial weight of the normalized fitting error for the j-th sampling point. It is the size of the sliding window.

3. The multi-point joint inversion method for azimuth electromagnetic wave logging based on a sliding window as described in claim 1, characterized in that, In step 1, for the current depth point index The actual size of the sliding window Determined adaptively based on rules: when hour, That is, to utilize all existing sampling points; when hour, That is, using the current point and its preceding points One sampling point.

4. The multi-point joint inversion method for azimuth electromagnetic wave logging based on a sliding window as described in claim 1, characterized in that, The weighted objective function in step 5 is: The first term is the dynamically weighted data fitting term, and the second term is the Tikhonov regularization term. This is the regularization parameter.

5. The multi-point joint inversion method for azimuth electromagnetic wave logging based on a sliding window as described in claim 1, characterized in that, Step 5 involves solving for the model parameter update amount. The formula is: , in, For Jacobian matrices, For adaptive damping matrix, For the residual vector, It is an identity matrix.

6. The multi-point joint inversion method for azimuth electromagnetic wave logging based on a sliding window according to claim 5, characterized in that, The adaptive damping matrix It is a diagonal matrix, and its diagonal elements The calculation formula is: , in, The initial damping coefficient, It is the first The absolute change of each parameter It is the first The values ​​of the parameters.

7. The multi-point joint inversion method for azimuth electromagnetic wave logging based on a sliding window according to claim 1, characterized in that, The logging response data in step 1 includes at least the following signal combinations: conventional conductivity signal azimuth conductivity signal Geological signal amplitude ratio Phase difference The amplitude ratio of anisotropic signals Phase difference .

8. The multi-point joint inversion method for azimuth electromagnetic wave logging based on a sliding window according to claim 1, characterized in that, The iteration termination conditions in step 6 include: the change in the objective function is less than a preset threshold, the parameter update is less than a preset threshold, or the maximum number of iterations is reached.

9. The multi-point joint inversion method for azimuth electromagnetic wave logging based on a sliding window as described in claim 1, characterized in that, In steps 3 and 5, the Broyden rank-one update strategy from the quasi-Newton method is used to approximately update the Jacobian matrix. .

Images