While-drilling azimuth electromagnetic foresight far exploration prediction method based on QR-iTransform-KAN

Abstract

The invention relates to the technical field of while-drilling azimuth electromagnetic wave measurement, in particular to a while-drilling azimuth electromagnetic forward-looking far-exploration prediction method based on QR-iTransform-KAN, which comprises the following steps of: acquiring signal characteristics and corresponding geological parameters of a while-drilling azimuth electromagnetic logging instrument, and constructing a training set and a test set of the signal characteristics and the geological parameters; an iTransform-KAN model is constructed, and the training set is used to train the iTransform-KAN model; according to the iTransform-KAN model, a plurality of layers of perceptron in a feedforward network of the iTransform model are replaced by a KAN network. The problem that an existing method is insufficient in prediction precision is solved.

Description

Technical Field

[0001] This invention relates to the field of azimuth electromagnetic logging technology, and in particular to a azimuth electromagnetic forward-looking remote prediction method based on QR-iTransformer-KAN. Background Technology

[0002] Azimuth electromagnetic logging while drilling is one of the irreplaceable key technologies in oil exploration and development. It greatly improves the drilling rate of reservoirs in highly deviated and horizontal wells, providing strong support for oil and gas resource exploration and development.

[0003] While drilling azimuth electromagnetic logging often employs one-dimensional analytical methods, two-dimensional semi-analytical semi-numerical methods, and three-dimensional numerical methods to perform extensive and detailed numerical simulations of instrument antenna system parameter variations and logging responses in anisotropic media models with biaxial anisotropic and fully tensor anisotropic properties. However, numerical simulations struggle to integrate, fuse, and efficiently utilize unstructured logging data with real-time, multi-source, and heterogeneous characteristics, thus making it impossible to verify, compensate, and correct numerical models based on the aforementioned measurement data.

[0004] Shahriari MD et al. used drilling electromagnetic wave logging data and applied a deep neural network (DNN) to approximate Maxwell's equations to generate forward functions. They constructed a three-layer formation forward model using real logging data and then used a DNN for inversion to obtain the resistivity prediction value of the model. Sergey A et al. used deep learning methods to construct a drilling azimuth electromagnetic wave ultra-deep logging prediction model. They compared the predicted values ​​of the model with the actual resistivity values ​​of a seven-layer geological model, thus verifying the feasibility of deep learning methods in drilling geological steering prediction modeling. Zhu Rixiang et al. proposed a large closed-loop control strategy based on multi-disciplinary data fusion. They suggested fully utilizing drilling azimuth logging parameters to construct a formation-aware and controllable probabilistic model, thereby achieving autonomous detection of reservoir boundaries and intelligent drilling guidance. Zhu GY et al. constructed a three-layer formation forward model based on real drilling electromagnetic wave logging data. Considering the phase difference resistivity superposition noise during drilling electromagnetic wave logging, they verified the accuracy of the inversion interpretation model constructed using a DNN. Muzammil HR et al. used deep learning methods, combined with historical and real-time data from electromagnetic logging while drilling, to propose a complete workflow for deep learning model preparation and real-time data assimilation during electromagnetic logging while drilling, and used this model to simulate and predict reservoir boundary distances; however, the prediction accuracy of these methods needs further improvement. Summary of the Invention

[0005] To address the shortcomings of existing methods, this invention solves the problem of insufficient prediction accuracy in existing methods.

[0006] The technical solution adopted in this invention is: a method for predicting drilling azimuth using electromagnetic forward-looking telemetry based on QR-iTransformer-KAN, comprising the following steps: Step 1: Collect signal characteristics and corresponding geological parameters of the azimuth electromagnetic logging instrument while drilling, and construct training and test sets for the signal characteristics and geological parameters; As a preferred embodiment of the present invention, the drilling azimuth electromagnetic logging instrument is model AziExpress.

[0007] In a preferred embodiment of the present invention, the signal includes: a transmitting antenna signal, a receiving antenna signal, and a compensation signal.

[0008] In a preferred embodiment of the present invention, the signal characteristics include: the amplitude ratio and phase difference of different signals.

[0009] In a preferred embodiment of the present invention, the geological parameters include: formation resistivity.

[0010] Step 2: Construct the iTransformer-KAN model and train it using the training set. The iTransformer-KAN model replaces the multilayer perceptron in the feedforward network of the iTransformer model with a KAN network. As a preferred embodiment of the present invention, the iTransformer-KAN model includes: an embedding layer, a multi-head attention layer, a layer normalization layer, a KAN network, and a layer normalization layer; wherein the KAN network includes: a first KAN layer, an activation layer, a Dropout layer, and a second KAN layer.

[0011] In a preferred embodiment of the present invention, the quantile regression model is divided into prediction intervals at different confidence levels using the signal features of the test set and the corresponding geological parameters. The test set is input into the trained iTransformer-KAN model, and the predicted geological parameter values ​​are output. The predicted geological parameter values ​​are evaluated using the prediction intervals.

[0012] As a preferred embodiment of the present invention, the quantile regression model includes: Given a signal feature vector matrix X and a geological parameter vector matrix Y; Construct the first Regression model of quantiles ; Solving for the parameter vector at a specific quantile can be transformed into solving for the minimum loss function. ;in, This represents a parameter vector related to quantiles. This represents the difference between the actual value and the predicted value.

[0013] As a preferred embodiment of the present invention, the drilling azimuth electromagnetic forward-looking prediction system based on QR-iTransformer-KAN includes: a memory for storing instructions executable by a processor; and a processor for executing the instructions to implement the drilling azimuth electromagnetic forward-looking prediction method based on QR-iTransformer-KAN.

[0014] As a preferred embodiment of the present invention, a computer-readable medium storing computer program code implements a drilling azimuth electromagnetic forward-looking prediction method based on QR-iTransformer-KAN when executed by a processor.

[0015] The beneficial effects of this invention are: 1. This invention constructs an iTransformer-KAN model, which enhances the global dependence between various logging variables through an inverted Transformer structure, and utilizes the learnable activation function of the KAN network to enhance the fitting ability for nonlinear features such as resistivity abrupt changes. 2. Based on point prediction, quantile regression (QR) is introduced to establish a probability interval prediction model. By optimizing the quantile loss function, the change in interval width can be used to identify reservoir interfaces: the interval is expanded near the interface to cover uncertainty, and the interval is narrowed in homogeneous strata to improve certainty.

[0016] 3. The QR-iTransformer-KAN model of this invention achieves multi-dimensional and probabilistic analysis of drilling electromagnetic wave signals through the synergy of point prediction and interval prediction; the model shows good prediction accuracy and generalization ability under different well depths, well inclinations and formation complexities. Attached Figure Description

[0017] Figure 1 This is a flowchart of the drilling azimuth electromagnetic forward-looking remote prediction method based on QR-iTransformer-KAN of the present invention; Figure 2 This is a schematic diagram of the basic structure of a drilling azimuth electromagnetic logging instrument; Figure 3 This is a schematic diagram of the KAN network structure of the present invention; Figure 4 This is a schematic diagram of point prediction under the T1R1A / 400K condition; Figure 5 This is a schematic diagram of point prediction under the T1R1A / 2M condition; Figure 6 This is a schematic diagram of point prediction under the T1R1P / 400K condition; Figure 7This is a schematic diagram of point prediction under the T1R1P / 2M condition; Figure 8 This is a schematic diagram comparing point predictions from different models under the T1R1A / 400K condition; Figure 9 This is a schematic diagram comparing point predictions from different models under the T1R1A / 2M condition; Figure 10 This is a schematic diagram comparing point predictions from different models under the T1R1P / 400K condition; Figure 11 This is a schematic diagram comparing point predictions from different models under the T1R1P / 2M condition; Figure 12 This is a schematic diagram of interval prediction under the T1R1A / 400K condition; Figure 13 This is a schematic diagram of interval prediction under the T1R1A / 2M condition; Figure 14 This is a schematic diagram of interval prediction under the T1R1P / 400K condition; Figure 15 This is a schematic diagram of interval prediction under the condition T1R1P / 2M; Figure 16 This is a schematic diagram of point prediction in the MD1 sample under the T1R1A / 400K condition; Figure 17 This is a schematic diagram of point prediction in the MD1 sample under the T1R1A / 2M condition; Figure 18 This is a schematic diagram of point prediction in the MD1 sample under the condition of T1R1P / 400K; Figure 19 This is a schematic diagram of point prediction in the MD1 sample under the T1R1P / 2M condition; Figure 20 This is a schematic diagram of point prediction in the MD2 sample under the T1R1A / 400K condition; Figure 21 This is a schematic diagram of point prediction in the MD2 sample under the condition of T1R1A / 2M; Figure 22 This is a schematic diagram of point prediction in the MD2 sample under the condition of T1R1P / 400K; Figure 23 This is a schematic diagram of point prediction in the MD2 sample under the T1R1P / 2M condition; Figure 24 This is a schematic diagram of point prediction in MD3 samples under the T1R1A / 400K condition; Figure 25 This is a schematic diagram of point prediction in MD3 samples under the T1R1A / 2M condition; Figure 26This is a schematic diagram of point prediction in MD3 samples under the T1R1P / 400K condition; Figure 27 This is a schematic diagram of point prediction in MD3 samples under the T1R1P / 2M condition; Figure 28 This is a schematic diagram of interval prediction in the MD1 sample under the condition of T1R1A / 400K; Figure 29 This is a schematic diagram of interval prediction in the MD1 sample under the condition T1R1A / 2M; Figure 30 This is a schematic diagram of interval prediction in the MD1 sample under the condition of T1R1P / 400K; Figure 31 This is a schematic diagram of interval prediction in the MD1 sample under the condition of T1R1P / 2M; Figure 32 This is a schematic diagram of interval prediction in the MD2 sample under the condition of T1R1A / 400K; Figure 33 This is a schematic diagram of interval prediction in the MD2 sample under the condition of T1R1A / 2M; Figure 34 This is a schematic diagram of interval prediction in the MD2 sample under the condition of T1R1P / 400K; Figure 35 This is a schematic diagram of interval prediction in MD2 samples under the condition of T1R1P / 2M; Figure 36 This is a schematic diagram of interval prediction in MD3 samples under the condition of T1R1A / 400K; Figure 37 This is a schematic diagram of interval prediction in MD3 samples under the condition of T1R1A / 2M; Figure 38 This is a schematic diagram of interval prediction in MD3 samples under the condition of T1R1P / 400K; Figure 39 This is a schematic diagram of interval prediction in MD3 samples under the condition of T1R1P / 2M. Detailed Implementation

[0018] The present invention will be further described below with reference to the accompanying drawings and embodiments. The drawings are simplified schematic diagrams, which only illustrate the basic structure of the present invention in a schematic manner, and therefore only show the components related to the present invention.

[0019] Definition of transmit and receive antenna signals and basic principles of resistivity measurement: This invention focuses on the AziExpress azimuth electromagnetic logging instrument, whose basic structure is as follows: Figure 2As shown, the system adopts a five-transmitter, dual-receiver, multi-source-distance antenna structure, with the instrument coils symmetrically installed. It integrates multi-band resistivity measurement and high-precision azimuth detection functions. Among them, T1, T2, T3, T4, and T5 are transmitting antennas; R1 and R2 are receiving antennas; the source distance of antenna combination T5-R2 is L1=40.64 cm; the source distance of antenna combination T3-R2 is L2=81.28 cm; and the source distance of antenna combination T1-R2 is L3=121.92 cm.

[0020] The drilling azimuth electromagnetic instrument uses two measurement frequencies, 2MHz and 400kHz. The receiving antennas R1 and R2 collect the raw electromagnetic signals, including the amplitude and phase of the electromotive force. Resistivity measurement is achieved by calculating the phase difference and amplitude ratio, based on the propagation characteristics of electromagnetic waves in the earth's strata. First, the phase difference between the two sets of receiving antennas, R1 and R2, is obtained. The logarithmic ratio of the electromotive force modulus yields the amplitude ratio. As shown in equations (1) and (2): (1) (2) In the formula, the electromotive force of the receiving antenna R1 is: V 1,;The electromotive force of the receiving antenna R2 is V 2,; , Represents the magnitude of the electromotive force; , This indicates the phase angle.

[0021] To reduce the impact of downhole noise, symmetrical source distance compensation was then adopted. The phase difference and amplitude ratio data corresponding to the transmitting antennas with equal source distance on both sides of the measurement point were weighted and averaged to obtain the compensation amplitude ratio and compensation phase difference. Finally, the compensation signal was mapped to the target formation resistivity value through a resistivity conversion table.

[0022] The data collected by the azimuth electromagnetic logging instrument while drilling is affected by multiple factors such as formation interface effect and formation anisotropy, and has significant nonlinear characteristics. On the other hand, in order to achieve effective prediction of formations more than 5 meters ahead of the drill bit, it is necessary to process a large number of time steps of logging data, which puts high demands on the long-term dependency modeling capability of the prediction model.

[0023] like Figure 1 As shown, a drilling azimuth electromagnetic forward-looking prediction method based on QR-iTransformer-KAN includes the following steps: Construction of iTransformer-KAN azimuth electromagnetic data point prediction model for drilling: Considering the characteristics of logging-while-drilling data, the point prediction model of this invention combines the long-term dependency modeling capability of iTransformer with the nonlinear feature fitting capability of KAN network. This model achieves accurate forward prediction of resistivity changes through multi-level feature extraction and fusion; it consists of an input module, a feature extraction module and an output module.

[0024] The input module of the iTransformer model includes an embedding layer. The Transformer prediction model embeds multiple variables at the same time step into a single time stamp. In the middle, as shown in the formula: (3) In the formula, Indicates the first The time step is embedded into the first time step. Data corresponding to each variable; However, a time stamp Embedding multiple variables can prevent the model from learning variable-centric representations, leading to a decline in predictive performance in long-term dependency modeling. Therefore, this invention employs the iTransformer model, inverting the Transformer module and embedding the variable at each time step into a separate variable label. In the middle, as shown in the formula: (4) In equation (2), Indicates the first Embedded variables The data corresponding to each time step.

[0025] Variable labeling It aggregates global representations of sequences, which can be more variable-centric, enabling the model to prioritize the identification of correlations between variables, and has certain advantages over Transformer in long-term dependency modeling.

[0026] The feature extraction module consists of a multi-head self-attention layer, layer normalization, and a feedforward network. The multi-head self-attention mechanism in iTransformer differs from that in Transformer. Transformer mainly uses multi-head self-attention to capture dependencies between different time steps, while iTransformer uses multi-head self-attention to capture correlations between multiple variables. This process enables each variable label to fully extract relevant information from the entire variable sequence, thereby enhancing the model's ability to model dependencies between multiple variables.

[0027] First, three types of vectors are calculated based on the input: query vector ( ), key vector ( ) and value vector ( ), then calculate the first i The query vector of the first variable and the first variable j The attention weights are obtained by scaling the dot product of the key vectors and then dividing by the dimension of the key vectors to make training more stable; finally, exponential normalization is performed using the Softmax function. As shown in the formula: (5) All attention weights calculated above As coefficients, the value vector of all variables We obtain the weighted summation. i The first variable h Feature representation vector of each attention head As shown in the formula: (6) The calculated value for each attention head These vectors are concatenated in dimensionality to form a longer vector, which is then passed through a multilayer perceptron. Linear transformations and nonlinear activations are performed to ultimately output multi-head attention. The formula is: (7) Layer normalization can increase the convergence of the network during training. However, the Transformer's simultaneous layer normalization of multivariate variables at the same time step may introduce noise and over-smooth the time series data. The iTransformer solves this problem by performing layer normalization on each variable separately. This method can not only reduce the potential noise in the data aggregation process, but also effectively handle non-stationarity issues, as shown in Equation (8). (8) in, Indicates the first n Variable tags embedded in each variable Multiply by attention weight ; R It is a set consisting of all embedded variable tags, that is , N This indicates the total number of variable labels.

[0028] like Figure 3In order to improve the model's ability to fit nonlinear features such as resistivity abrupt changes, this invention uses a KAN network to replace the multilayer perceptron in the traditional feedforward network. In the traditional feedforward network architecture of the multilayer perceptron, fixed activation functions and weight parameters are usually used for neuron connection and adjustment of input signal weights; while the KAN network is a neural network architecture based on the Kolmogorov-Arnold theorem, which uses learnable activation functions. These activation functions are dynamically optimized according to the network training, and can flexibly adapt to the characteristics of the input signal, thereby adaptively capturing local nonlinear features. Given an input vector First, a nonlinear transformation is performed using B-spline basis functions, as shown in the equation: (9) In the formula, These are learnable parameters; For the first j indivual B spline basis functions in Mapping value on, Indicates the size of the grid. This indicates the order of the polynomial.

[0029] Next, calculate the input vector. The value after passing through the basic function, named the silu activation function, is subjected to a linear transformation, as shown in the equation: (10) (11) In the formula, The weight matrix of the basic function, This is a bias term.

[0030] The residual activation strategy involves adding the B-spline basis functions to the fundamental functions to obtain a learnable activation function, as shown in the equation: (12) The learnable activation function is transformed by a composite function of a multi-layer KAN network, and finally combined with residual connections and subjected to layer normalization again to output the prediction result, as shown in the equation: (13) (14) The QR-iTransformer-KAN model is an interval prediction based on quantile regression. Quantile regression (QR) regresses the independent variables by estimating the conditional quantiles of the dependent variable to obtain a regression model at a given quantile. This model does not rely on the error distribution assumption, but instead obtains the prediction interval at different confidence levels by optimizing the quantile loss function, thus providing a more comprehensive uncertainty quantification for geological guidance.

[0031] Given signal eigenvector matrix Geological parameter vector matrix The feature vector matrix X represents the amplitude ratio and phase difference of the signal directly measured by the input feature selection instrument; it includes the transmitting antenna signal, the receiving antenna signal, and the compensation signal; the geological parameter vector matrix Y represents the corresponding formation resistivity. Then the first quantiles ( The regression model expression for ) can be represented as: (15) In the formula, Indicates conditional quantiles, This represents a parameter vector related to quantiles.

[0032] When the test set is known, solving for the parameter vector at a specific quantile can be transformed into solving for the minimum loss function. The formula is: (16) In the formula, Represents the true value. This represents the predicted value.

[0033] The quantile loss function can be defined as: (17) Substituting into the loss function, we get: (18) in, That is, the difference between the actual value and the predicted value.

[0034] Experimental procedure: Data Preprocessing: This invention uses measured data from the AziExpress azimuth electromagnetic logging instrument in a certain oil and gas block in China as the research object. The input features are selected from the signals directly measured by the instrument, including three types of data: transmitting antenna signals, receiving antenna signals, and compensation signals. Among them, the transmitting antenna signals include the amplitude ratio and phase difference of antennas T1 to T5, covering the 400kHz and 2MHz frequencies; the receiving antenna signals include the amplitude ratio and phase difference of antennas R1 and R2, covering the 400kHz and 2MHz frequency bands; the compensation signals include the compensation amplitude ratio and compensation phase difference, covering all combinations of long / short source distance and high / low frequency; the output target is the combined transmitting and receiving antenna signals.

[0035] Because the coils of the AziExpress azimuth electromagnetic logging instrument are symmetrically structured, the amplitude ratio and phase difference of the output antenna combinations can be ignored when considering the symmetrical structure. Taking the T1R1A / 400K output as an example, its input is a 400kHz transmitting antenna. The amplitude ratio of the signal, 400kHz receiving antenna The amplitude ratio signal and the compensation amplitude ratio signal of the long source low frequency are combined to reflect the formation resistivity change under specific source distance and frequency; the output target is shown in Table 1.

[0036] Table 1. Multi-frequency, multi-source distance parameters of the transmit / receive antenna combined signal.

[0037] In azimuth electromagnetic logging (AEM) data during drilling, extreme values ​​and high-frequency noise interference are common due to complex downhole environments (such as formation abrupt changes and vibrations). To address these data characteristics, robust normalization is employed. This normalization maintains a reasonable scaling range for the data using the median and IQR, filtering out noise and outliers at both ends and scaling only the stable data in the middle. The formula is: (19) Where IQR represents the interquartile range, IQR =Q 3 Q 1 ( Q 3 represents the 75th percentile. ，Q 1 represents the 25th percentile, and Median represents the median of the data.

[0038] Model parameter settings: The experiment was conducted using the PyTorch deep learning framework. The hardware configuration and model parameters were set as follows: the iTransformer module had 8 heads per layer for the multi-head attention mechanism and an embedding dimension of 128; the network adopted a 3-layer basis function combination structure, with each layer containing 64 learnable basis functions, and the activation function was a B-spline basis function of order 3 with 10 basis functions; during training, the Adam optimizer was used with a learning rate of 0.001, a batch size of 128, and 200 training epochs. Table 2 Hyperparameters of the iTransformer-KAN model

[0039] Training and test set partitioning: The logging data was obtained by sampling the AziExpress azimuth electromagnetic logging instrument at 40ms intervals. In this study, a total of 4,000 valid samples were selected for each class, corresponding to sandstone-mudstone interbedded sections with a measurement depth between 4,187 and 4,217 m. In order to optimize the generalization ability of the model, a two-stage time-series cross-validation strategy was adopted to divide the dataset.

[0040] Two-phase verification architecture: Phase I: Training scale optimization, fixing the test set to the last 400 samples, and constructing a progressive training set: (20) in, k It is a positive integer from 0 to 5.

[0041] Then, the optimal training scale is selected based on the model's performance at each training scale.

[0042] Phase II, Sensitivity Analysis of the Test Set: Based on the optimal training size determined in Phase I, a test set expansion experiment was set up to analyze the impact of the test set proportion on the model: (twenty one) in, m It is a positive integer from 0 to 5.

[0043] The phased cross-validation architecture fully considers the temporal continuity of downhole data and the abrupt changes in formation. Through the temporal cross-validation strategy, it effectively balances the needs of model training efficiency and generalization ability assessment, and provides a scientific basis for data partitioning for the robustness verification of prediction models under complex geological conditions.

[0044] Predictive evaluation indicators: The point prediction evaluation index uses the coefficient of determination (COP). R 2), mean absolute error ( MAE ) and mean square error ( MSE The formula is as follows: (twenty two) (twenty three) (twenty four) In the formula, This is the actual value; This is a predicted value; This is the average value.

[0045] The evaluation index for interval forecasting uses the forecast interval coverage rate ( PICP ), interval normalized average width ( PINAW ) and comprehensive coverage index ( CWC ); PICP Used to define the probability that the actual measured value falls within the prediction interval. PICP The closer the interval prediction is to the preset confidence level, the better the model's reliability. The formula is: (25) in, n For the number of samples, , These are the lower and upper bounds of the prediction interval, respectively. When the actual measured value is within the prediction interval, =1, otherwise =0.

[0046] PINAW Used to evaluate the width of the prediction interval. PINAW This reflects the accuracy of interval prediction. The smaller the value, the tighter the interval and the higher the prediction accuracy. The formula is: (26) In the formula, It represents the difference between the maximum and minimum values ​​of the actual measured value.

[0047] CWC is a comprehensive evaluation index that encompasses both the reliability and accuracy of interval predictions. A smaller CWC indicates that the prediction interval achieves optimal accuracy while ensuring reliability. The formula is: (27) (28) In the formula, Let be the penalty coefficient, when PICP When the probability is less than the preset probability value, CWC Increase exponentially, and vice versa. CWC It will decrease; This is a preset probability value, determined by the confidence interval. When the confidence interval is 90%, =0.9.

[0048] Prediction Result Analysis: Resistivity Point Prediction Analysis, such as Figure 4-7 As shown, the resistivity point prediction results corresponding to amplitude ratio and phase difference under different combinations of frequency and source distance are presented. It can be seen that under the condition of long source distance and low frequency amplitude ratio (T1R1A / 400K), the resistivity curve changes relatively smoothly, and the model of this invention can capture the trend of resistivity change well, and the predicted value is basically consistent with the actual value. However, under the condition of long source distance and high frequency amplitude ratio (T1R1A / 2M), the resistivity curve fluctuates significantly, and the prediction difficulty increases. However, the model still shows good response sensitivity at resistivity abrupt change points (such as peaks and inflections), and overall it can effectively capture the trend of resistivity change.

[0049] Table 3. Statistics of Prediction Error Indicators for Test Set Points

[0050] According to the statistical results in Table 3, for amplitude ratio and phase difference data of different frequency and source distance combinations, the mean square error (MSE) and mean absolute error (MAE) obtained by the model of this invention during the prediction process are both maintained within a reasonable range; the coefficient of determination (R²) can reach above 0.96, indicating a high degree of data fitting; by comparing the performance under different frequency conditions, it can be found that: at a frequency of 400kHz, the overall prediction error is the smallest due to the stable signal change trend; while at a frequency of 2MHz, due to the significant fluctuation of electromagnetic wave response, the average MAE reaches 0.3, resulting in an increase in the overall prediction error, and the R² is relatively low, thus reducing the fitting accuracy.

[0051] To further verify the superiority of the iTransformer-KAN model of this invention, DNN, Transformer, and iTransformer models were compared. The DNN model has been used by Sergey A et al. for long-range prediction in azimuth electromagnetic wave logging while drilling, verifying its feasibility in geological steering prediction modeling during drilling (Sergey A et al., 2021). The Transformer model is a deep learning model commonly used for processing time series data and has been verified as an efficient reconstruction model in the logging field (SUN YZ et al., 2024). During training, all four models used the same data preprocessing and training procedures to predict logging data from the same formation. The prediction results of each model were compared, and the comparison results are as follows: Figure 8-11As shown, the model of this invention has the best overall performance among all algorithms. It can not only effectively predict the trend of resistivity, but also show the best fitting effect in local details. As shown in the magnified local figure, at the fluctuation point of the resistivity curve, the predicted value obtained by the model of this invention is closest to the true value, while the other models deviate relatively much.

[0052] In addition, Table 4 provides the point prediction evaluation index for each model.

[0053] Table 4 Prediction Evaluation Indicators for Each Model Point

[0054] According to the evaluation results in Table 4, the MSE and MAE of the iTransformer-KAN model of this invention are lower than those of the three benchmark models: DNN, Transformer, and iTransformer, across all logging parameters. This invention's model enhances feature extraction capabilities by combining iTransformer and KAN. iTransformer focuses on modeling the global correlation between multiple variables, while KAN, with its learnable activation function, enhances the dynamic fitting ability of nonlinear features. The combination of these two technologies enables the model to more accurately capture the changing trends in non-stationary resistivity signals. Taking T1R1A / 400K as an example, the iTransformer-KAN model reduces MSE and MAE by 25% and 13.85% respectively compared to the iTransformer model; and by 51.16% and 32.53% respectively compared to the Transformer model. Therefore, introducing the KAN module into the iTransformer module optimizes and enhances the model's nonlinear fitting ability, thereby improving the model's prediction accuracy.

[0055] Interval forecasting analysis: In azimuth-based electromagnetic forward-looking drilling, relying solely on point prediction models to output a single geological parameter has certain limitations. Firstly, point prediction results lack quantitative evidence of reliability, making it difficult to provide effective uncertainty assessment. Secondly, the downhole environment is complex, and electromagnetic signals are susceptible to formation interface effects, anisotropy, and noise interference. Point prediction models are quite sensitive to such interference, potentially affecting the accuracy of guidance decisions. To overcome these shortcomings, this invention introduces a quantile regression (QR) mechanism based on the iTransformer-KAN point prediction model, constructing a probabilistic prediction framework capable of generating prediction intervals at specific confidence levels. The uncertainty of the prediction results is quantified through three indicators: prediction interval width (PINAW), prediction interval coverage (PICP), and comprehensive coverage width index (CWC).

[0056] To select an appropriate confidence interval, Table 5 details the interval prediction results for each prediction parameter at confidence intervals of 95%, 90%, and 85%. Analysis of Table 5 shows that as the confidence interval expands (i.e., the confidence level increases), the prediction interval coverage (PICP) improves, indicating enhanced reliability. Simultaneously, the prediction interval width (PINAW) increases, while the coverage width composite index (CWC) shows a downward trend, indicating improved overall prediction accuracy. Therefore, considering both reliability and accuracy, a 95% confidence interval is selected.

[0057] Table 5. Interval prediction results of logging parameters at different confidence levels

[0058] Within the 95% confidence interval, four different combinations of source distance and frequency are output as transmit / receive antenna combination signals for analysis. Figure 12-15 It can be seen that the confidence interval obtained by the model follows the changing trend of the point prediction curve, and the model provides a reasonable prediction for various uncertain fluctuations of the curve. Unlike the static single curve output by traditional point prediction, this model realizes the dynamic adjustment of the prediction interval through the quantile regression mechanism: when the electromagnetic signal fluctuates significantly (such as abrupt changes in the thin-layer interface or noise interference), the prediction interval is relatively wide; conversely, when the electromagnetic signal is stable, the prediction interval is relatively narrow.

[0059] Traditional methods for determining stratigraphic boundaries based on polarization angles rely on manual intervention and lack intuitive data support. This invention proposes a dynamic adjustment mechanism for prediction intervals, with a quantile regression model at its core. This mechanism achieves adaptive changes in interval width by optimizing the quantile loss function. The loss function applies different penalty mechanisms based on different prediction bias types. To obtain the minimum loss function, the model formulates different optimization strategies, thereby driving interval optimization, as shown in Table 6. Table 6 Different optimization strategies for the loss function

[0060] The following sections will elaborate on the two cases: homogeneous strata and thin-layer interfaces.

[0061] 1. At thin-layer interfaces, electromagnetic wave signals are prone to fluctuations and noise interference, leading to increased uncertainty in the model. In this case, the model optimizes the loss function of quantile regression by adjusting the lower quantile (τ). 下 =0.025) Lower while raising the upper quantile (τ) 上The strategy of using a coefficient of 0.975 (=0.975) expands the prediction interval width. At this time, a weak penalty (penalty coefficient of 0.025) is applied to the prediction that deviates from the true value, while avoiding a strong penalty (penalty coefficient of 0.975). The model believes that under the condition of high uncertainty, the cost of suffering multiple small weak penalties is lower than suffering a strong penalty once. Therefore, in the thin interface segment where the signal is prone to sudden changes, interval expansion is the optimal solution under the condition of high uncertainty.

[0062] 2. In uniform geological formations with gently changing resistivity, electromagnetic signals are relatively stable, and model uncertainty is low. In such cases, setting the prediction interval too wide, while avoiding strong penalties, can introduce unnecessary accumulation of weak penalties, thus increasing the loss function value. Therefore, the model adopts a strategy of narrowing the interval to minimize the loss function. This strategy reflects the model's adaptability to low-uncertainty environments and avoids overly conservative predictions.

[0063] Analysis shows that the dynamic change in the interval width can reflect the formation characteristics. When the predicted interval widens significantly and is accompanied by significant curve fluctuations, it indicates that the drill bit is approaching the formation boundary and timely guidance decisions are needed. Conversely, when the predicted interval narrows and the curve is flat, it reflects that the formation is uniform and minor fluctuations can be ignored, and the current drilling parameters can be maintained.

[0064] Generalization performance analysis: Due to the anisotropy of reservoirs, the data distribution varies significantly at different formation depths. The trained model performs well on existing data, but its adaptability to well logging data with different input data scales has not been fully verified. Therefore, we conduct a generalization performance evaluation of the QR-iTransformer-KAN model. By designing generalization experiments with different input data scales, we analyze the model's generalization performance under different input data scale conditions.

[0065] This invention is based on measured data from the AziExpress azimuth electromagnetic logging instrument in an oil and gas block in China. Three sets of samples with different well depths and inclinations were selected: MD1 (well depth 4009–4032m, well inclination 34.8°), MD2 (well depth 4187–4219m, well inclination 72.3°), and MD3 (well depth 4423–4458m, well inclination 90.7°) to verify the stability of the model's predictions under different geological structures and measurement scales.

[0066] In terms of point prediction performance evaluation, by Figure 16-27 As shown in Table 7, in the prediction of the MD1 sample, the model has a significant effect on predicting the resistivity changes of the three strata, R 2Overall, the resistivity was above 0.94, with MAE and MSE remaining at low levels. In the more complex MD2 (five-layer) and MD3 (seven-layer) samples, the model was still able to effectively identify abrupt changes in electromagnetic response caused by formation interfaces, and all error indicators were well controlled. Combining the prediction results of the three samples, the model accurately reflects the dynamic changes in resistivity under different formation complexities and well inclination conditions, indicating its strong generalization ability for cross-stratum point prediction.

[0067] Table 7. Point prediction evaluation indicators under different well depths and inclinations

[0068] In terms of interval prediction performance evaluation, Figures 28-39 Table 8 shows the prediction intervals generated by the model at a 95% confidence level. In the MD1 and MD2 samples, the prediction interval coverage is close to the preset confidence level, the average interval width remains within a narrow range, and the CWC index performs well, indicating the reliability of the model's predictions in medium-complexity formations. In the MD3 sample, due to the increased formation interfaces and the lengthening of the time series, the interval coverage slightly decreased, and the interval width also moderately expanded due to increased uncertainty. However, the overall prediction interval still completely covers the actual logging curves, demonstrating the model's adaptive adjustment capability under uncertain environments. In summary, the QR-iTransformer-KAN model can predict the trend of formation resistivity changes relatively accurately under different well depths and inclinations. In most cases, the prediction interval can fully cover the actual values, and the model's interval prediction part has good generalization ability.

[0069] Table 8. Evaluation Indicators for Interval Prediction under Different Well Depths and Inclinations

[0070] To overcome the limitations of single information and insufficient uncertainty quantification in the field of azimuth electromagnetic wave logging during drilling, this invention establishes a QR-iTransformer-KAN prediction model that integrates point prediction and interval prediction. Addressing the issue of limited accuracy of point prediction in complex formations, this invention constructs the iTransformer-KAN model. The model enhances the global dependence between various logging variables through an inverted Transformer structure and utilizes the learnable activation function of the KAN network to enhance the fitting ability for nonlinear features such as resistivity abrupt changes. Experimental results show that under various frequency and source distance combinations, the model achieves an R² of 0.9724 and a MAE of 0.168 in the typical T1R1A / 400K interval, outperforming commonly used benchmark models in the logging field and demonstrating its high sensitivity in tracking formation interface changes. To further output information on prediction uncertainty, quantile regression (QR) is introduced on the basis of point prediction to establish a probability interval prediction model. This model, by optimizing the quantile loss function, can be used to identify reservoir interfaces based on changes in interval width: expanding the interval near the interface to cover uncertainty, and narrowing the interval in homogeneous strata to improve certainty. At a 95% confidence level, the interval coverage probability (PICP) is consistently higher than 0.96, and the PINAW and CWC indices show that the interval width is reasonable.

[0071] The QR-iTransformer-KAN model of this invention achieves probabilistic forward-looking remote detection of electromagnetic wave signals while drilling through the synergy of point prediction and interval prediction. Under different well depths, well inclinations and formation complexities, the model exhibits good prediction accuracy and generalization ability.

[0072] Based on the above-described preferred embodiments of the present invention, and through the foregoing description, those skilled in the art can make various changes and modifications without departing from the inventive concept. The technical scope of this invention is not limited to the contents of the specification, but must be determined according to the scope of the claims.

Claims

1. A method for predicting drilling azimuth using electromagnetic forward looking-through based on QR-iTransformer-KAN, characterized in that, Includes the following steps: Step 1: Collect signal characteristics and corresponding geological parameters of the azimuth electromagnetic logging instrument while drilling, and construct training and test sets for the signal characteristics and geological parameters; Step 2: Construct the iTransformer-KAN model and train it using the training set. The iTransformer-KAN model replaces the multilayer perceptron in the feedforward network of the iTransformer model with a KAN network.

2. The drilling azimuth electromagnetic forward-looking prediction method based on QR-iTransformer-KAN according to claim 1, characterized in that, The iTransformer-KAN model includes: an embedding layer, a multi-head attention layer, a layer normalization layer, a KAN network, and layer normalization; wherein, the KAN network includes: a first KAN layer, an activation layer, a Dropout layer, and a second KAN layer.

3. The drilling azimuth electromagnetic forward-looking prediction method based on QR-iTransformer-KAN according to claim 1, characterized in that, The quantile regression model is divided into prediction intervals at different confidence levels using the signal features of the test set and the corresponding geological parameters. The test set is input into the trained iTransformer-KAN model, which outputs the predicted geological parameter values. The predicted geological parameter values ​​are evaluated using the prediction intervals.

4. The drilling azimuth electromagnetic forward-looking prediction method based on QR-iTransformer-KAN according to claim 3, characterized in that, Quantile regression models include: Given a signal feature vector matrix X and a geological parameter vector matrix Y; Construct the first Regression model of quantiles ; Solving for the parameter vector at a specific quantile can be transformed into solving for the minimum loss function. ;in, This represents a parameter vector related to quantiles. This represents the difference between the actual value and the predicted value.

5. The drilling azimuth electromagnetic forward-looking prediction method based on QR-iTransformer-KAN according to claim 1, characterized in that, The model of the azimuth electromagnetic logging instrument used for drilling is AziExpress.

6. The drilling azimuth electromagnetic forward-looking prediction method based on QR-iTransformer-KAN according to claim 1, characterized in that, The signals include: Transmit antenna signal, receive antenna signal, and compensation signal.

7. The drilling azimuth electromagnetic forward-looking prediction method based on QR-iTransformer-KAN according to claim 6, characterized in that, Signal characteristics include the amplitude ratio and phase difference of different signals.

8. The drilling azimuth electromagnetic forward-looking prediction method based on QR-iTransformer-KAN according to claim 1, characterized in that, Geological parameters include: formation resistivity.

9. A drilling azimuth electromagnetic forward-looking prediction system based on QR-iTransformer-KAN, characterized in that, include: Memory is used to store instructions that can be executed by the processor; A processor for executing instructions to implement the drilling azimuth electromagnetic forward-looking prediction method based on QR-iTransformer-KAN as described in any one of claims 1-8.

10. A computer-readable medium storing computer program code, characterized in that, The computer program code, when executed by a processor, implements the drilling azimuth electromagnetic forward-looking prediction method based on any one of claims 1-8.

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