Logging Components Extraction Method and Anisotropy Recognition Based on 3D Holographic LWD Instrument Open Access

According to statistics, nearly half of the oil and gas fields are stored in sand-mudstone interlayers, equivalent to macroscopic uniaxial anisotropic formations [1]. Therefore, as an essential factor in evaluating reservoir potential, formation resistivity anisotropy measurement has critical practical needs for oil and gas development [2-4]. To complete the identification task, obtaining the most comprehensive formation information through logging exploration is necessary. Electromagnetic resistivity logging while drilling technology has always played an essential role in exploring and developing earth resources. With the development of this technology, electromagnetic wave logging has experienced three development stages. In the first stage, because the logging instrument adopts the axial transmitting and axial receiving antenna system structure, the formation resistivity can only be obtained by measuring the V_zz signal [5, 6]. In the second stage, the instrument introduces transverse or tilted transmitter and receiver antennas and constructs signals composed of V_zz and V_zx or V_xz components, which can obtain information on formation resistivity and adjacent interface [7]. In the current stage of development, instruments are required to adopt a multi-direction transmitter and receiver antenna structure, which can obtain nine components in all three directions: V_xx, V_yy, V_zz, V_xy, V_xz, V_yx, V_yz, V_zx, V_zy, which are the requirements of 3D holography. Based on the completion of the logging task to obtain formation resistivity and interface information, the instrument is also required to obtain all kinds of cross-components with anisotropy information and get the formation information in all directions [8-10].

Over the years, electromagnetic resistivity logging instruments have developed rapidly, such as the ADR series [11, 12] of Halliburton, the DWPR [13] of CNOOC, and so on. Based on the above logging instruments and the theoretical background of azimuthal electromagnetic waves summarized by Moran [14-16], the research on logging components and signals in the initial stage, since the logging instrument contains only axial coils, only the component can be measured directly to obtain a single resistivity information. In the subsequent development, each study further measured the magnetic field form of components V_xx, V_yy, and V_xz through the symmetrical coil of the instrument to reflect and resist the anisotropic influence of the formation [17]. To further obtain the azimuth of the instrument, the follow-up study expresses the downhole orientation information of the logging instrument by combining the signals constructed by all cross-components of the xz-plane. It is not affected by the negative influence of anisotropy and large deviation wells [18]. CNOOC researchers constructed signals using the ratio of rotation components containing the unique V_yz and V_zy of tilt coil through instrument rotation measurement, making instrument orientation information more accessible by signals [19]. However, the logging components of the above instruments are mainly extracted through the coil calculation in the first two stages, and the components are obtained by directly measuring the electromagnetic field of the receiving antenna. The expression effect of these components on the electrical anisotropy is still poor, and the identification of anisotropic layers inevitably needs the expression of full components. Since the above instruments only contain the Co-planar antenna structure in the instrument coordinate system [20, 21], they do not have the instrument and theoretical method conditions to complete the extraction of the full component. In the Periscope series of Schlumberger [22], additional pairs of cross-antennas were added, and a method for completely extracting components was adopted (23; Zhao et al., 2012 [24]). However, this extraction method is achieved through decoupling the two components of a single cross-coil measurement, which is difficult to combine with the proprietary multi-source-distance symmetric antenna configuration of the self-developed 3D holographic Logging While Drilling (LWD) instrument. This leads to extraction results that do not meet logging requirements when applying the method to this instrument, making it impossible to achieve true 3D holographic imaging to obtain comprehensive downhole formation information. Therefore, how to apply component extraction to the instrument’s specific antenna layout and realize true 3D holographic imaging has become a key research focus.

To solve this problem, based on the newly developed 3D holographic LWD instrument and the basic measurement principle of the logging coil system, we deduce the transmit–receive response of various antenna structures, define the component calculation method of each coil system, and summarize the analytical extraction formula of all nine components, to form electromagnetic logging components extraction method suitable for current logging. Based on this, verifying the effect of the new anisotropy signal constructed by the instrument. Calculate the signal combination curve distribution patterns through forward modeling, then use a typical sandstone-mudstone interbedded model for imaging and inversion calculations to verify the instrument’s capability for accurate anisotropy identification.

A newly developed 3D holographic LWD instrument adopted the full-symmetric antenna system structure of six transmitters and six receivers. The structure of the instrument coil system is shown in Figure 1. Other instrument parameters and related circuit antenna methods have been detailed in previous work [25, 26]. The azimuth sector division diagram of the instrument and the antenna spacing are shown in Figure 2 and Table 1.

The transmitter coils T2, T4, and T6 exhibit fully symmetric antenna spacing configurations with respect to T1, T3, and T5, ensuring balanced electromagnetic coupling and enhanced azimuthal resolution in the 3D holographic LWD instrument. Compared to logging instruments from companies like Schlumberger and Halliburton, which only use asymmetric or Co-planar antenna systems for formation parameter measurements, extracting and calculating full formation components is challenging. In contrast, this instrument introduces a symmetric Antiplanar antenna system that includes five modes of transmit–receive antenna configurations: coaxial, X transmitter -Z receiver, Z transmitter-tilted receiver, X transmitter-tilted receiver, and X transmitter -YZ-tilted receiver. This design enables the instrument to directly measure and calculate electromagnetic information of the formation in all 3D directions, significantly simplifying the process of obtaining full components. All antenna system modes in different directions enable the instrument to obtain formation information from all directions, provide antenna system layout conditions for extracting full electromagnetic logging components, and allow the instrument to extract full components. Therefore, based on this condition, deducing and summarizing the extraction method of the full component is an inevitable requirement for the instrument to play the irreplaceable advantage of 3D holography in the logging engineering task. The full component is also the basis for the azimuthal anisotropy signal to maximize the formation of electrical anisotropy information.

Under the instrument coordinate system x̅ y̅ z̅ as shown in Figure 3. Set a hypothetical instrument with unit magnetic moment emission in three directions and unit magnetic moment reception in three directions. The received signal voltage has nine components, which can be expressed as:

Where V_mn(m, n=x, y, z) represents a voltage signal with transmitter and receiver magnetic moment direction of m and n, respectively; nine components of the formula (1) contain all the transmitter and receiver combinations along the 3D axis and thus have the formation information in all directions, which can be used as the fundamental component of the MWD signal.

To obtain the rotating azimuth information of the instrument, the rotating azimuth angle corresponds to the logging response in this state for easy calculation. The multi-sector azimuth measurement is often used for logging while drilling instruments, which divide the rotation period 2π into N sectors, and the response under the corresponding instrument rotation angle ф is recorded, respectively, to express the azimuth measurement information of the instrument and realize the target of azimuth measurement.

Set general single transmitter and receiver coil model in‾x‾y‾z, the transmitter magnetic moment is M_T, the tilt angle satisfies θ_T = θ_Tra, the instrument rotation axis angle is ф_T= ф_Tra, the receiver magnetic moment is M_R, the tilt angle satisfies θ_R= θ_Rec, the instrument rotation axis angle is ф_R= ф_Rec, the instrument rotation angle is ф, the instrument high side angle is ф = 0°, and the instrument low side angle is ф = 180° as shown in Figure 4.

It is well known that the response of transmitter–receiver is:

Equation (2) contains all nine logging components, and extracting these components inevitably requires independent solving. For this reason, formula (2) should be introduced into the more specific Co-planar and Antiplanar antenna system models to calculate and solve them.

Based on equation (2), set the tilt angles of the transmitter and receiver to be θ′_T and θ′_R. The angle of the magnetic moment is the generally tilted transmitter—tilted receiver, that is, θ′_T = θ_Tra, θ′_R= θ_Rec, the rotation angle of the instrument is ф, when the magnetic moments of the transmitter and the receiver are in the same plane, which satisfies ф_Tra = ф_Rec= ф; this antenna mode is the Co-planar mode of the instrument coil system as shown in Figure 5. According to formula (2), the response can be organized as:

In formula (3), the signal V_c is the weighting function of the nine components, θ_Tra, θ_Rec, the rotation angle ф of formula (1), and the extraction of the full component needs to be analyzed and calculated in formula (3). Set parametric variable equations as follows:

By substituting formula (4) into formula (3) and measuring by multi-sector rotation of the instrument, the response formula can be simplified as follows:

Where i is the sector number, V_i is the voltage response value of the receiver antenna under the sector, and ф_i is the instrument rotation angle corresponding to the sector.

To solve A_c0 to A_c4, e need to perform complex transformations individually and sum their values over N sectors. After simplification, the fixed solution of five parameters can be obtained as follows:

Thus, parameter variables A_c0 to A_c4 are solved. Currently, in equation (4), A_c0 to A_c4, θ_Tra and θ_Rec are definite known quantities. The nine components in equation (1) need to be solved, but because there are only five independent equations in equation (4), it is still impossible to analyze all components even after the rotation orientation measurement. Therefore, it is necessary to discuss the signal response under the specific Co-planar antenna arrangement mode and further simplify the number of variables. The particular antenna classification modes are shown in Figure 6. Based on the above calculation methods, the analysis and extraction of components of various Co-planar antenna system models can be obtained, as shown in Table 2.

Combining all modes of the Co-planar coil system, the following components can be directly resolved: V_xx, V_yy, V_zz, V_xz, V_yz, V_zx, V_zy, (V_xy + V_yx). Among them, in the case of antenna systems (d), (g), and (h), the number of components is not equal to the independent equations. The components V_xy and V_yx need to be regarded as one component, and the equation system can be solved. The problem is that these two components cannot be independently analyzed, and 3D holography cannot be achieved. Therefore, it is necessary to use the coil system in Antiplanar antenna mode to solve the problem.

Set tilt angles of the transmitter and receiver are, respectively, θ′_T and θ′_R, the magnetic moment angle satisfies θ′_T = θ_Tra, θ′_R= θ_Rec, and the rotation angle of the instrument is ф. When the magnetic moments of the transmitter and the receiver antennas are located on two orthogonal planes, respectively, this antenna mode is called the Antiplanar mode of the instrument coil system, as shown in Figures 7(a) and 7(b), which respectively represent the two general Antiplanar modes of XZ transmitter -YZ receiver (ф_Tra = ф, ф_Rec = ф + 90°) and YZ transmitter -XZ receiver (ф_Tra = ф + 90°, ф_Rec = ф). According to the response formula (2), the response of XZ transmitter-YZ receiver mode can be summarized as:

YZ transmitter - XZ receiver can arrange to receive mode:

Similarly, the analytical calculation of equations (11) and (12) requires a system of parametric variables:

Also, since there are only five independent equations in equations (13) and (14), it is impossible to analyze all the components, so discussing the signal response under a more specific pattern of Antiplanar antenna arrangement is necessary. The specific antenna mode is shown in Figure 8. The component analysis and extraction of various types of Antiplanar antenna system models can be obtained by adopting the same calculation method shown in Table 3.

Synthesizing all modes of different surface coil systems, directly analyze the following parameters: (V_xx-V_yy), V_zz, V_xy, V_xz, V_yx, V_yz, V_zx, V_zy. Among them, components V_xy and V_yx cannot be resolved independently. Combined with the resolvable components in Co-planar coil system mode, all nine components can be extracted independently. So far, in the logging instrument for any of the above single-transmitter and single-receiver antenna systems, the log response of a single component can be directly calculated through the component analytic extraction formula in the method.

Since the method includes all the antenna system modes of the newly developed 3D holographic LWD instrument, the component extraction method can be used to use nine full components containing all-directional information in the instrument to achieve true 3D holography, and the full component is used as the basis for anisotropy identification signals in logging while drilling.

Resistivity anisotropy is a vital formation parameter in downhole operation, and its combined analysis with formation average resistivity and layer interface can directly evaluate the geological composition of the well. Due to the limited transmission bandwidth of the instrument, in order to complete the task of identifying the anisotropy in the process of real-time measurement while drilling, the logging instrument needs to obtain different components through the combination of different frequencies, source distance, and antenna modes. Combining the characteristics of the instrument’s complete symmetric antenna and the advantages of 3D holography, the orientation is incorporated into the formation detection signal to build a new signal. On the premise of ensuring a small amount of data, the information obtained by the instrument is sensitive enough to the formation resistivity anisotropy to support various types of subsequent logging work.

In the previous study, the selected operating frequencies of the instrument’s anisotropy measurement have been specified as 2 MHz and 400 kHz. As the source distance increases, the directional signal strengthens, allowing for predictions of greater distances to the layer interfaces. Conversely, a smaller source distance enhances the sensitivity of the signal to the electromagnetic field of the formation, resulting in richer information. However, when using signals constructed through traditional methods to measure anisotropy with M_az and M_pz, issues arise with the initial values of amplitude ratio and phase difference being nonzero, which severely affects measurement accuracy in engineering and complicates subsequent inversion calculations. Based on these concepts and issues, the following antenna configurations are selected for signal construction: T5-R5, T6-R6 to extract components V_xx and V_yy; T5-R3, T6-R4 to extract V_xy and V_yx; T3-R5, T4-R6, and T1-R5, T2-R6 two groups of antenna system to extract V_zx and V_zy; T5-R5, T6-R6 and T5-R3, T6-R4 to extract V_xz and V_yz. Symmetric antenna inverse compensation is used for all components involved to amplify the anisotropic response of the formation, and the signal is constructed in the form of the sum ratio corresponding to the vertical axial component. Because the control operation system of the LWD resistivity logging instrument has the function of synchronously calculating the amplitude ratio signal and phase difference signal, the attenuation ratio M_at and phase difference M_pd are constructed as anisotropy signals:

All components were acquired at identical operating frequencies, with the transmitter-receiver spacing rigorously maintained constant throughout the measurement process. In formula (16), angle means to take the complex angle (°). The essence of the above anisotropy signal is the same as that of the mainstream logging instrument: combining different components. The signal includes the main component V_xx, V_yy and the cross-component V_xy, V_yz, V_xz, V_zx, V_yz, V_zy. Among them, the main components are mainly used to detect the resistivity change information from the formation interface, indicating the formation orientation of the instrument, and cross-components from the three directions can measure the formation resistivity anisotropy information to the greatest extent in the full 3D direction. The cross-synthesis of multiple types of information can make the instrument maximize the completeness of the evaluation of anisotropy information.

Anisotropic signals need to indicate changes in the anisotropy coefficient of the formation. When the instrument approaches or passes through the anisotropic target layer, its response characteristics must indicate the relativity of the formation’s anisotropy coefficient and reflect the formation interface’s azimuth differentiation.

Set a three-layer uniform formation model, well inclination α = 50°, the upper surrounding rock formation boundary position for vertical depth TVD = 5(m), the lower surrounding rock formation boundary position for TVD = 10(m), set the surrounding rock for isotropic layer, the target layer λ increased from 1 to 5, the relationship is satisfied λ² = R_v/R_h, R_v means vertical resistivity, R_h means horizontal resistivity. Under the condition of choosing the operating frequency of the instrument to be 2 MHz and 400 KHz, the forward simulation results of the anisotropy signal response calculated by the generalized reflection coefficient analysis method are shown in Figure 8.

In isotropic surrounding rock, the attenuation ratio M_at and phase difference signal M_pd remain consistently at 0 when the instrument lands. As the instrument nears the target layer from the surrounding rock layer, the response of the signal M_at and M_pd decreases, and then the response value rises to the maximum value. As the instrument lands on the target layer, both signals initially decrease from their maximum values, eventually stabilizing at the minimum value with fluctuations. The target layer is isotropic, and the stability value remains constant at 0. The target layer is anisotropic, and this constant value will be higher than the constant zero value response of the surrounding rock layer. When the instrument exits the target layer and reaches the lower surrounding rock layer, both signals exhibit a symmetrical response upon entering the surrounding rock layer, maintaining a constant value of 0.

When the instrument lands in the layers with different anisotropy coefficients, the response has noticeable differences with regular changes. The stronger the anisotropy, the more extensive the EDR (Effective Dynamic Range). Before λ increases to 3, the EDR increases more obviously, and the EDR increases more slowly after more significant than 3. Compared with Figures 9(a)–9(d), it can be seen that the value distribution of anisotropic strata is more dispersed, and the response differentiation is significant so that it can produce better recognition of anisotropic formations. Compared with Figures 8(a)–8(d), it can be seen that the signal M_at response value of 400 kHz is smaller than that of 2 MHz, and the anisotropy differentiation performance is weaker. Compared with 2 MHz, the response of the 400 kHz signal at the formation interface can exceed the international standard measurement accuracy (0.02dB/0.2°) by about 0.6m. The azimuth characteristics of the instrument can be more clearly expressed.

Attenuation ratio signal M_at and phase difference signal M_pd due to the difference in anisotropy coefficient, the response produces a constant value of different EDR, showing the excellent recognition ability of anisotropic formation, produces a clear symmetric peak response at the formation interface, showing the orientation of the instrument, and meets the requirements of the 3D holographic resistivity while drilling instrument for anisotropy signals. Although both signals can recognize the anisotropic formation, the downhole transmission bandwidth resources are insufficient in the actual drilling logging, requiring instruments to use the most limited signal to obtain adequate logging information. In order to solve this problem, signals should be further screened by combining well inclination factor.

Keep other parameters of the formation model unchanged, λ of the target layer is fixed at 5, select instruments operating frequency of 2MHz and 400KHz, change the inclination angle α gradually from 0° to 90°, and carry out forward simulation; the results are shown in Figure 10.

By comparison, it can be seen that the EDR of M_at and M_pd gradually increases from α = 0° to α = 55°, reaches the maximum value, and begins to decline after 55°. With the increase of inclination angle α, the response of M_at near the interface is no longer monotonous but gradually becomes a fluctuation, which is affected by the inclination angle to a certain extent. The response of M_pd is only affected by the inclination angle in the EDR, the response position is not affected by the change of inclination angle, and the detection ability of the anisotropy is not weakened.

The above forward simulation shows that M_at and M_pd have the recognition ability under different formations, but the M_pd recognition ability of formation resistivity anisotropy is superior, and the measurement advantage is shown at both the operating frequencies of 2 MHz and 400 KHz. It is necessary to perform a feature analysis of the signal imaging to validate the effectiveness of the signal during the logging process. Additionally, using the same inversion method, comparing the accuracy of anisotropy coefficient calculations between this signal and traditional signals should be conducted.

The azimuth imaging of the instrument response was carried out by simulating the typical sand-mudstone interlayer model composed of five layers. The specific parameters of the model are shown in Table 4. In Figure 11, from top to bottom, the first section is the formation model and well track, where TVD represents the true vertical depth of the hole and THD represents the true horizontal distance of the hole. The second line is the phase difference signal M_pd imaging response curve; the third is the anisotropy image of the joint tool face angle under the signal.

The formation model and well track can be seen in Figure 10. Layers 1, 3, and 4 are isotropic formations, while layers 2 and 5 are anisotropic. In this model, the simulation instrument drilled from Layer 1 into Layer 5 with a large inclination (α = 60°) and then drilled back into Layer 1 after adjusting the drilling angle to a symmetrical angle in Layer 5. The imaging curve of the phase difference signal M_pd is expressed by the combination of responses under two frequencies. The combination of two frequency-weighted expressions expresses the peak response at the interface. The response of the stable value is expressed by the 2 MHz signal response to obtain more intuitive anisotropy information and clearly express the azimuth characteristics of the instrument. The instrument tool face angle digamma is introduced through the curve, and the azimuth imaging method is used to form the instrument’s anisotropy imaging.

It can be seen from the imaging figure that when the well track is drilled through the formation interface, the signal imaging shows obvious sine and cosine characteristics and uses the form of bright and dark spots to characterize the azimuth characteristics of the instrument entering or leaving the formation interface. In the descending stage of TVD value, when the well track is landed in isotropic Layer 1, the imaging has no feature because the signal response value is 0. When the borehole track is drilled from Layer 1 into anisotropic Layer 2, the image shows bright spots through the signal’s peak, which represents entering a new formation. Then, it shows symmetrical bands for the anisotropic layer characteristics. When drilled into Layer 3, the imaging shows dark spots through the next signal peak, which represents entering a new formation. Moreover, because Layer 3 is an isotropic formation, the imaging has no apparent characteristics. When drilled into Layer 4, the imaging shows bright spots again. Although the resistivity of Layer 4 is different from that of Layer 3, it is still an isotropic layer, and the imaging has no apparent characteristics, proving that the resistivity contrast does not interfere with the signal. When drilling into Layer 5 from Layer 4, the imaging cross-presented dark spots. In the anisotropic Layer 5, the imaging still showed symmetrical bands. The inclination angle at this stage was a change value. The symmetrical bands gradually changed from bright to dark according to the direction of THD growth, which was convenient for the instrument to adjust the inclination of azimuth in the anisotropic formation. In the TVD ascending stage, when the well track was drilled from Layer 5 back to Layer 4, the signal response was symmetrical with that of drilling in. The bright spots that should have been crisscrossed turned dark because the response amplitude was less than 0. This phenomenon represented that the instrument crossed the same formation interface again. In the subsequent trajectory, the imaging followed the rule; according to the layer interface, alternating bright and dark spots were produced, and symmetrical bands were presented in the anisotropic formation.

This study employs a dual-path analysis framework integrating attention mechanism and Long Short-Term Memory (LSTM) network for anisotropic signal inversion. Addressing the spatio-temporal coupling characteristics, the model utilizes an LSTM gating system to dynamically screen key time nodes, with its architecture illustrated in Figure 12.

Simultaneously, by leveraging the attention mechanism, the model can calculate directional correlation and achieve spatio-temporal feature decoupling in the parameterized space, with its structure shown in Figure 13.

And the hybrid model combining LSTM and attention mechanism is presented in Figure 14.

In this framework, the LSTM cell state continuously updates the signal’s time-varying dynamics, while the attention tensor constructs a direction-sensitive subspace through attention-based operations. The fusion of gated features and attention-weighted representation ultimately realizes the inversion of anisotropic signals. The corresponding mathematical formulation is as follows:

The attention weights are computed for the hidden states $H=[h1,...,hT]$ across all time steps of the LSTM.

Here, $uT$ is a learnable vector. The weighted context vector is given by:

The attention-weighted context vector c is fused with the final hidden state $hT$ through feature integration:

The final output is generated by fusing the attention-weighted context vector with the final hidden state. This architecture enables intuitive verification of the model’s focus on anisotropic features through attention weight visualization, thereby providing an interpretable basis for signal feature analysis.

The study uses both traditionally constructed signals and M_pd signals as neural network inputs, with anisotropic coefficients as outputs for inversion calculation. During deep neural network training, the learning rate and batch size parameters serve as key regulatory factors that significantly control model performance. To meet the requirements of anisotropic characterization in the LSTM-Attention hybrid architecture, this study designs learning rates of 0.0001, 0.0004, 0.0008, and 0.001, and batch sizes of 32, 64, and 128, constructing a multi-dimensional parameter analysis experiment.

1. Loss function comparison across batch sizes (32/64/128) at learning rate 0.0004

2. Loss function comparison across batch sizes (32/64/128) at learning rate 0.0008

3. Loss function comparison across batch sizes (32/64/128) at learning rate 0.001

As evidenced by the training loss curves in Figures 15–16 and the comparative data of minimum loss values and RMSE in Tables 5–6, the LSTM-attention network attains optimal convergence on both types of signal datasets (constructed by different methods) when configured with batch size n = 64 and learning rate η = 0.0004.

Experimental results demonstrate: (1) for traditionally constructed signals, the network achieves minimum training loss 0.099 with RMSE 0.195 and (2) for M_pd signal, superior performance is observed with training loss 0.064 and RMSE 0.128.

These results demonstrate that the proposed M_pd-based signal construction method exhibits significant advantages in inversion accuracy. The inversion calculation results are presented in Figure 17, and a comparative analysis is detailed in Table 7.

The comparative results demonstrate that signals constructed using conventional methods exhibit nonzero values in isotropic formations, leading to significant errors and pronounced fluctuations when employing neural network methods for anisotropy inversion. In contrast, the proposed method achieves an average inversion error of λ values within 0.01, with both identification accuracy and stability outperforming traditional signals.

The above imaging effects are sufficient to prove that the newly developed LWD instrument can identify the anisotropic formation with the help of the signal and imaging and obtain the instrument’s orientation information at different formation interfaces, which can support the instrument’s guidance while drilling in the anisotropic formation and the subsequent inverse evaluation of resistivity anisotropy.

Due to the susceptibility of the instrument to various noise interferences under complex operating conditions, which leads to signal transmission distortion, robustness verification of anisotropic signal inversion is required to evaluate its noise immunity performance. To validate the identification capability of M_pd signal in noisy environments for anisotropic formations, this study simulated a Gaussian random noise environment with a noise variance of 0.2. For each noise level, 1000 random noise samples were generated to statistically analyze the inversion results and absolute error distributions between M_pd anisotropic signals and conventionally constructed anisotropic signals. To ensure comparability across experiments, the neural network parameters were maintained consistent with the benchmark configuration: batch size n = 64 and learning rate η = 0.0004.

Under this parameter configuration, the traditional method for anisotropic signal inversion in noisy environments achieved a minimum training loss of 0.167 and RMSE of 0.339, while the M_pd signal demonstrated superior performance with a minimum training loss of 0.089 and RMSE of 0.175. The inversion results indicate that the proposed M_pd signal construction method exhibits notable robustness advantages in inversion performance, providing valuable guidance for geosteering applications. The inversion calculation results are presented in Figure 18, with detailed comparative analysis provided in Table 8.

Extracting and calculating full components of logging is challenging to achieve solely through the response formulas of general antenna patterns. It is necessary to derive response formulas separately for specific Co-planar and Antiplanar antenna systems, corresponding to solving parametric equations to obtain the nine components in all three directions. These components are then extracted using fixed formulas within the respective antenna systems. In practical engineering, various instruments can combine the designed antenna models with the above extraction method to directly calculate the logging response of selected components, supporting the construction of the instrument’s functional signals.

The newly developed 3D holographic LWD instrument has Co-planar and Antiplanar antenna systems, and all nine components can be extracted using the above extraction method. The forward simulation shows that the anisotropy of formation resistivity can be directly indicated using the attenuation ratio signal M_at and phase difference signal M_pd constructed using the full 3D cross-component combined with the characteristics of the full symmetrical antenna and the advantage of 3D holography. Compared to M_pd with the M_at, the recognition effect of anisotropy is better. The anisotropy signal selected M_pd as the instrument can show sufficient anisotropic recognition ability even though it only occupies the transmission bandwidth of one group of signals. In azimuth imaging, the signal can express the resistivity anisotropy information of the formation employing symmetrical banding and express the azimuth information of the instrument in the form of bright and dark spots to effectively identify the anisotropic formation. The inversion training results of the LSTM-attention neural network demonstrate significant improvements over the traditional Co-planar component anisotropic signal method (training loss: 0.099, RMSE: 0.195), achieving reduced values of 0.064 for training loss and 0.128 for RMSE. In inversion calculations, the average inversion error of anisotropic coefficients decreased from 0.1714 using traditional methods to 0.0624 with the M_pd signal, indicating substantially enhanced computational accuracy. Considering that instruments are prone to various noise interferences under complex working conditions, robustness verification was performed for anisotropic coefficient inversion. Under noisy conditions, the LSTM-attention network outperformed the traditional Co-planar component method (training loss: 0.167, RMSE: 0.339) by reducing these metrics to 0.089 and 0.175, respectively. Furthermore, the average inversion error improved from 0.3406 with conventional approaches to 0.136 using the M_pd signal. These results confirm that the anisotropic signals constructed based on the M_pd signal exhibit notable robustness, providing valuable guidance for practical engineering applications.

The data used to support the findings of this study are included within the article.

The authors declare that they have no conflicts of interest.

This work was supported by the Frontier Technologies R&D Program of Jiangsu (BF2024018).