Plane-wave Destruction Research Articles

Enhanced wave modeling & optimal plane-wave destruction (OPWD) method for diffraction separation and imaging

One of the primary challenges faced in seismic exploration is to determine the methodology for analyzing the dispersive wave in various models while maintaining the wave's stability at a low-rank one-step approximation. An optimal signal-to-noise ratio can be achieved by utilizing time-stepping in a low-rank one-step wave extrapolation. It is important to note that the ideal time step should be complex valued. Preserving subsurface diffractions can be quite challenging and demands careful monitoring. To tackle this challenge, we suggest implementing the optimal plane-wave destruction (OPWD) method. To ensure the stability of wave propagation, a fundamental three-layer velocity model is calculated at various time intervals. Afterward, a practical model is used to monitor the movement of the mentioned model. The model being discussed includes a syncline, anticline, distinct edges, and a fault with a steep dip angle. The model is evaluated for the process of simultaneous stepping and marching. Based on the research findings, it is evident that there are variations in the time-stepping between the simple and complex models. These differences align with the Nyquist limit of the sampling interval, as expected. Extending the model beyond the Nyquist limit can cause fluctuations in its stability. OPWD achieved excellent results in diffraction separation and high-resolution imaging on both the synthetic data and real data. The synthetic data included a complex model with anticlines, synclines, sharp edges, and deeper faults. The real data was obtained from the Gulf of Mexico, specifically the Walker Ridges line no. 331. The results suggest that the OPWD method is successful in preserving diffraction in both simulated and actual subsurface environments.

Imaging point diffractors using a low-rank approximation method

Diffraction separation plays a critical role in obtaining high-resolution images of subsurface diffractors by eliminating the diffractions’ contribution from reflections. It is usually based on the difference in spatial coherency between seismic reflection and diffraction energy in the time domain. Methods based on local slope differences, e.g., plane-wave destruction (PWD) method, tend to separate point and line diffractors simultaneously. This paper applies a rank-based diffraction separation method, known as the localized rank-reduction (LRR) method, to distinguish point diffractors in poststack data sets from line diffractors, thereby obtaining a higher resolution when characterizing point discontinuities such as karst caves. To make the LRR method more adaptive, a novel rank determination method based on a newly defined accumulated singular value ratio sequence is developed. The effectiveness of the proposed method is proved via a variety of 2D/3D synthetic and real data examples and a detailed discussion of its practical potential. Despite a larger computational cost compared to the PWD method, the proposed method helps interpretation by enabling us to distinguish between line and point diffractors.

Denoising and wavefield separation method for DAS VSP via deep learning

Distributed acoustic sensing (DAS) vertical seismic profiling (VSP) is, a new combined method of borehole seismic exploration, that has the advantages of low cost, high resistance to temperature and pressure, and high sampling rate. However, the collected data generally suffer from high noise, detracting from the potential high-precision imaging benefits and limiting the full application of the technique. The quality of wavefield separation is also crucial to VSP processing. To mitigate the various problems, a regularized residual channel attention network (RRCAN) is proposed for improved denoising and wavefield separation. Based on two prediction tasks, the networks are built (i.e., RRCAN_1 and RRCAN_2) by adding a regularization term to the loss function. To reduce the loss of effective signals during the denoising process, a wavefield separation method that includes secondary effective information extraction is adopted. The final separation results reflect the denoised and removed noise data, a total of 500 geological models are constructed using a random method and RRCAN_1 is trained with synthetic and field noise data. The conventional plane-wave destruction method is improved by using velocity information, and high-precision separation results for upgoing and downgoing waves are obtained for RRCAN_2 training. The test results obtained for the synthetic and field data show that the proposed network effectively suppresses DAS VSP noise while yielding excellent separation results for downgoing and upgoing waves. Therefore, denoising and wavefield separation methods based on RRCAN provide effective high-precision DAS VSP imaging.

Simulation of Lunar Comprehensive Substructure With Fracture and Imaging of Later LPR Data From Chang’e-4 Mission

As one of the most important geophysical methods for detecting the lunar underground structure of the Moon, the lunar penetrating radar (LPR) is applied to the Chang’e-4 (CE-4) mission to explore the Von Kármán crater on the far side of the Moon. With the Yutu-2 rover continues to move towards the Zhinyu crater at the west, radar will likely detect the fractures created by the impact that formed the Zhinyu Crater. Therefore, the establishment of a comprehensive lunar subsurface structure model with fracture, random media and fractal terrain is crucial for the LPR data processing and the understanding of the lunar geological impact process. In addition, the method that can image the radar data with fractures well has great significance to the interpretation of the LPR data. In this paper, we establish a comprehensive lunar subsurface structure model firstly, the considering factors including fractures, random media, fractal terrain, and the radar response are calculated through forward modeling. Secondly, according to the high resolution and the sensitive to inhomogeneities of LPR data, we design a set of processing flow including plane-wave destruction, velocity analysis based on the focusing analysis method and migration imaging based on the velocity continuation. Finally, the results including simulation data and Antarctic fracture data are used to verify the effectiveness of imaging method.

Seismic Data Enhancement Based on Common-Reflection-Surface-Based Local Slope and Trimmed Mean Filter

Seismic data often contain noise that can disturb or mask effective information. Noise elimination is an important and challenging task in seismic signal processing. Considering the high amplitude continuity of seismic events in the shot domain, this article proposes a structure-oriented denoising method that can enhance the effective events and suppress disturbing noise, including both incoherent and coherent noise. Based on the common-reflection-surface (CRS) travel time, the local slope of seismic events in the shot domain is deduced and estimated to provide structural information for plane-wave prediction. The proposed CRS-based slope depends on fewer parameters (two in 2D) than the conventional full CRS travel time (three in 2D), making it computationally efficient. Using the local slope, the third dimension is created using the plane-wave differential equation to predict the current trace from its neighbor traces and trimmed mean filtering (TMF) is applied in this dimension. The added dimension can be regarded as flattening the seismic events within a neighboring window and collapsing after application of the TMF. Synthetic and field datasets are employed to demonstrate the effectiveness of the proposed structure-oriented TMF. Compared with wavelet and plane-wave destruction methods, the proposed method can preserve more useful information with greater continuity in amplitude.

Improving the plane-wave destruction method by parameterizing the local slope for VSP wavefield separation

Improving the plane-wave destruction method by parameterizing the local slope for VSP wavefield separation

3-D pre-stack diffraction separation by extending the PWD method with parametrized local slope

SUMMARY Diffractions comprise the seismic response of subsurface geological discontinuities and thus can provide detailed geological information during 3-D seismic exploration. The separation of weak diffractions from specular reflections is challenging, especially when the diffractions and reflections have similar kinematical characteristics in the 3-D pre-stack case. Conventional separation methods often estimate the local slope based on optimization or the Hilbert transform, which directly depends on the distribution behaviour of seismic events and may lead to the aliasing effects of the hyperbolic reflected and diffracted slopes in the shot domain. In this study, a different method is employed: local slopes are parametrized and constrained to the normal moveout velocity and ray parameter, which can distinguish reflections and diffractions in the shot domain and enhance the stability and accuracy of local slopes. Interestingly, when the receiver line and the geological edge are coplanar, the corresponding edge diffractions and reflections exhibit extremely similar behaviour, rendering them indistinguishable. Considering this phenomenon, a 3-D pre-stack diffraction separation strategy is proposed based on the estimation of the local slopes in two orthogonal directions. Thus, the accurate local slope can be used for plane-wave destruction when separating diffractions in the 3-D pre-stack domain. Synthetic and field data applications demonstrate that the proposed separation strategy is effective and can obtain high-quality diffraction wavefields for detecting the subsurface discontinuous structure.

Diffraction Extraction and Least-Squares Reverse Time Migration Imaging for the Fault-Karst Structure With Adaptive Sampling Strategy

The ultra-deep fault-karst structure discovered in the Tarim Basin in Western China is a fractured-vuggy carbonate reservoir with great potential for development. The diffraction generated by fractures, small-scale caves and vugs is often used for reservoir identification and seismic interpretation. Since the diffraction is much weaker than the reflection, it is difficult to separate the diffraction from the full wavefield. We use a plane-wave destruction (PWD) filter to extract the diffraction from the full data. In order to obtain a high-accuracy and amplitude-preserving imaging profile, we use the least-squares reverse time migration (LSRTM) method to image the separated diffraction. The large amount of calculation is the most challenging problem of the LSRTM algorithm. In view of this, we develop an adaptive sampling strategy to improve computing efficiency and reduce memory requirement. We use a fault model, a vugs-fractures model, and a fault-karst model to demonstrate the effectiveness and practicability of the proposed method. The numerical examples show that the proposed method can enhance the imaging resolution of the fault-karst structure and save computing cost without losing accuracy. In addition, a test on field data processing demonstrates the advantages of our algorithm.

A MATLAB code package for 2D/3D local slope estimation and structural filtering

Local slope is an important attribute that can help distinguish seismic signals from noise. Based on optimal slope estimation, many filtering methods can be designed to enhance the signal-to-noise ratio of noisy seismic data. We present an open-source MATLAB code package for local slope estimation and corresponding structural filtering. This package includes 2D and 3D examples with two main executable scripts and related subfunctions. All code files are in the MATLAB format. In each main script, local slope is estimated based on the well-known plane-wave destruction algorithm. Then, the seismic data are transformed to the flattened domain by utilizing this slope information. Furthermore, the smoothing operator can be effectively applied in the flattened domain. We introduce the theory and mathematics related to these programs and present the synthetic and field data examples to show the usefulness of this open-source package. The results of local slope estimation and structural filtering demonstrate that this package can be conveniently and effectively applied to the seismic signal analysis and denoising.

Nonstationary local slope estimation via forward-backward space derivative calculation

The local slope estimated from seismic images has a variety of meaningful applications. Slope estimation based on the plane-wave destruction (PWD) method is a widely accepted technique in the seismic community. However, the PWD method suffers from sensitivity to noise in the seismic data. We have developed an improved slope estimation method based on the PWD theory that is more robust in the presence of strong random noise. The PWD operator derived in the Z-transform domain contains a phase-shift operator in space corresponding to the calculation of the first-order derivative of the wavefield in the space domain. The first-order derivative is discretized based on a forward finite difference in the traditional PWD method, which lacks the constraint from the backward direction. We have developed an improved method by discretizing the first-order space derivative based on an averaged forward-backward finite-difference calculation. The forward-backward space derivative calculation makes the space-domain first-order derivative more accurate and better at antinoise because it takes more space grids for the derivative calculation. In addition, we introduce nonstationary smoothing to regularize the slope estimation and to make it even more robust to noise. We determine the performance of the new slope estimation method with several synthetic and field data examples in different applications, including 2D/3D structural filtering, structure-oriented deblending, and horizon tracking.

Automatic Extraction of Seismic Data Horizon Across Faults

Most of the traditional horizon interpretation methods are based on the dip of the seismic data. Since the dip does not correctly reflect the discontinuous reflection characteristics of the events, these methods usually cannot extract the horizons containing faults well. Meanwhile, the field seismic data observed in complex areas are generally with low signal-to-noise ratio (SNR), which makes the extraction of horizons difficult. To address these problems, an automatic horizon extraction approach under fault control is investigated in this article. First, the horizon dip is obtained by using plane wave destruction (PWD), and the dip information can be utilized to control the overall trend of the horizon curve. Based on the dip information, we can also calculate the weight coefficients to characterize the faults. The fault characterization results can better guide the horizon extraction. Then, the dynamic time warping (DTW) is used for phase matching to further obtain the similar slope and describe the details of the horizontal curve. Finally, the horizon extraction equation is developed with the dip and phase information as the guide and solved iteratively to obtain the final horizon curve. The effectiveness of the presented approach is tested by both synthetic and field data. The results demonstrate that the presented approach can accurately pick the horizon information across faults and is more stable in the condition of low SNR compared with previous methods.

3-D Structural Complexity-Guided Predictive Filtering: A Comparison Between Different Non-Stationary Strategies

Predictive filtering methods are widely used in industry to remove random noise, owing to their stability and efficiency. Traditional predictive filtering methods use a fixed autoregressive order (filtering factor) in the spatial direction. However, denoising spatially varying seismic data has thus far been ineffective. In this study, the effect of non-stationary seismic data variations is overcome using local windowing or non-stationary denoising methods. We propose a non-stationary predictive filtering method in which an autoregressive model is constructed using spatially varying filtering factors. First, we evaluate the structural complexity of the global data based on a local window selection using plane-wave destruction. Then, adaptive filtering factors are proposed depending on the structural complexity of the seismic data. Finally, the autoregressive model containing the adaptive filtering factors is solved. We use three quality measures to evaluate the denoising performance: the signal-to-noise ratio (S/N), the peak signal-to-noise ratio (PSNR), and local similarity (LS). The proposed method acts on both synthetic and field data, including both pre- and post-stack seismic data. Compared with prior non-stationary filtering methods, experimental results demonstrate that structural complexity-guided predictive filtering enables efficient random noise attenuation and reduces signal leakage.

A Born–WKBJ Pre-Stack Seismic Inversion Based on a 3-D Structural-Geology Model Building

Estimation of subsurface properties by using the scattering integral equation is a method that finds increasing use in near-surface and shallow oil/gas exploration, based on seismic, low-frequency electromagnetic, and surface-radar surveys. The method can accurately simulate physical realizations induced by small-scale perturbations, but its accuracy depends on a suitable low-frequency property model. We propose a 3-D geological-structure-guided model building to provide a reliable low-frequency model and combine it with the Born-Wentzel-Kramers-Brillouin-Jeffreys (WKBJ)-approximation-based inversion algorithm. Instead of the traditional approach based on artificially interpreted horizons, we use 3-D seismic-slope attributes as lateral constraints, which contain more geological information. Plane-wave destruction (PWD) in 3-D is exploited to extract the 2-D slopes along the inline and crossline directions, which are the key factors in computing 3-D slopes. Then, by introducing the shaping regularization, we build low-frequency models by solving the inverse problem. Numerical analysis indicates that an appropriate background model is essential for seismic modeling with the Born-WKBJ approximation. The methodology is applied to synthetic and 3-D field data, and the examples show that it provides reliable background models and improves the inversion performance.

Prestack diffraction separation by parameterizing the reflection local slope

Diffracted waves provide an opportunity to detect small-scale subsurface structures because they give wide illumination direction of geologic discontinuities, such as faults, pinch outs, and collapsed columns. However, separating diffracted waves is challenging because diffracted waves have greater geometric amplitude losses and are generally weaker than reflections. To retain more diffracted waves, we have developed a prestack diffraction separation method based on the local slope pattern and plane-wave destruction (PWD) method. In general, it is difficult to distinguish between hyperbolic reflections and hyperbolic diffractions using data-driven local slope estimation in the shot domain. Therefore, we transfer slope estimation in the shot domain to velocity analysis in the common-midpoint domain and ray parameter calculation in the stack domain. The connection between local slope and the normal moveout velocity and the surface-ray parameter is known, which provides a novel approach for estimating the local slope of hyperbolic reflected waves in the shot domain. The estimated slope can provide an exact slope-based operator for the PWD method, thus allowing the PWD to separate diffracted waves from reflected waves in the shot domain. Synthetic and field data tests demonstrate the feasibility and effectiveness of our prestack diffraction separation method.

A Probabilistic Approach to Seismic Diffraction Imaging

Abstract We propose and demonstrate a probabilistic method for imaging seismic diffractions based on path-integral imaging. Our approach uses oriented velocity continuation to produce a set of slope-decomposed diffraction images over a range of plausible migration velocities. Utilizing the assumption that each partial image in slope is independent enables us to construct an object resembling a probability field from the slope-decomposed images. That field may be used to create weights for each partial image in velocity corresponding to the likelihood of a correctly migrated diffraction occurring at a location within the seismic image for that migration velocity. Stacking these weighted partial images over velocity provides us with a path-integral seismic diffraction image created using probability weights. We illustrate the principles of the method on a simple toy model, show its robustness to noise on a synthetic, and apply it to a 2D field dataset from the Nankai Trough. We find that using the proposed approach creates diffraction images that enhance diffraction signal while suppressing noise, migration artifacts, remnant reflections, and other portions of the wavefield not corresponding to seismic diffraction relative to previously developed diffraction imaging methods, while simultaneously outputting the most likely migration velocity. The method is intended to be used on data which has already had much of the reflection energy removed using a method like plane-wave destruction. Although it suppresses residual reflection energy successfully, this suppression is less effective in the presence of strong reflections typically encountered in complete field data. The approach outlined in this paper is complimentary to existing data domain methods for diffraction extraction, and the probabilistic diffraction images it generates can supplement existing reflection and diffraction imaging methods by highlighting features that have a high likelihood of being diffractions and accentuating the geologically interesting objects in the subsurface that cause those features.

Data-driven edge detectors for seismic data interpretation

We have developed a novel method to assist in seismic interpretation. The algorithm learns data-driven edge detectors for structure enhancement when applied to time slices of 3D poststack seismic data. We obtain the operators by distilling the local and structural information retrieved from patches taken randomly from the input time slices. The filters conform to an orthogonal family that behaves as structure-aware Sobel-like edge detectors, and the user can set their size and number. The results from marine Canada and New Zealand 3D seismic data demonstrate that our algorithm allows the semblance attribute to improve the delineation of subsurface channels. This fact is further supported by testing the method with realistic synthetic 2D and 3D data sets containing channeling and meandering systems. We contrast the results with standard plain Sobel filtering, multidirectional Sobel filters of variable size, and the dip-oriented plane-wave destruction Sobel attribute. Our method gives results that are comparable or superior to those of Sobel-based approaches. In addition, the obtained filters can adapt to the geologic structures present in each time slice, which reduces the number of unwanted artifacts in the final product.

Multi-domain diffraction identification: A supervised deep learning technique for seismic diffraction classification

The seismic wavefield arises from interactions of a source wavefield with subsurface heterogeneities as the wavefield propagates through the earth. In a conventional seismic processing workflow, the reflected portion of the wavefield is enhanced at the expense of the rest of the wavefield. While this is useful, considerable information which is contained outside of the reflections is lost. To alleviate this issue, we propose a deep learning technique which aims to separate the wavefield into three of the wavefield components: reflections, diffractions, and noise. This technique involves first performing several data domain transformations on the input and applying these as input classes on a pixel-by-pixel basis to guide the neural network. A simple separation is performed to remove the reflections and noise, allowing the diffractions to be processed independently. This technique, called Multi-domain diffraction identification, gives a high standard classification of the diffractions in a fraction of the time and computational cost of plane-wave destruction. These diffractions have then been removed from the data and compared with separation results from plane-wave destruction, showing similarities in the diffractions and demonstrating the denoising capability of the method.

Large Dip Calculation via Robust Nonstationary Plane-Wave Destruction

The omnidirectional plane-wave destruction (OPWD) algorithm can estimate the large dip by using circle-interpolating plane-wave destruction (PWD) filter but at the expense of causing potential instabilities due to the small values of the denominator in the regularized division problem. To mitigate the instability, one needs to use a relatively larger smoothing radius for a stronger regularization of the element-wise division, which however significantly decreases the resolution of dip estimation. We propose a new OPWD method without compromising the dip resolution for the large dip calculation by applying a nonstationary smoothness constraint to the model. We use a larger smoothing radius for areas that tend to cause instabilities and vice versa. The nonstationary smoothing is carried out in a simple and efficient recursion way. The synthetic and real seismic data examples demonstrate the performance of the proposed algorithm.

Velocity Analysis Using Separated Diffractions for Lunar Penetrating Radar Obtained by Yutu-2 Rover

The high-frequency channel of lunar penetrating radar (LPR) onboard Yutu-2 rover successfully collected high quality data on the far side of the Moon, which provide a chance for us to detect the shallow subsurface structures and thickness of lunar regolith. However, traditional methods cannot obtain reliable dielectric permittivity model, especially in the presence of high mix between diffractions and reflections, which is essential for understanding and interpreting the composition of lunar subsurface materials. In this paper, we introduce an effective method to construct a reliable velocity model by separating diffractions from reflections and perform focusing analysis using separated diffractions. We first used the plane-wave destruction method to extract weak-energy diffractions interfered by strong reflections, and the LPR data are separated into two parts: diffractions and reflections. Then, we construct a macro-velocity model of lunar subsurface by focusing analysis on separated diffractions. Both the synthetic ground penetrating radar (GPR) and LPR data shows that the migration results of separated reflections have much clearer subsurface structures, compared with the migration results of un-separated data. Our results produce accurate velocity estimation, which is vital for high-precision migration; additionally, the accurate velocity estimation directly provides solid constraints on the dielectric permittivity at different depth.

Diffraction imaging for the fault-karst structure by least-squares reverse time migration

The fault-karst reservoir, which evolved from the deformation and karstification of carbonate rock, is one of the most important reservoir types in Western China. Along the deep-seated fault zones, there are a lot of widely spread and densely distributed fractures and vugs. The energy of the diffractions generated by heterogeneous structures, such as faults, fractures, and vugs, is much weaker than that of the reflections produced by continuous formation interface. When using the conventional full-wavefield imaging method, the imaging results of continuous layers usually cover small-scale heterogeneities. Given that, we have used a plane-wave destruction filter to separate the diffractions from the full data and image the separated diffractions using the least-squares reverse time migration (LSRTM) method. We use several numerical examples to demonstrate that the newly developed diffractions using LSRTM can improve the definition of the heterogeneous structures, characterize the configuration and internal structure of the fault-karst structure well, and enhance the interpretation accuracy for the fault-karst reservoir.