Wavefield Decomposition Research Articles

Fault slip and seismic source response characteristics under induced stress wave

As coal mining depth and structural complexity increase, the failure severity of mining-induced fault activation leading to rock bursts escalates. Fault fracture zones, consisting of various secondary structures, are essential for understanding tectonic evolution and seismic wave propagation. The interaction between mining-induced stress waves and in-situ stress complicates the dynamics and activation markers of fault fracture zones. This paper aims to clarify the patterns of stick–slip instability and stress evolution in these zones under coal mining-induced stress waves. Using theoretical models and continuous-discrete coupling simulations, the study explores the dynamic response of fault fracture zones in the meta-instability stage, the micro-scale fracture force chain structure, and the distribution and synergistic instability of fault plane seismic sources. The research shows that fault fracture zones changes stress wave propagation path and energy redistribution due to its heterogeneity leads to multiple times decomposition of wave field. Minor delamination between the hanging wall and footwall can trigger unstable slip. Tensional seismic sources with extensive failure drive fault slip. Dynamic stress waves disrupt force chains near seismic sources, increasing hazard levels. Static in-situ stress affects shear seismic sources by influencing porosity and crack angles. Seismic sources along the fault strike transition from divergent to concentrated, trending horizontally. In the meta-instability stage, the initial fracture area locks, with strong structures causing cohesive fractures in the middle of the fault zone, releasing strain energy and forming a sudden increase in slip intensity. These findings provide crucial insights into fault fracture-development-activation markers, fault region stress deformation evolution mechanisms, and risk control of fault-induced rock bursts.

The qP- and qSV-wave separation in 2D vertically transversely isotropic media and their applications in elastic reverse time migration

Compressional and shear wave separation is an important step in anisotropic elastic reverse time migration (ERTM). With separated wavefields, we can generate images between different wave types and reveal more subsurface physical properties, as well as remove unwanted crosstalk and improve image quality. Traditional Helmholtz decomposition based on divergence and curl operations for isotropic media cannot be directly extended to vertically transversely isotropic (VTI) media. Wave-mode separation methods, similar to the nonstationary spatial filter and Poynting vector, cannot preserve the phase and amplitude information of the original coupled wavefield, thus limiting their application in ERTM. Currently, the anisotropic wavefield decomposition methods include the wavenumber-domain approach, the low-rank approximation, and other separation approaches based on different approximations, e.g., weak or elliptical anisotropy. These methods are either computationally intensive or involve large separation errors, especially in models with strong heterogeneities and anisotropy. The VTI wavefield separation operator is essentially defined in a mixed space-wavenumber domain. We introduce scalar operators to transfer operations from this mixed space-wavenumber domain to the space domain. The local wave propagation direction in the scalar operators is estimated using the Poynting vector, which is highly computationally efficient in the space domain. When we apply the wave separation method to ERTM, we not only obtain the vectorized qP and qSV waves but also retrieve the scalar qP wavefield. The scalar and vector wavefields preserve the amplitude and phase information in the original coupled wavefield. For anisotropic ERTM, we suggest using the scalar imaging condition to generate the PP image and the magnitude- and sign-based vector imaging condition to produce the PS image, both having higher image accuracy than the dot-product imaging condition. Numerical examples are used to validate our anisotropic wavefield separation method and the related ERTM workflow.

Elastic reverse time migration based on first-order velocity-dilatation-rotation equations using the optical flow vector

The determination of the P- and S-wave propagation directions is crucial for wavefield decomposition, polarity reversal correction, and noise suppression in elastic reverse time migration (RTM). Compared with the conventional decoupled elastic wave equation, the first-order velocity-dilatation-rotation equations enable more accurate computation of propagation directions for P and S waves. Moreover, compared with the Poynting vector, the optical flow vector signifies the wavefield propagation directions more accurately. To effectively enhance the accuracy of elastic wave imaging, we develop an elastic RTM based on first-order velocity-dilatation-rotation equations using the optical flow vector. Numerical tests illustrate that our method, with or without noise, can better eliminate migration artifacts and improve the imaging accuracy of the elastic RTM than conventional methods, achieving more accurate wavefield decomposition and superior S-wave polarity reversal correction.

Coherent Noise (Ground roll) Consideration: Local Wave-field Decomposition (LWD) Based Approaches to Suppression

There is always a signal and a noise component in seismic data. Noise can be defined as any recorded energy that tampers with the desired signal of interest. Although it might be difficult to separate signal from noise due to the variety of noise kinds, effective noise suppression is crucial for high-quality imaging. Surface waves or ground roll are a prominent source-generated coherent noise in exploration seismology. Ground roll contains little to no information about the deeper subsurface as it moves laterally through the earth’s near surface. The low-frequency contents and strong amplitudes of these arrivals often mask recordings of body waves reflected by deeper subsurface targets. This discussion paper will describe ground rolls, a significant form of seismic coherent noise, as well as their unique characteristics, how they appear on acquired seismic data, the significance of suppressing them in seismic processing applications, and an examination of local wave-field decomposition (LWD) techniques and their applications.

Wavefield decomposition for viscoelastic anisotropic media

Separating wave modes on seismic records is an essential step in imaging of multicomponent seismic data. Viscoelastic anisotropic models provide a realistic description of subsurface formations that exhibit anisotropy of velocity and attenuation. However, mode separation has not been extended to viscoelastic anisotropic media yet. Here, we propose an efficient approach to wavefield decomposition that takes velocity and attenuation anisotropy into account. Our algorithm operates in the frequency-wavenumber domain and, therefore, is suitable for general dissipative models. We present exact equations for wavefield decomposition in arbitrarily anisotropic attenuative homogeneous media. Then the proposed approach is applied to viscoelastic constant-[Formula: see text] VTI (transversely isotropic with a vertical symmetry axis) models. Numerical examples demonstrate the accuracy and efficiency of our approach for piecewise-homogeneous media characterized by pronounced velocity and attenuation anisotropy.

Generative adversarial network-enhanced directional seismic wavefield decomposition and its application in reverse time migration

Reverse time migration (RTM) is an accurate method for imaging complex geologic structures without imposing any dip limitations. However, a large amount of high-amplitude low-frequency noise, which is mainly generated by the crosscorrelation of source and receiver wavefields propagating in the same directions, seriously contaminates the image quality. The causal imaging condition with separated up- and downgoing wavefields is an effective approach to reduce these low-frequency artifacts. Explicit up- and downgoing wavefield decomposition based on the Hilbert transform is computationally expensive due to additional wavefield extrapolation and storage for the imaginary parts. Directionally propagating wavefields have distinctive kinematic patterns such as traveltime and wavefront curvature, which provide us an opportunity to implement the wavefield decomposition using the statistical neural network method. Using extrapolated wavefields as the input and the decomposed up-, down-, left-, and rightgoing wavefields as the labeled data, we train a pair of generative adversarial networks to predict the directional wavefields. The training data sets are generated using seismic full-waveform modeling and explicit wavefield decomposition based on the Hilbert transform. Then, the decomposed directional wavefields are incorporated into a novel imaging condition that depends on the subsurface dip angles to compute the reflectivity perpendicular to the reflectors. Numerical experiments demonstrate that our method can produce accurate directional wavefield decomposition results and high-quality reflectivity images without low-wavenumber artifacts.

The effect of 3D surface roughness on acoustic wave propagation in a cylindrical waveguide

This paper studies the acoustic wave scattering and attenuation in a cylindrical waveguide (pipe) with wall roughness varying along all three dimensions and roughness height smaller than the acoustic wavelength. Using the decomposition of the acoustic wave field into deterministic and random components, small perturbation method and Fourier transform the analytical solution of a 3-D averaged acoustic wave field is obtained. The correction term describing the mechanism of wave attenuation caused by roughness and determined by the modal cross-talk is also derived. The solution for the plane wave is validated in the frequency range extended well beyond the second cut-off frequency, where the crosstalk between the fundamental and non-axisymmetric modes are observed. The analytical solution is compared with the numerical results obtained with the Monte-Carlo method and Finite Element solver. The numerical study results have demonstrated a close agreement with the analytical solution for the averaged sound field, dispersion curves, and the wave attenuation effect expressed as the wavenumber correction term. A key novelty of this work is a comprehensive analysis of wave dispersion and cut-off frequency changes due to the presence of 3-D wall roughness in a pipe.

Reverse time migration angle gathers in acoustic anisotropic media using direction vectors

The application of direction vectors in the generation of reverse time migration (RTM) angle gathers in complex acoustic anisotropic media often encounters three main challenges: not pointing to the phase-velocity direction (PVD) of the Poynting vector, inaccuracy due to overlapping wavefields, and instability due to zero points of the direction vector. In general anisotropic media, the standard Poynting vector indicates the group-velocity direction (GVD), whereas reflection and transmission phenomena rely on the PVD. Anisotropy introduces discrepancies between the GVD and the PVD. To overcome this issue, we use the so-called PVD vector to directly calculate the PVD from anisotropic wavefields, eliminating the need for an approximated conversion from the GVD to the PVD. To mitigate the inaccuracy problem, we apply the Hilbert transform-based wavefield decomposition method to separate overlapping wavefields into their up/down components, and then we calculate the PVDs using the separated wavefields. To tackle the instability problem, we incorporate the additionally simulated quadrature wavefield during the wavefield decomposition procedure. By combining the direction vector of the quadrature wavefield with that of the original wavefield, we can eliminate the zero points and thus obtain a stabilized PVD vector. With those problems solved or alleviated, we present a scheme for the generation of anisotropic RTM angle gathers in complex areas. Two numerical examples using synthetic data sets demonstrate our method’s effectiveness.

Amplitude-preserving P-/S-wavefield separation with the discontinuous Galerkin method on unstructured meshes

The decoupling of P and S waves is an essential prerequisite for elastic reverse time migration, which effectively reduces crosstalk artifacts, but most wavefield separation algorithms are implemented on uniform rectangular grids. We develop an amplitude- and phase-preserving P- and S-wavefield separation approach on unstructured meshes, which can effectively decompose the original elastic wavefield into P and S wavefields. The isotropic case is considered. With the aid of viscoelastic theory, we choose to attenuate P or S waves and preserve the other wave mode, so as to achieve wavefield decomposition. Viscoelastic wave equations are first reformulated as decoupling wave equations with a selective strong attenuation. We then use the discontinuous Galerkin (DG) method to simulate decoupling P or S wavefield propagation on triangular and tetrahedral meshes. We adopt a quadrature-free DG approach and the arbitrary mesh is mapped into the reference mesh for numerical calculation, where no additional volume and surface integrations are involved. The amplitude and phase information of this vector decomposition agrees with that of the original elastic data. Four numerical examples are used to demonstrate the superior performance of this vector decomposition algorithm. The isotropic example indicates the applicability and correctness of our scheme and the second example displays superiority in handling strong velocity contrasts. The third example exhibits mesh flexibility in dealing with complex structures, such as caves, faults, and undulating surfaces. The last example indicates the effectiveness of our developed algorithm extended to a 3D case.

Excitation time imaging condition reverse time migration based on physics-informed neural network traveltime calculation with wavefield decomposition using optical flow vector

Abstract Although the excitation-time imaging condition offers a lower memory consumption and higher computational efficiency compared to cross-correlation imaging condition, it has not been widely used in industrial applications because of the accuracy problem of traveltime calculation and the influence of low-wave-number noise. In this paper, we introduce the physics-informed neural network (PINN) algorithm to achieve a high-precision traveltime calculation of the source forward wavefield. Subsequently, we introduce a technique for high-precision wavefield decomposition of the reverse-time wavefield via the optical flow vector, enabling us to realize a correlation-weighted stacking imaging of each wavefield. Model experiments and real data processing show that the proposed traveltime calculation algorithm based on PINN offers high accuracy and good applicability in the excitation time reverse-time migration imaging of complex models, and correlation-weighted stacking imaging based on optical flow vector-based wavefield separation can significantly suppress the noise with low wavenumber and achieve high-precision imaging of complex models.

Multi-image, reverse time, and Kirchhoff migrations with compact Green’s functions

Using compact representations of Green’s functions we derive a common framework for reverse time migration (RTM) and Kirchhoff migration. These compact Green’s functions (CGFs) are 3D volumes containing traveltimes and amplitudes for the N most representative events in the upcoming/downgoing decomposed 4D wavefields originating from a point source. Within this framework, we implement an RTM algorithm using a multivalued excitation time/amplitude imaging condition. This new approach produces four complementary imaging volumes (different combinations of source and receiver decomposed wavefields) and angle/azimuth gathers with computational effort less than 15% greater than that of plain (one image and no gathers) RTM algorithms. The advantages of separating the image volume into four complementary volumes are well established in the literature (low-frequency noise separation and turning wave imaging); however, its use has been limited by the computational cost. Despite using two source propagations to decompose the source wavefield, we reduce the computations to less than 20% of a single source propagation by performing finite-difference propagation with half the frequency limit used in the receiver wavefield propagation. The combination of CGF and an excitation time/amplitude imaging condition allows receiver wavefield decomposition with only one wavefield propagation. Our RTM algorithm constructs angle/azimuth gathers using a postmigration computation of the source and receiver wavefield’s propagation directions. To compute the propagation directions after migration, we use a new concept: the cumulative wavefield volumes, which are 3D, imaging-condition-guided compressions, of the 4D source and receiver wavefields. We also use CGF to implement a Kirchhoff migration algorithm that produces four complementary image volumes with RTM-like quality. Furthermore, we present synthetic and field data examples to clarify the new concepts and illustrate the results obtained using these methods.

Seismic reverse time migration based on biaxial wavefield decomposition

Seismic images generated by reverse time migration (RTM) are often contaminated by low-wavenumber artifacts. Decomposition of up- and downgoing waves during propagation can effectively reduce these artifacts. However, decomposition along the vertical axis is not sufficient to eliminate the migration artifacts. We introduce biaxial wavefield decomposition to decompose seismic wavefields in the lateral and vertical directions. After decomposition, there are 16 crosscorrelation terms between different components, and there are only four crosscorrelation terms that can be used separately to image flat layers and tilted interfaces. Within these four terms, the remaining artifacts can be easily identified and reduced by other methods, and the resolution can be further improved by adjusting the weights of the four terms. The decomposition method based on the analytic wavefield via the Hilbert transform has been shown to agree with the viscoacoustic wave equation with fractional spatial derivatives. Therefore, this biaxial wavefield decomposition method is suitable for decomposing the wavefields for the attenuation-compensated RTM. The decomposed and recombined migration results can better image a complex subsurface structure with high resolution.

Converted-wave reflection traveltime inversion with free-surface multiples for ocean-bottom-node data

Advancements in ocean-bottom-node (OBN) technologies have enabled the recording of high-quality multicomponent seismic data, which can provide crucial information about subsurface properties through elastic seismic imaging. However, imaging multicomponent data is challenging due to the requirement for P- and S-wave velocity models. Conventional processing relies on estimating the S-wave velocity model using a primary converted wave (C wave) because the pure S-wave primaries are not available if using standard air-gun sources. When a free surface is present, the C waves recorded with geophones can be contaminated by source-side P-wave multiples, especially water-layer reverberations, which are difficult to remove even using state-of-the-art wavefield decomposition methods. These C-wave multiples can cause significant mismatches between synthetic and observed data during reflection traveltime or waveform inversion if only primary P-to-S (PS) conversions are simulated. To address these issues and reliably build an S-wave velocity model for PS imaging, we develop a C-wave reflection traveltime inversion method that takes source-side free-surface multiples into account. The traveltime misfit of C-wave data is extracted using dynamic image warping to ensure a better match between the synthetic and observed data. The functional gradient of the objective function is derived using the adjoint state method. Based on sensitivity kernel analyses, a convenient gradient preconditioning strategy is developed to robustly separate the contribution of primary and multiple C waves during backpropagation. This strategy can effectively mitigate the high-wavenumber crosstalk associated with nonphysical wavepaths in the gradient and thus allow more accurate updating for the S-wave velocity model. The synthetic data and shallow-water OBN data from the East China Sea indicate that this approach can reliably recover the S-wave macrovelocity structures for PS imaging.

Crosswell frequency-domain reverse time migration imaging with wavefield decomposition

Abstract Crosswell seismic technique can provide high-resolution imaging and monitoring of the subsurface. However, compared to the surface seismic, crosswell data contain more complex wave components, which increases the difficulty of seismic processing and migrations. Conventional acoustic reverse time migration (RTM) mainly uses the cross-correlation of the source forward and the receiver backward wavefields. The redundant information generated by cross-correlation may undermine the imaging reliability in the crosswell models. Thus, we develop a novel wavefield decomposition imaging condition and only used cross-correlation information of incident and reflection waves in the same propagation directions, which eliminates the artifacts generated from the cross-correlation of wave information unrelated to reflections in the crosswell image. We perform RTM in the frequency domain to maintain efficiency in multi-shot problems. A mono-frequency wavefield decomposition method is applied to separate and process the seismic data. The forward and backward wavefields are reclassified into the up- and downpropagating components. The L1 norm is introduced to enhance the robustness of the proposed imaging method. We then use this method to synthesize data from layering models and analyze the imaging results generated from each pair of cross-correlations using source and receiver wavefields. Results show that the cross-correlation information belonging to the same propagation contributes most to the crosswell image, and the other information always generates migration noises. Moreover, we apply the proposed method to a real-field dataset. Processing results validate the effectiveness of the proposed means for eliminating false events in the crosswell models and improving image quality.

Correction to: Joint estimation of S-wave velocity and damping ratio of the near-surface from active Rayleigh wave surveys processed with a wavefield decomposition approach

Correction to: Joint estimation of <i>S</i>-wave velocity and damping ratio of the near-surface from active Rayleigh wave surveys processed with a wavefield decomposition approach

Steeply dipping structure imaging with prismatic waves incorporating wavefield decomposition

AbstractPrismatic waves in seismic data can effectively delineate steeply dipping subsurface structures. However, the conventional migration of prismatic wave either requires the exact location of basement reflectors embedded in the accurate migration velocity model or the explicit isolation of prismatic wave from the recorded data to avoid crosstalk artefacts caused by mistaken imaging of primary reflections. Neither of the requirements is a trivial task for field data application with complicated subsurface structures. To image steeply dipping structures with an accurate but smooth enough migration velocity and without the need to extract prismatic waves from the recorded data, we analyse the prismatic imaging condition based on wavefield decomposition. In the up‐ and down‐going wavefield decomposition, the prismatic imaging condition can effectively remove the high‐wavenumber artefacts with incorrect polarity. However, the expected steeply dipping image is buried in low‐wavenumber noises. In contrast, the prismatic imaging condition based on left‐ and right‐going wavefield decomposition can accurately isolate the artefacts induced by the mistaken migration of primary waves from the steeply dipping interfaces in the image and is free of low‐wavenumber noises. Based on this analysis, we develop a reverse time migration workflow using the modified prismatic imaging condition to depict steeply dipping structures: First, we use the primary imaging condition based on the up‐and‐down‐going wavefield decomposition to obtain an image that can approximate the basement reflectors. Then, we use the modified prismatic imaging condition based on left‐ and right‐going wavefield decomposition to recover the steep interfaces. Finally, a combined subsurface image containing both basement reflectors and faults or steeply dipping structures is generated. We verify the feasibility and robustness of the modified prismatic imaging condition based reverse time migration method for delineating steeply dipping structures using several synthetic tests.

Correction to: Joint estimation of S-wave velocity and damping ratio of the near-surface from active Rayleigh wave surveys processed with a wavefield decomposition approach

Correction to: Joint estimation of <b>S</b>-wave velocity and damping ratio of the near-surface from active Rayleigh wave surveys processed with a wavefield decomposition approach

Three-dimensional elastic reverse-time migration using a high-order temporal and spatial staggered-grid finite-difference scheme

Three-dimensional (3D) elastic reverse-time migration (ERTM) can image the subsurface 3D seismic structures, and it is an important tool for the Earth’s interior imaging. A common simulation kernel used in 3D ERTM is the current staggered-grid finite-difference (SGFD) method of the first-order elastic wave equation. However, the mere second-order accuracy in time of the current SGFD method can bring non-negligible time dispersion, which reduces the simulation accuracy and further leads to the distortion of the imaging results. This paper proposes a vector-based 3D ERTM using the high-order accuracy SGFD method in time to obtain high-accuracy images. This approach is a new high-resolution ERTM workflow that improves the imaging accuracy of conventional ERTM from numerical simulation. The proposed ERTM workflow is established on a quasi-stress–velocity wave equation and its vector wavefield decomposition form. Advanced SGFD schemes and their corresponding coefficients with fourth-order temporal accuracy solve the quasi-linear wave equation system. The normalized dot product imaging condition produces high-quality images using high-accuracy vector wavefields solved using the SGFD method. Through the numerical examples, we test the simulation efficiency and analyze how temporal accuracy in numerical simulations affects migration imaging quality. We include that the proposed method obtains highly accurate images.

Joint estimation ofS-wave velocity and damping ratio of the near-surface from active Rayleigh wave surveys processed with a wavefield decomposition approach

SUMMARYThe use of surface wave measurements to derive an S-wave velocity profile of the subsurface has become a widely applied procedure; however, their potential use to reconstruct the S-wave material damping properties of the subsoil is generally overlooked, due to the difficulties in obtaining consistent surface wave amplitude information from field data and translating them into robust estimates of the dissipative properties of the near-surface. In this work, we adapt a wavefield decomposition technique for the processing of elastic surface wave data to the extraction of the complete set of properties of Rayleigh waves generated by a controlled source and propagating in dissipative geomaterials. Retrieved information includes multimodal phase velocity and ellipticity as well as the frequency-dependent attenuation coefficient. We exploit the key advantages of wavefield decomposition processing (joint interpretation of multicomponent recordings, coupled estimation of wave propagation parameters, modelling of multiple superimposing modes) to maximize the robustness of the retrieval of Rayleigh wave properties, especially of the dissipative ones. For the subsequent interpretation of Rayleigh wave dispersion, ellipticity and attenuation data we implement a joint Monte Carlo inversion yielding a coupled estimate of S-wave velocity and damping ratio profile for the subsurface; we incorporate a series of geophysical constraints to narrow down the searched parameter space to realistic soil models. We apply this processing and inversion scheme to a bespoke synthetic data set and to a field survey for the characterization of a strong motion station; in both cases, we succeed in retrieving Rayleigh wave multimodal dispersion, ellipticity and attenuation curves. From the inversion of data from the simulated seismogram we are able to reconstruct the properties of the synthetic model. As for the real case, we determine an S-wave velocity and damping ratio model for the soil column below the station, through which we are able to model the inelastic earthquake local response observed at the site. Basing on the results obtained for the real case, we argue that one of the advantages brought by our processing method—the possibility to process active Rayleigh wave data acquired by a 2-D array illuminated by different source positions—may play a key role in allowing to retrieve dissipative properties of the near-surface closer to the material damping of the soil materials, and less influenced by scattering determined by possible discontinuities in the subsurface.

Diffraction Separation and Least-Squares Imaging Based on Multiscale and Multidirectional Wavefield and Image Decomposition

Diffraction Separation and Least-Squares Imaging Based on Multiscale and Multidirectional Wavefield and Image Decomposition