Reverse Time Migration Research Articles

Ocean bottom dual-sensorQ-compensated elastic least-squares reverse time migration based on acoustic and separated-viscoelastic coupling equations

The ocean bottom dual-sensor (OBD) observation system places water detectors (pressure sensors) and land detectors on the irregular seabed interface to receive acoustic pressure fields and elastic wavefields, respectively. These data are usually applied to effectively remove ghost waves and ringing interference in the seawater layer, rather than being jointly used for migration. We propose an ocean bottom dual-sensor viscoacoustic and separated-viscoelastic coupled Q-compensated least-squares reverse time migration (OBD-VSV- QLSRTM) in curvilinear coordinates. In this method, to solve the Q-compensated elastic inverse problem, we jointly use the recorded acoustic pressure and elastic multicomponent seismic data from the OBD observation system. A new misfit function in the sense of least-squares inversion is constructed based on viscoacoustic and separated viscoelastic wavefields. Acoustic and separated viscoelastic equations are used to describe the acoustic wavefield in the acoustic medium and the Q-compensated P and S wavefields in the underlying viscoelastic medium, respectively. On the acoustic-viscoelastic interface, we implement a stable governing equation to ensure continuous and steady transmission of Q-compensated stresses in the subseabed and pressure in the seawater. To address the irregular seabed problem, we mesh the acoustic-viscoelastic models onto curvilinear grids and apply coordinate transformations to map the models and equations to a new curvilinear coordinate system. We derive viscoacoustic and separated-viscoelastic coupled adjoint and demigration operators in the curvilinear coordinates, enabling linear acoustic-viscoelastic modeling and stable receiver-side back-propagated wavefield continuation. Numerical examples conducted on two typical acoustic-viscoelastic models demonstrate that our proposed OBD-VSV- QLSRTM in curvilinear coordinates can produce highly accurate P- and S-wave images efficiently.

Efficient reverse time migration method in tilted transversely isotropic media based on a pure pseudoacoustic wave equation

In general, velocity anisotropy in shale media has been widely observed in laboratory and field work, which means that disregarding this characteristic can lead to inaccurate imaging locations when data are imaged with reverse time migration (RTM). Wavefields simulated with the conventional coupled pseudoacoustic wave equation may introduce S-wave noise and this equation is only valid in transversely isotropic media ([Formula: see text]). Certain decoupled qP-wave equations require the use of the pseudospectral method, which makes them computationally inefficient. To address these issues, we develop a new pure qP acoustic wave equation based on the acoustic assumption, which can be solved more efficiently using the finite-difference (FD) method. This equation can also be used in the forward-modeling process of RTM in tilted transversely isotropic (TTI) media. First, we perform a Taylor expansion of the root term in the pure qP-wave dispersion relation. This leads to an anisotropic dispersion relation that is decomposed into an elliptical anisotropic background factor and a circular correction factor. Second, we obtain the pure qP-wave equation in TTI media without a pseudodifferential operator. The new equation can be efficiently solved using FD methods and can be applied to RTM in TTI media with strong anisotropy. Our method indicates greater tolerance to numerical errors and is better suited for strong anisotropy, as compared with previously published methods. Numerical examples indicate the high kinematic and phase accuracy of our pure qP-wave equation along with its stability in TTI media characterized by ([Formula: see text]). By using a sag model and an overthrust TTI model, we determine the efficiency and accuracy of our TTI RTM.

Wavefield simulation and reverse time migration for acoustic TTI media

Seismic imaging necessitates precisely separating P and S waves to mitigate undesirable crosstalk between them. Failure to properly handle this crosstalk can lead to distorted or misinterpreted images. In an elastic anisotropic medium, the polarization of a P wave is not necessarily parallel to its propagating direction, making the separation of P and S waves more difficult than in the case of an elastic isotropic medium. A pure acoustic transversely isotropic (TI) wave equation involves a mixed-domain problem. This usually means the space dependencies and wavenumbers are coupled in the wavefield extrapolator. An efficient solution to the wavefield requires a separation between the space dependencies and wavenumbers in the extrapolator. There are two primary approaches: (1) an analytical separation of the mixed-domain term; and (2) a numerical solution to the mixed-domain term, such as low-rank and Poynting vector methods. In this study, the acoustic approximation is derived by setting the S-wave phase velocity to zero in all phase directions. An analytical separation is developed in this study by employing a Taylor series to linearize the anellipticity term, thereby decoupling the space-dependent and wavenumber-dependent variables within the wavefield extrapolator. The kinematics analysis demonstrates that our method has competitive phase velocity accuracy compared with existing methods. Moreover, the corresponding TI acoustic wave equation can be efficiently solved by the hybrid finite-difference/pseudospectral method. In a 2D case, it only requires one fast Fourier transform, two inverse Fourier transforms, and a few additional spatial differentiations at each time step. Remarkably, our wavefield solution remains independent of the wavefield heterogeneity (as observed in the low-rank approach) and is immune to wavefield interference (as encountered in the Poynting vector method). The developed acoustic approximation ensures the absence of any S-wave artifacts with relatively cheap computation. Numerical examples indicate our acoustic tilted transversely isotropic wave equation is reliable for accurate wavefield modeling and reverse time migration.

Multi-Scale Acoustic Velocity Inversion Based on a Convolutional Neural Network

The full waveform inversion at this stage still has many problems in the recovery of deep background velocities. Velocity modeling based on end-to-end deep learning usually lacks a generalization capability. The proposed method is a multi-scale convolutional neural network velocity inversion (Ms-CNNVI) that incorporates a multi-scale strategy into the CNN-based velocity inversion algorithm for the first time. This approach improves the accuracy of the inversion by integrating a multi-scale strategy from low-frequency to high-frequency inversion and by incorporating a smoothing strategy in the multi-scale (MS) convolutional neural network (CNN) inversion process. Furthermore, using angle-domain reverse time migration (RTM) for dataset construction in Ms-CNNVI significantly improves the inversion efficiency. Numerical tests showcase the efficacy of the suggested approach.

Consistency of the inverse scattering imaging condition, the energy norm imaging condition and the impedance kernel in acoustic and elastic reverse-time migration

Abstract In this work, we draw connections between the imaging conditions using the impedance kernel, the inverse scattering imaging condition, and the energy norm imaging condition in acoustic and elastic reverse-time migration (RTM). Traditional RTM often introduces large low-wavenumber artifacts that degrade image quality in intricate geological structures with large velocity variations. In practice, the Laplacian filter is commonly used to remove these low-wavenumber artifacts, but it changes the image wavenumber spectrum. The advanced imaging conditions of the inverse scattering, the energy norm, and the impedance kernel can effectively remove the low-wavenumber artifacts while not changing the wavenumber spectrum. This study aims to build a connection between these three types of imaging conditions by conducting detailed analysis in the wavenumber domain for acoustic and elastic RTMs. We find that they are exactly the same except for the varying weights of the source-receiver wavefield cross-correlation. All three imaging conditions can generate clear RTM images that are not affected by low-wavenumber artifacts. Numerical examples for a simple model, Sigsbee 2a, and BP models verify the consistency of these three imaging conditions and show their advantage over conventional simple zero-lag cross-correlation imaging conditions. This is important for improving the quality and reliability of seismic imaging technology.

Efficient least-squares reverse time migration in TTI media using a finite-difference solvable pure qP-wave equation

Abstract The anisotropic characteristics of underground media play a crucial role in seismic wave propagation and should be accounted for during seismic imaging. The least-squares reverse time migration (LSRTM) method achieves ideal imaging results by suppressing migration artifacts and balancing amplitude. Therefore, pure quasi-P (P-qP) wave equations in tilted transversely isotropic (TTI) media have been widely used to implement LSRTM, owing to their ability to produce stable and noise-free wavefields. However, solving the anisotropic P-qP-wave equations typically necessitates the use of spectral-based methods, making them computationally inefficient, especially in 3D applications. In this study, we first develop a P-qP-wave equation in TTI media that can be efficiently computed through the finite-difference (FD) approach. Numerical tests show that, in comparison to the previous TTI P-qP-wave equation, the newly derived FD solvable TTI P-qP-wave equation yields reasonably accurate and highly efficient wavefield simulations. Then, building on our newly derived wave equation, we derive its adjoint migration and demigration operator to implement TTI LSRTM. Two synthetic examples suggest that the newly presented P-qP-wave TTI LSRTM approach effectively correct for the anisotropy effects, providing high-quality imaging results. Additionally, our approach has superior computational efficiency over the conventional P-qP-wave TTI LSRTM technique based on a hybrid FD pseudo-spectral (HFDPS) solver.

Imaging of cylindrical inhomogeneites in a parallel plate waveguide with reverse time migration method

Abstract While reverse time migration (RTM) algorithm is commonly used in geophysical explorations, this paper addresses the RTM imaging procedure for reconstructing of lossy dielectric discontinuities in a planar waveguide using electromagnetic waves at a single frequency. The direct problem of the related configuration is solved via method of moments (MoM) to produce the synthetic scattered data to be used in RTM. The achievements of the method are examined and verified by including different numerical examples. It is shown that the RTM approach can be used as an alternative imaging methodology in parallel plate waveguide problems.

High-resolution source imaging and moment tensor estimation of acoustic emissions during brittle creep of basalt undergoing carbonation

SUMMARY As the high-frequency analogue to field-scale earthquakes, acoustic emissions (AEs) provide a valuable complement to study rock deformation mechanisms. During the load-stepping creep experiments with CO2-saturated water injection into a basaltic sample from Carbfix site in Iceland, 8791 AE events are detected by at least one of the seven piezoelectric sensors. Here, we apply a cross-correlation-based source imaging method, called geometric-mean reverse-time migration (GmRTM) to locate those AE events. Besides the attractive picking-free feature shared with other waveform-based methods (e.g. time-reversal imaging), GmRTM is advantageous in generating high-resolution source images with reduced imaging artefacts, especially for experiments with relatively sparse receivers. In general, the imaged AE locations are found to be scattered across the sample, suggesting a complicated fracture network rather than a well-defined major shear fracture plane, in agreement with X-ray computed tomography imaging results after retrieval of samples from the deformation apparatus. Clustering the events in space and time using the nearest-neighbour approach revealed a group of ‘repeaters’, which are spatially co-located over an elongated period of time and likely indicate crack, or shear band growth. Furthermore, we select 2196 AE events with high signal-to-noise-ratio (SNR) and conduct moment tensor estimation using the adjoint (backpropagated) strain tensor fields at the locations of AE sources. The resulting AE locations and focal mechanisms support our previously assertion that creep of basalt at the experimental conditions is accommodated dominantly by distributed microcracking.

Study Investigates Seismic Monitoring for Carbon Storage Leak Detection

_ This article, written by JPT Technology Editor Chris Carpenter, contains highlights of paper IPTC 22980, “Carbon Storage Leak Detection Through Seismic FWI and RTM: Different Survey Analyses,” by Sajjad Amani, Kyoto University. The paper has not been peer reviewed. Copyright 2023 International Petroleum Technology Conference. Reproduced by permission. _ In the complete paper, marine seismic data processing is investigated as a tool for monitoring possible leakages in geological carbon storage. Because of the great importance of storage permanence, a precise leakage-monitoring strategy is crucial. The proficiency of seismic monitoring solutions for leakage monitoring can be affected by shallower layers as a result of structure, seismic wave attenuation, and leak size. The authors explore two popular seismic monitoring methods used in this application in different scenarios: full waveform inversion (FWI) and reverse-time migration (RTM). Introduction Among the various carbon capture and storage (CCS) options, underground storage in saline aquifers is the best-understood solution. To assure storage consistency and permanence, finding the best strategy to precisely detect possible carbon leaks is essential. A perfect method must demonstrate the difference between stored CO2 and injected CO2 to detect potential fast- and slow-leakage areas. The seismic monitoring technique is the most efficient approach in this respect. Two popular tools for seismic monitoring are FWI and RTM. Several studies of their use in this application have been conducted. However, previous research did not analyze different survey arrays for carbon-leak detection using FWI and RTM. The current research aims to investigate quantitative aspects of CCS monitoring to conduct sensitivity analysis of the three different survey arrays [vertical seismic profile (VSP), crosswell, and surface] for different amounts of CO2-storage leakage in a saline aquifer reservoir. The capability of seismic-imaging methods for small amounts of leakage was tested. Comparison of these three arrays using monitoring methods such as RTM and FWI reveals their pros and cons in providing detailed information about the reservoir. In this research, a simple synthetic model was built that closely fits actual reservoirs characterized by suitable physical features such as velocity and density. Subsequently, elastic wave propagation simulation was implemented by use of a finite-difference scheme over a physical model of the reservoir. Then, FWI was applied to enhance the accuracy of the model parameters. With an efficient forward-modeling and inversion scheme, RTM was used as a powerful imaging tool that provides final high-resolution results for monitoring CO2 migration and possible leakage. This process examined the synthetic model for different amounts of CO2 leakage in saline aquifers to evaluate the performance of CO2 leakage monitoring using the seismic method. The results of the different receiver and source arrays also were compared to establish their effectiveness.

A numerical scheme based on the Taylor expansion and Lie product formula for the second‐order acoustic wave equation and its application in seismic migration

AbstractWe have developed a numerical scheme for the second‐order acoustic wave equation based on the Lie product formula and Taylor‐series expansion. The scheme has been derived from the analytical solution of the wave equation and in the approximation of the time derivative for a wavefield. Through these two equations, we obtained the first‐order differential equation in time, where the time evolution operator of the analytic solution of this differential equation is written as a product of exponential matrices. The new numerical solution using a Lie product formula may be combined with Taylor‐series, Chebyshev, Hermite and Legendre polynomial expansion or any other expansion for the cosine function. We use the proposed scheme combined with the second‐ or fourth‐order Taylor approximations to propagate the wavefields in a recursive procedure, in a stable manner, accurately and efficiently with even larger time steps than the conventional finite‐difference method. Moreover, our numerical scheme has provided results with the same quality as the rapid expansion method but requiring fewer computations of the Laplacian operator per time step. The numerical results have shown that the proposed scheme is efficient and accurate in seismic modelling, reverse time migration and least‐squares reverse time migration.

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.

Bayesian reverse time migration with quantified uncertainty

Reverse time migration (RTM) has been proven capable of producing high-quality images of subsurface structures. However, limited subsurface illumination combined with inaccurate forward modeling and migration velocities all lead to uncertainty in the seismic images. We quantify the migration uncertainty of RTM using an iterative inversion method based on a Bayesian inference framework. The posterior covariance matrix, computed at the maximum a posteriori (MAP) model, provides the foundation for estimating uncertainty. In the Bayesian inference framework, we combine an explicit sensitivity matrix based on a Green’s function representation with an iterative extended Kalman filter method. This enables us to determine the MAP solution of RTM and an estimate of its uncertainty. Numerical examples using synthetic data demonstrate how well the method can measure RTM uncertainty and produce reliable imaging results.

Ultrasonic imaging of delamination in thick CFRP laminates using an energy-compensation reverse time migration method

In ultrasonic reflection method, the precision of defect detection in thick carbon fiber reinforced plastics (CFRP) is compromised by acoustic energy attenuation. An energy-compensation reverse time migration (ECRTM) method is proposed to identify multiple defects accurately. Forward and backward wavefields are formed using the finite element method within an anisotropic acoustic model based on the Christoffel equation and Bond transformation. To enhance the imaging quality of CFRP laminates, a novel cross-correlation imaging condition is introduced to compensate for energy dissipation caused by geometric diffusion and variations of the far-field radiation intensity at the emitter with the propagation direction. Employing ultrasonic detection technology with a multi-element array, numerical and experimental research on defect imaging was conducted, considering delamination with various sizes and positions in a multidirectional CFRP laminate. In comparison to other ultrasonic imaging methods, the near-surface artifacts in RTM images are mitigated by the far-field radiation directivity factor, while the deep information is enhanced by the geometric diffusion compensation factor in the ECRTM images. As a result, the precise position of delamination in CFRP laminates is achievable, demonstrating superior imaging capabilities, especially for deep delamination.

3D Reverse-Time Migration Imaging for Multiple Cross-Hole Research and Multiple Sensor Settings of Cross-Hole Seismic Exploration

The two-dimensional (2D) cross-hole seismic computed tomography (CT) imaging acquisition method has the potential to characterize the target zone optimally compared to surface seismic surveys. It has wide applications in oil and gas exploration, engineering geology, etc. Limited to 2D hole velocity profiling, this method cannot acquire three-dimensional (3D) information on lateral geological structures outside the profile. Additionally, the sensor data received by cross-hole seismic exploration constitute responses from geological bodies in 3D space and are potentially affected by objects outside the well profiles, distorting the imaging results and geological interpretation. This paper proposes a 3D cross-hole acoustic wave reverse-time migration imaging method to capture 3D cross-hole geological structures using sensor settings in multi-cross-hole seismic research. Based on the analysis of resulting 3D cross-hole images under varying sensor settings, optimizing the observation system can aid in the cost-efficient obtainment of the 3D underground structure distribution. To verify this method’s effectiveness on 3D cross-hole structure imaging, numerical simulations were conducted on four typical geological models regarding layers, local high-velocity zones, large dip angles, and faults. The results verify the model’s superiority in providing more reliable and accurate 3D geological information for cross-hole seismic exploration, presenting a theoretical basis for processing and interpreting cross-hole data.

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.

Waveform Imaging Based on Linear Forward Representations for Scalar Wave Seismic Data

The current reverse-time migration, which is based on wave equations for imaging wavefields, employs an imaging formula derived from Claerbout’s imaging principle. This imaging formula is only valid for plane waves with small incident angles on the perfectly flat reflecting surface. However, the complexity of seismic wave propagation may lead to situations that do not meet this requirement. Therefore, this paper divides the subsurface into local scattering and reflecting bodies. It proposes linear forward representations for scattering and reflection data based on perturbations in the physical parameters and wave impedance, respectively. To further describe the effect on the reflecting body boundary, the local reflection coefficient is defined and the linear forward representation for the reflection data based on it is obtained. After that, the proposed linear forward representations are used as the forward equations for the linear inverse of the seismic data, and the seismic data waveform imaging method is developed based on linear inversion theory. At the same time, the specific waveform imaging calculation formulas for scalar wave scattering data and scalar wave reflection data are provided and validated via numerical experiments. Compared with the current reverse-time migration, waveform migration not only has the correct phase and higher resolution in theory but also does not increase the computational complexity. To some extent, it improves the deficiencies of the current structural imaging and provides a basis for subsurface lithological imaging.

Power-Law Frequency-Dependent Q Simulation and Reverse-Time Migration in Transversely Isotropic Acoustic Media

ABSTRACT Velocity and attenuation (Q) anisotropy are widely distributed in the Earth’s interior, significantly affecting the kinematic and dynamic characteristics of seismic-wave propagations. Previous studies developed to simulate these effects are mainly restricted to the constant-Q assumption. However, seismic attenuation in high-temperature and high-pressure regions is demonstrated to be frequency-dependent and usually follows a power-law formulation. To simulate this Q effect in transversely isotropic (TI) attenuating media, we derive a new pure-viscoacoustic wave equation with decoupled fractional Laplacians, which can simultaneously simulate amplitude dissipation and velocity dispersion effects. Based on the wavenumber relationship between the observation and physical coordinate systems, the tilted TI (TTI) wave equation is further derived. Compared with the pseudoviscoacoustic wave equation, the proposed pure-viscoacoustic equation can simulate stable P wavefields in complex geological structures without S-wave artifacts. To solve this new equation, two low-rank decompositions are introduced to approximate the real and imaginary parts and avoid the separation of wavenumbers and dip angles, making it much simpler in programming and implementation. We further use this equation to perform Q-compensated reverse-time migration to generate high-resolution migration images in anisotropic attenuating media. Numerical examples demonstrate the effectiveness of the proposed method for pure-viscoacoustic wavefield simulations and migrations in TTI attenuating media with power-law frequency-dependent Q effects.

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.

GPR detection localization of underground structures based on deep learning and reverse time migration

Ground penetrating radar (GPR) is widely used in detection localization of underground structure anomalous bodies. However, it is impossible to achieve accurate imaging localization of underground structures targets only by the waveform of GPR detection profiles due to the interference of clutter signals in engineering application. In this paper, a RefineNet deep learning network based on hybrid loss function is proposed to remove clutter signals in GPR profiles, and a reverse time migration (RTM) imaging algorithm based on total variation(TV) regularization is developed to perform migration imaging on GPR profiles processed by RefineNet network to realize accurate imaging localization of underground structures targets. Numerical simulations demonstrate that the developed RefineNet deep learning network can significantly remove clutter signals and improve GPR profiles quality, and the proposed RTM imaging algorithm based on TV regularization can accurately obtain location and shape information of underground structures targets. The full-scale experiment and field detection show that the proposed algorithm can accurately obtain the location of underground pipelines, cavities and other anomaly bodies. It is concluded that the developed algorithm provides a strong technical support for the GPR detection localization of underground structures targets.

Seismic reverse time migration with random boundary and frequency modulation

Seismic reverse time migration with random boundary and frequency modulation