Kirchhoff Migration Research Articles

Seismic wavefield information extraction method based on adaptive local singular value decomposition

The key to seismic data processing is to extract the wavefield information related to the subsurface geological targets. In this paper, we first introduce the low-rank signal priority and the strong energy signal priority characteristics of the Singular Value Decomposition (SVD) method. By analyzing the characteristics of the second-order difference spectrum of typical seismic data, we find two indicative parameters to adaptively select the singular value threshold for extracting reflection and diffraction events. Our proposed Adaptive Local Singular Value Decomposition (ALSVD) method takes advantage of the local analysis, and can effectively extract the weak signals in the seismic data. It is a robust method with good resolution and separation integrity, which is beneficial to seismic migration, seismic imaging, and evaluation of Oil and gas traps. Synthetic examples and field examples demonstrate the effectiveness of this method.

3C-3D tunnel seismic reverse time migration imaging: A case study of Pearl River Delta Water Resources Allocation Project

In recent years, tunnel boring machines (TBMs) have been widely used because of their fast construction speed and economical benefits, and the need to obtain geological information ahead of the tunnel to ensure the TBM tunnel construction safety has also arisen. Faced with the complex geological environment, seismic forward-prospecting is the primary method for predicting the unfavorable geological structure in front of the tunnel face. As a crucial step in seismic forward-prospecting method, migration can image geological characteristics and help learn the distribution of unfavorable geology. To achieve all-round imaging of unfavorable geology, we suggested a three-component (3C) three-dimensional (3D) tunnel seismic reverse time migration imaging method. The acoustic wave equation is employed for the forward and backward wavefield extrapolation after the P/S-wave separation to eliminate the imaging artifacts from severe converted waves in tunnels. GPU parallelization is used to accelerate the calculation to further adapt to the rapid excavation of TBMs. The proposed method is validated in two typical numerical models, especially for 3C seismic data that provides all-round geological information to achieve enhanced imaging energy and artifact reduction, which demonstrates the significance of 3C seismic data to migration imaging. This case study was conducted in the Pearl River Delta Water Resources Allocation Project in Guangdong Province, China. The reliability of 3C3D tunnel seismic reverse time migration imaging in field tunnel engineering was investigated. Two consecutive detections were performed, and then the spatial positions of faults and fractures in front of the tunnel face were accurately judged by the combination of the two imaging results. Based on the detection results, the excavation rate was slowed down and the tunnel lining support was increased. The TBM then successfully passed through the risk areas. This case study can serve as a reference for other tunnels with similar concerns regarding the necessity of 3C seismic data and consecutive detections.

2D Q-compensated multi-component elastic Gaussian beam migration

Elastic waves are affected by viscoelasticity during the propagation through the Earth, resulting in energy attenuation and phase distortion, in turn resulting in low seismic imaging accuracy. Therefore, viscoelasticity should be considered in seismic migration imaging. We propose a Q compensated multi-component elastic Gaussian beam migration (Q-EGBM) method to (1) separate the elastic-wave data into longitudinal (P) and transverse (S) waves to perform PP-wave and PS-wave imaging; (2) recover the amplitude loss caused by attenuation; (3) correct phase distortions caused by dispersion; (4) improve the resolution of migration imaging. In this paper, to accomplish (2), (3), and (4), we derive complex-valued traveltimes in viscoelastic media. The results of numerical experiments using a simple five-layer model and a sophisticated BP gas model show that the method presented here has significant advantages in recovering energy decay and correcting phase distortion, as well as significantly improving imaging resolution.

Pre‐stack depth imaging techniques for the delineation of the Carosue Dam gold deposit, Western Australia

AbstractIn this study, we explore the latest generation of seismic imaging algorithms (migration) that have been successful in the oil and gas exploration industry and apply them in the more challenging hard rock environment. Seismic migration is a crucial processing step required to build an accurate image of the Earth's subsurface. The seismic method applied in a hard rock environment has a specific set of challenges: complex geological settings often comprised of steeply dipping interfaces and heterogeneities (faults, fracture zones, thrusts, etc.); spatially variable zones of alteration, low intrinsic signal‐to‐noise ratio; complex near‐surface conditions (the weathered overburden has a very high contrast in seismic properties with base formations). Here, we present how a dense source–receiver 3D grid in combination with the latest pre‐stack depth imaging techniques can image the geology with a remarkable level of detail and to depths as shallow as the top of fresh rock. We also propose a comprehensive velocity model building strategy applied specifically to the Carosue Dam deposit, Western Australia, which is mainly characterized by volcaniclastic and volcanic rocks within the Carosue Basin disrupted by a complex system of gold‐bearing faults. To arrive at an optimized velocity model for pre‐stack depth imaging, we combine drillhole data with tomographic refinement. Excellent correlation between resultant seismic images and refraction tomography, vertical seismic profiling and drillholes can be attributed to the integrated velocity model building workflow used for depth migration.

Imaging of thrust structures under Colombian foothills landscape through Marchenko approach

The Marchenko imaging approach successfully deals with multiple scattering during seismic migration, obtaining clear images in structurally complex geological zones below at a specific depth. Through the Marchenko equation, the method retrieves Green's function of a virtual source in profundity using reflections recorded on the surface and a smoothed velocity model. According to the theorem of reciprocity, Green's function represents the medium's response to a source on the surface recorded by a virtual receiver in-depth and decomposes it into a down-going wavefield and an up-going wavefield. Both wave fields' deconvolution provides the reflection response of virtual sources and virtual receivers repositioned in the subsurface, mimicking redatumming. The result is an image free of multiple internal reflections from the area below virtual both sources and receivers. After successfully testing with synthetic seismograms generated in a plane-horizontal layers model, we applied the Marchenko algorithm to seismic data of the Upper Magdalena Valley project using an available velocity model. Compared to an image supplied by a Kirchhoff pre-stack depth migration algorithm, the new image correctly positions the seismic events avoiding misleading interpretations in locating complex structures.

Internal Structure of the Central Garlock Fault Zone From Ridgecrest Aftershocks Recorded by Dense Linear Seismic Arrays

AbstractWe provide high‐resolution seismic imaging of the central Garlock fault using data recorded by two dense seismic arrays that cross the Ridgecrest rupture zone (B4) and the Garlock fault (A5). Analyses of fault zone head waves and P‐wave delay times at array A5 show that the Garlock fault is a sharp bimaterial interface with P waves traveling ∼5% faster in the northern crustal block. The across‐fault velocity contrast agrees with regional tomography models and generates clear P‐wave reflections in waveforms recorded by array B4. Kirchhoff migration of the reflected waves indicates a near‐vertical fault between 2 and 6 km depth. The P‐wave delay times imply a ∼300‐m‐wide transition zone near the Garlock fault surface trace beneath array A5, offset to the side with faster velocities. The results provide important constraints for derivations of earthquake properties, simulations of ruptures and ground motion, and future imaging studies associated with the Garlock fault.

Fractional laplacians viscoelastic wave equation low-rank temporal extrapolation

The fractional Laplacians constant-Q (FLCQ) viscoelastic wave equation can describe seismic wave propagation accurately in attenuating media. A staggered-grid pseudo-spectral (SGPS) method is usually applied to solve this wave equation but it is of only second-order accuracy in time, due to a second-order finite-difference (FD) time differentiation. Visible time dispersion and numerical instability could appear in the case of a large timestepping size. To resolve this problem, we develop a more accurate low-rank temporal extrapolation scheme for the FLCQ viscoelastic wave equation. We realize this goal by deriving an analytical time-marching formula from the general solution of the FLCQ wave equation. Compressional (P) and shear (S) wave velocities dependent k-space operators are involved in the formula and they can compensate for the time dispersion errors caused by the FD time differentiation. To implement the k-space operators efficiently in heterogeneous media, we adopt a low-rank approximation of these operators, which reduces the computational cost at each time step to several fast Fourier transforms (FFTs). Another benefit of the low-rank extrapolation is explicit separation of P and S waves, which is helpful for further developing vector wavefield-based seismic migration methods. Several numerical examples are presented to verify the higher accuracy and the less restrictive stability condition of the low-rank temporal extrapolation than the traditional SGPS extrapolation.

Inversion of Deep-Water Velocity Using the Munk Formula and the Seabed Reflection Traveltime: An Inversion Scheme That Takes the Complex Seabed Topography Into Account

The sound speed of seawater is not constant. It varies with season, day time, depth and range. This variation was not considered in marine seismic data processing and imaging before deep-water seismic acquisition became a routine activity. As a result, non-ignorable errors may be contained in the final migrated-image of deep-water seismic data. To eliminate such errors, we propose here a scheme for inverting the seawater velocity under the condition that the seabed has a complex topography. In this scheme, the seabed topography is represented by step grids constrained by measured water depth data, and the sound profile is assumed to be the one satisfying the Munk formula. Thus, only the parameters appearing in the Munk formula need to be inverted. This is quite different from the conventional inversion schemes that take the velocity as the inversion target. We use the conjugate gradient method to minimize the objective function given as the sum of squares of traveltime differences. Tests on synthetic common-shot data set show that our scheme presented here works as expected. Applications to real marine data set further validates the reasonability and feasibility of our scheme under complex seabed topography. To investigate the reliability of our inversion scheme, we migrate the real 2D data set using the Kirchhoff migration with the inverted Munk profile as the velocity model. The corresponding results show that the seawater velocity obtained by our inversion scheme improves the imaging quality of underwater structures.

Bayesian Physics-Informed Neural Networks for the Subsurface Tomography Based on the Eikonal Equation

The high cost of acquiring a sufficient amount of seismic data for training has limited the use of machine learning in seismic tomography. In addition, the inversion uncertainty due to the noisy data and data scarcity is less discussed in conventional seismic tomography literature. To mitigate the uncertainty effects and quantify their impacts in the prediction, the so-called Bayesian Physics-Informed Neural Networks (BPINNs) based on the eikonal equation are adopted to infer the velocity field and reconstruct the travel-time field. In BPINNs, two inference algorithms including Stein Variational Gradient Descent (SVGD) and Gaussian variational inference (VI) are investigated for the inference task. The numerical results of several benchmark problems demonstrate that the velocity field can be estimated accurately and the travel-time can be well approximated with reasonable uncertainty estimates by BPINNs. This suggests that the inferred velocity model provided by BPINNs may serve as a valid initial model for seismic inversion and migration.

Imaging the Subsurface With the High-Speed Train Seismic Data-Based Elastic Reverse Time Migration

Imaging the Subsurface With the High-Speed Train Seismic Data-Based Elastic Reverse Time Migration

Seismic Image Dip Estimation by Multiscale Principal Component Analysis

Dip estimation of geological structures plays an important role in geophysical applications. Principal component analysis (PCA) is a common approach to estimating local dips by decomposing the local gradients of a seismic migration image and obtaining its principal eigenvector. However, PCA is difficult to obtain robust and high-resolution dip estimations for low signal-to-noise ratio (SNR) migration images, while multiscale schemes in digital image processing can achieve a better compromise between noise robustness and dip resolution. Therefore, we propose to adopt a multiscale PCA (MPCA) method coupled with a propagation-weight-based fusion mechanism for seismic dip estimation of low SNR migration image. MPCA consists of three steps: 1) constructing an image pyramid by repeating the low-pass filter from fine to coarse scales; 2) estimating the dip using the PCA method at each scale of the image pyramid; and 3) fusing the multiscale dip estimations using propagation weights from coarse to fine scales. We test the MPCA method on an omnidirectional dip pattern and three seismic migration images and compare with the conventional PCA and multiscale methods. The results demonstrate that MPCA yields robust and high-resolution dip estimations for low SNR seismic migration images.

Reflection and diffraction separation in the dip-angle common-image gathers using convolutional neural network

In exploration seismology, reflections have been extensively used for imaging and inversion to detect hydrocarbon and mine resources, which are generated from subsurface continuous impedance interfaces. When the interface is not continuous and its size reduces to less than half-wavelength, reflected wave becomes diffraction. Reflections and diffractions can be used to image subsurface targets, and the latter is helpful to resolve small-scale discontinuities, such as fault plane, pinch out, Karst caves, and salt edge. However, the amplitudes of diffractions are usually much weaker than that of reflections. This makes it difficult to directly identify and extract diffractions from unmigrated common-shot or common-middle-point gathers. Migrating seismic data into a subsurface location for different reflector dip angles yields a dip-angle-domain common-image gather (DACIG). One DACIG represents the migrated traces at a fixed lateral position for different reflector dips. The reflection and diffraction have different geometric characteristics in DACIG, which provides one opportunity to separate diffractions and reflections. In this study, we present an efficient and accurate diffraction separation and imaging method using a convolutional neural network (CNN). The training data set of DACIGs is generated using one pass of seismic modeling and migration for velocity models with and without artificial scatterers, respectively. Then, a simplified end-to-end CNN is trained to identify and extract reflections from the migrated DACIGs that contain reflections and diffractions. Next, two adaptive subtraction strategies are presented to compute the diffraction DACIGs and stacked images, respectively. Numerical experiments for synthetic and field data demonstrate that the proposed method can produce accurate reflection and diffraction separation results in DACIGs, and the stacked image has a good resolution for subsurface small-scale discontinuities.

Attenuation of seismic migration smile artifacts with deep learning

Attenuation of migration artifacts on Kirchhoff migrated seismic data can be challenging due to the relatively low amplitude of migration artifacts compared to reflections as well as the overlap in the kinematics of reflection and migration smiles. Several ‘conventional’ filtering methods exist and recently deep learning based workflows have been proposed. A deep learning workflow can be a simple and fast alternative to existing methods. In case of supervised training of a deep neural network using training data made by physics-based modelling or actual migrations is expensive and lacks diversity in terms of noise, amplitude, frequency content and wavelet. This can result in poor generalization beyond the training data without re-training and transfer learning. In this paper we demonstrate successful applications of migration smile separation using a conventional U-net architecture. The novelty in our approach is that we do not use synthetic data created from physics-based modelling, but instead use only synthetic data build form basic geometric shapes. Our domain of application is the migrated common offset domain, or simply the stack of the pre-stack migrated data, where reflections resemble local geology and migration smiles are upward convex hyperbolic patterns. Both patterns were randomly perturbed in many ways while maintaining their intrinsic features. This approach is inspired by the common practice of data augmentation in deep learning for machine vision applications. Since many of the standard data augmentation techniques lack a geophysical motivation, we have instead perturbed our synthetic training data in ways to make more sense for a signal processing perspective or given our ‘domain knowledge’ of the problem at hand. We did not have to retrain the network to produce good results on the field dataset. The large variety and diversity in examples enabled the trained neural network to show encouraging results on synthetic and field datasets that were not used in training.

Neural Eikonal solver: Improving accuracy of physics-informed neural networks for solving eikonal equation in case of caustics

The concept of physics-informed neural networks has become a useful tool for solving differential equations due to its flexibility. A few approaches use this concept to solve the eikonal equation that describes the first-arrival traveltimes of waves propagating in smooth heterogeneous velocity models. However, the challenge of the eikonal is exacerbated by the velocity models producing caustics, resulting in instabilities and deterioration of accuracy due to the non-smooth solution behavior. In this paper, we revisit the problem of solving the eikonal equation using neural networks to tackle caustic pathologies. We introduce the novel Neural Eikonal Solver (NES) for solving the isotropic eikonal equation in two formulations: the one-point problem is for a fixed source location; the two-point problem is for an arbitrary source-receiver pair. We present several techniques which provide stability in the case of caustics: improved factorization; non-symmetric loss function based on Hamiltonian; gaussian activation; symmetrization. In our tests, NES showed the relative mean-absolute error of 0.2-0.4% from the second-order factored Fast Marching Method with a similar inference time, and outperformed existing neural-network solvers giving 10-60 times lower errors and 2-30 times faster training. The one-point NES provides the most accurate solution, while the two-point NES gives slightly lower accuracy but an extremely compact representation with all spatial derivatives. It can be useful in many seismic problems: massive computations of traveltimes for millions of source-receiver pairs in Kirchhoff migration; modeling of ray amplitudes using spatial derivatives; traveltime tomography; earthquake localization; ray multipathing analysis.

High‐efficiency and high‐precision seismic trace interpolation for irregularly spatial sampled data by combining an extreme gradient boosting decision tree and principal component analysis

AbstractIn seismic data acquisition, because of several factors, such as surface barriers, receiver failure, noise contamination and budget control, seismic records often exhibit irregular sampling in the space domain. As corrupted seismic records have a negative effect on seismic migration, inversion and interpretation, seismic trace interpolation is a key step in seismic data pre‐processing. In this paper, we propose a high‐efficiency and high‐precision seismic trace interpolation method for irregularly spatially sampled data by combining an extreme gradient boosting decision tree and principal component analysis in a semi‐supervised learning method. The adjacent trace number, sampling number and amplitudes of the effective seismic data were taken as features to build the training data set for the extreme gradient boosting decision tree. Principal component analysis is applied to remove redundant information and accelerate the training speed. This is different from the traditional trace interpolation method in that the proposed method is data‐driven; therefore, it does not require any assumptions. Compared with other deep learning‐based trace interpolation methods, the proposed method has fewer control parameters and learning labels and a smaller training cost. Experiments using synthetic and field data demonstrated the validity and flexibility of this trace interpolation method.

Seismic forward modelling of the Kvalhovden outcrop, Spitsbergen, Norway

With the advent of seismic forward modeling, it is now possible to investigate and bridge the resolution gap between outcrop, reservoir, and seismic-scale observations. Seismic processing is central to seismic technology and has grave consequences on the work of a seismic interpreter, reserve estimation, and economic decisions. To investigate the strength and inadequacies of contemporary processing algorithms used for seismic simulations, this work provides several modeled seismic sections from the Kvalhovden outcrop, Spitsbergen, Norway. We emphasize the differences in migrated and inverted seismic sections and their ability to accurately render the geological model. Our results show that Reverse Time Migration (RTM) significantly improves the geological model compared to the Kirchhoff migration and that the elastic RTM migration is excessive. In the RTM case, a smooth velocity model was sufficient to achieve realistic results. However, all migrated images have a false continuity, structures, apparent truncations, and false low-angle terminations. Introducing colors to the modeled sections create illusionary details, exaggerated the stratification, and reinforced the occurrence of seismic artifacts. In the inverted images, sandstone blocks and the underlying collapse structures are better imaged than on the migrated sections and are with a reduced number of artifacts. Importantly, our work shows the relevance of inverted sections for general structural and stratigraphic interpretation, albeit low resolution compared to the migrated data. Migrated and inverted sections should be used jointly to improve seismic interpretation quality.

Tunable High‐Resolution Synthetic Aperture Radar Imaging

AbstractWe have recently introduced a modification of the multiple signal classification method for synthetic aperture radar. This method incorporates a user‐defined parameter, ϵ, that allows for tunable quantitative high‐resolution imaging. However, this method requires relatively large single‐to‐noise ratios (SNR) to work effectively. Here, we first identify the fundamental mechanism in that method that produces high‐resolution images. Then we introduce a modification to Kirchhoff Migration (KM) that uses the same mechanism to produce tunable, high‐resolution images. This modified KM method can be applied to low SNR measurements. We show simulation results that demonstrate the features of this method.

Q-compensated least-squares reverse time migration with velocity-anisotropy correction based on the first-order velocity-pressure equations

Anisotropy and Q attenuation bring great challenges to seismic wave migration. On migrated images, anisotropy creates structural and positioning errors, and Q attenuation leads to weak amplitudes and misplacement of reflectors. A 2D Q-compensated least-squares reverse time migration with velocity-anisotropy correction ( QLSRTM-VA) is proposed through the construction of velocity-anisotropic Q-compensated forward modeling, Q-compensated adjoint, and Q-attenuated demigration operators to simultaneously correct velocity-anisotropy and Q-attenuation in the migration process. The preceding operators are derived using first-order velocity-anisotropic viscoacoustic quasi-differential wave equations with variable densities, which are stable, capable of conveniently dealing with variable density media and are easy to transform between velocity-anisotropic Q-compensation and Q-attenuation versions. As exemplified by two synthetic and field data sets, our QLSRTM-VA method increases the imaging resolution, signal-to-noise ratio, and amplitude preservation in deep regions. Our method is capable of producing better images than viscoacoustic isotropic least-squares reverse time migration (LSRTM) and acoustic anisotropic LSRTM.

Fast iterative method for seismic wave travel time calculation under undulating surface conditions

Seismic wave travel time is an important seismic attribute information and is widely used in various seismic forward and inversion methods, including seismic migration imaging, seismic tomography, seismic wave forward modeling and other core seismic data processing methods. The accuracy and efficiency of the travel time algorithm are important for the above methods. In the practical application of seismic exploration, it is often carried out under the condition of undulating surface, which has a significant impact on the travel time calculation. Therefore, it is of great significance to study an efficient and high-precision travel time calculation method that can adapt to undulating surface condition. In this paper, Fast iterative method (FIM) is modified to a topography travel time calculation method. The method employs an iterative method to solve the equation of function to obtain seismic wave travel time by maintaining a narrow band called the active list, and the algorithm can update all grid nodes in the active list at a time. We will verify the travel time computing power of the FIM method through several different velocity models.

An enhanced GPR-based data processing approach for detecting subsurface utilities in urban distribution networks

Ground-penetrating radar (GPR) is a non-destructive technique that helps find subsurface utilities. In geophysical investigations, the availability of noise sources, and the complexity of utility networks mean that performing a routine field operation and processing may not reveal the wanted anomalies. Thus, we use data acquisition and processing strategy to detect every single hyperbolic event (which means a probable anomaly) more accurately. In this approach, we first acquire data in parallel lines that cross the predetermined utility line path, use pre-processing techniques (zero-time correction, dewowing, etc.), and then use compensated time reversal (CTR) processing technique. Moreover, we group detected events depending on how frequently they occur through all traverses, where repeated events are probably caused by a utility line. For a better understanding, we compared CTR outputs with conventional processing (using filtering and Kirchhoff migration). This approach was used in a field that comprises buried utilities, such as pipelines and cables. Data were acquired along 4 parallel traverses with a GPR MALA tool and an antenna frequency of 250 MHz. Results indicate that the CTR generates better resolution/higher signal-to-noise ratio, and precise utility location as confirmed by drillings.