Wavefield Propagation Research Articles

3D Seismic-Wave Modeling with a Topographic Fluid–Solid Interface at the Sea Bottom by the Curvilinear-Grid Finite-Difference Method

ABSTRACTThe curvilinear-grid finite-difference method (FDM), which uses curvilinear coordinates to discretize the nonplanar interface geometry, is extended to simulate acoustic and seismic-wave propagation across the fluid–solid interface at the sea bottom. The coupled acoustic velocity-pressure and elastic velocity-stress formulation that governs wave propagation in seawater and solid earth is expressed in curvilinear coordinates. The formulation is solved on a collocated grid by alternative applications of forward and backward MacCormack finite difference within a fourth-order Runge–Kutta temporal integral scheme. The shape of a fluid–solid interface is discretized by a curvilinear grid to enable a good fit with the topographic interface. This good fit can obtain a higher numerical accuracy than the staircase approximation in the conventional FDM. The challenge is to correctly implement the fluid–solid interface condition, which involves the continuity of tractions and the normal component of the particle velocity, and the discontinuity (slipping) of the tangent component of the particle velocity. The fluid–solid interface condition is derived for curvilinear coordinates and explicitly implemented by a domain-decomposition technique, which splits a grid point on the fluid–solid interface into one grid point for the fluid wavefield and another one for the solid wavefield. Although the conventional FDM that uses effective media parameters near the fluid–solid interface to implicitly approach the boundary condition conflicts with the fluid–solid interface condition. We verify the curvilinear-grid FDM by conducting numerical simulations on several different models and compare the proposed numerical solutions with independent solutions that are calculated by the Luco-Apsel-Chen generalized reflection/transmission method and spectral-element method. Besides, the effects of a nonplanar fluid–solid interface and fluid layer on wavefield propagation are also investigated in a realistic seafloor bottom model. The proposed algorithm is a promising tool for wavefield propagation in heterogeneous media with a nonplanar fluid–solid interface.

Migration deconvolution using domain decomposition

Least-squares migration (LSM) is an effective technique for mitigating blurring effects and migration artifacts generated by limited data frequency bandwidth, incomplete coverage of geometry, source signature, and unbalanced amplitudes caused by complex wavefield propagation in the subsurface. Migration deconvolution (MD) is an image-domain approach for LSM that approximates the Hessian operator using a set of precomputed point spread functions. We have developed a new workflow by integrating the MD and domain decomposition (DD) methods. DD techniques aim to solve large and complex linear systems by splitting problems into smaller parts, facilitating parallel computing, and providing a higher convergence in iterative algorithms. We suggest that instead of solving the problem in a unique domain, as conventionally performed, splitting the problem into subdomains that overlap and solve each of them independently. We accelerate the convergence rate of the conjugate-gradient solver by applying the DD methods to retrieve better reflectivity, which is mainly visible in regions with low amplitudes. Moreover, using the pseudo-Hessian operator, the convergence of the algorithm is accelerated, suggesting that the inverse problem becomes better conditioned. Experiments using the synthetic Pluto model demonstrate that our algorithm dramatically reduces the required number of iterations while providing a considerable enhancement in image resolution and better continuity of poorly illuminated events.

Seismic event detection in urban Singapore using a nodal array and frequency domain array detector: earthquakes, blasts and thunderquakes

SUMMARYDetection of seismic events at or below the noise level is enabled by the use of dense arrays of receivers and corresponding advances in data analysis methods. It is not only important to detect tectonic events, but also events from man-made, non-earthquake sources and events that originate from coupling between the solid Earth and the atmosphere. In urban environments with high ambient noise levels the effectiveness of event detection methods is unclear, particularly when deployment restrictions result in an irregular receiver array geometry. Here, we deploy a dense nodal array for 1 month in the highly populated city state of Singapore. We develop a new detection method based on image processing that we call spectrogram stacking, which detects anomalous, coherent spectral energy across the array. It simultaneously detects multiple classes of signal with differing spectral content and aids event classification, so it is particularly useful for signal exploration when signal characteristics are unknown. Our approach detects more local events compared to the traditional short-term average over long-term average and waveform similarity methods, while all methods detect similar numbers of teleseismic and regional earthquakes. Local events are principally man-made non-earthquake sources, with several events from the same location exhibiting repeating waveforms. The closest earthquake occurs in peninsular Malaysia, in an area where no earthquakes have previously been detected. We also detect ground motion over a wide frequency range from discrete thunder events that show complex coupling between acoustic and elastic wavefield propagation. We suggest that care should be taken deciphering local high-frequency tectonic events in areas prone to thunder storms.

Extracting angle domain common image gather with variable density acoustic-wave equation

Abstract Angle domain common image gathers (ADCIGs), commonly regarded as important prestacked gathers, provide the information required for velocity model construction and the phase and amplitude information needed for subsurface structures in oil/gas exploration. Based on the constant-density acoustic-wave equation assumption, the ADCIGs generated from reverse time migration ignore the fact that the subsurface density varies with location. Consequently, the amplitude versus angle (AVA) analysis extracted from these ADCIGs is not accurate. To partially solve this problem and to improve the accuracy of the AVA analysis, we developed amplitude-preserving ADCIGs suitable for density variations with the assumption of acoustic approximation. The Poynting vector approach, which is efficient and computationally inexpensive, was used to calculate the high-resolution wavefield propagation. The ADCIGs generated from the velocity and density perturbations match the theoretical AVA relationship better than ADCIGs with constant density. The extraction of the AVA analysis of the various combinations of the subsurface medium indicates that the density is non-negligible, especially when the density contrast is sharp. Numerical examples based on a layered model verify our conclusions.

Binormal schrodinger system of Heisenberg ferromagnetic equation in the normal direction with Q-HATM approach

In this paper, we first study the applications of the wave propagation flow in the normal direction, which is assumed to be the path of the propagated light radiated by Heisenberg ferromagnetic equation. Then the Coriolis phase is mainly used to demonstrate the relationship between the geometric magnetic phase and parallel transportation of the wave propagation field of the evolving light radiating in the normal orientation with Heisenberg ferromagnetic equation. Moreover, we investigate the geometric magnetic interpretation of the binormal evolution of the wave propagation field in the normal direction by considering the nonlinear fractional system with the repulsive type. Finally, we obtain numerical fractional solutions for the nonlinear fractional systems with the repulsive type by using the [Formula: see text]-Homotopy analysis transform ([Formula: see text]-HATM) method.

Determination of the time-dependent moment tensor using time reverse imaging

We have developed an approach to determine the time-dependent moment tensor and the origin time in addition to commonly derived locations of seismic events using time reverse imaging (TRI). It is crucial to locate and characterize the occurring microseismicity without making a priori assumptions about the sources to fully understand the subsurface processes inducing seismicity. Low signal-to-noise ratios (S/Ns) often force standard methods to make assumptions about sources or only characterize selected larger magnitude events. In TRI, microearthquakes are located by back propagating the full-recorded time-reversed wavefield through a velocity model until it ideally convergences on the source location. Therefore, it is less affected by low S/Ns and potentially locates and characterizes most of the events. After distinguishing artificial convergence locations from source locations, the quality of the source location and the moment tensors are derived by recording the stress at the determined source locations during the back propagation of the time-reversed wavefield. A robust workflow is derived using synthetic test cases in a realistic scenario with velocity models that only approximate the true velocity model and/or noisy displacement traces. The influence of a rudimentary velocity model on the source-location accuracy and characterization is significant. Our workflow handles these less-than-optimal station distributions and velocity models. Finally, the derived workflow is successfully applied to field data recorded at the geothermal field of Los Humeros, Mexico. Although only a 1D velocity model is currently available, source locations and (time-dependent) moment tensors could be determined for selected events.

Binormal schrodinger system of wave propagation field of light radiate in the normal direction with q-HATM approach

In this manuscript, we study applications of flows of wave propagation in normal orientation of curved direction, which is concluded to be path of generated light radiate. Also, Coriolis phase is very productively used to illustrate the communication between geometric magnetic phase and parallel transport assumption of wave propagation field of evolving light radiate in normal orientation of curved direction. Thus, we present a consolidated geometric magnetic interpretation of binormal evolution of wave propagation field in the normal orientation of curved direction by the nonlinear fractional Schrodinger system with repulsive type. Additionally, we conclude obtain new numerical fractional solutions for nonlinear fractional Schrodinger system by using the q-HATM algorithm.

Angle domain common image gathers from reverse time migration by combining the Poynting vector with directional decomposition

ABSTRACTAngle domain common image gathers are crucial for seismic applications such as the migration velocity analysis and amplitude variation with angle analysis. Angle domain common image gathers are the gather of reflection coefficients when seismic waves incident at different angles on the same image point. The curvature of gathers can be used to update the migration velocity model. The amplitude variation of gathers characterizes different rock properties. Estimating the wavefield propagation direction is the most important step in the process of generating angle domain common image gathers. The wavefront propagation direction is perpendicular to the wavefront. Accurately estimating the wavefield propagation direction is crucial for calculating the reflection angle. Existing methods cannot provide the propagation direction with the high angular resolution when the subsurface structure is complex, meaning overlapped wave events exist. We propose a new method to overcome this problem. The proposed method separates overlapped waves with a directional filter bank after the up‐going and down‐going wavefield decomposition. Then, we apply the Poynting vector method to decomposed wavefield slices to determine the propagation directions of corresponding wavefield components. The key feature of the proposed method is that it does not require spatial local windows, and it is computationally efficient. Numerical tests demonstrate that our proposed method can accurately obtain the propagation direction of seismic waves in a wavefield including overlapped waves. The angle domain common image gathers generated using our proposed method have improved image quality with more accurate amplitudes and less noise compared with the angle domain common image gathers produced by the conventional Poynting vector method. It means our proposed method provides high‐quality prestack angle gathers for seismic attribute analysis.

Fundamentals of Passive Seismohydroacoustic Methods for Arctic Shelf Investigation

A paper reviews existing and future seismohydroacoustic technologies, equipment, and novel scientific approaches to studying the Arctic Ocean. Particular attention is paid to the state of scientific and practical groundwork in the possibilities of developing passive geohydroacoustic methods for monitoring the ice-covered shelf of Russia’s northern seas. New knowledge on the structure and conditions of the formation and propagation of wave fields in the layered lithosphere–hydrosphere–ice–cover-atmosphere system generated by induced geodynamic processes has been obtained in the course of solving a separate class of problems within the fundamental scientific problem of seeking ways to build innovative, environmentally friendly geophysical technologies for delineating local heterogeneities, including hydrocarbon deposits, in ice-covered water areas.

Detector Tilt Considerations in Bragg Coherent Diffraction Imaging: A Simulation Study

This paper addresses the three-dimensional signal distortion and image reconstruction issues in X-ray Bragg coherent diffraction imaging (BCDI) in the event of a general non-orthogonal orientation of the area detector with respect to the diffracted beam. Growing interest in novel BCDI adaptations at fourth-generation synchrotron light sources has necessitated improvisations in the experimental configuration and the subsequent data analysis. One such possibly unavoidable improvisation that is envisioned in this paper is a photon-counting area detector whose face is tilted away from the perpendicular to the Bragg-diffracted beam during the acquisition of the coherent diffraction signal. We describe a likely circumstance in which one would require such a detector configuration, along with the experimental precedent at third-generation synchrotrons. Using physically accurate diffraction simulations from synthetic scatterers in the presence of such tilted detectors, we analyze the general nature of the observed signal distortion qualitatively and quantitatively and provide a prescription to correct for it during image reconstruction. Our simulations and reconstructions are based on an adaptation of the known theory of BCDI sampling geometry, as well as the recently developed projection-based methods of wavefield propagation. Such configurational modifications and their numerical remedies are potentially valuable in realizing unconventional coherent diffraction measurement geometries, eventually paving the way for the integration of BCDI into new material characterization experiments at next-generation light sources.

Joint reconstruction of initial pressure distribution and spatial distribution of acoustic properties of elastic media with application to transcranial photoacoustic tomography

Photoacoustic computed tomography (PACT) is an emerging computed imaging modality that exploits optical contrast and ultrasonic detection principles to form images of the photoacoustically induced initial pressure distribution within tissue. The PACT reconstruction problem corresponds to a time-domain inverse source problem, where the initial pressure distribution is recovered from the measurements recorded on an aperture outside the support of the source. A major challenge in transcranial PACT brain imaging is to compensate for aberrations in the measured acoustic data that are induced by propagation of the photoacoustic wavefields through the skull. To properly account for these effects, previously proposed image reconstruction methods for transcranial PACT require knowledge of the spatial distribution of the elastic parameters of the skull. However, estimating the spatial distribution of these parameters prior to the PACT experiment remains challenging. To circumvent this issue, in this work a method to jointly reconstruct the initial pressure distribution and a low-dimensional representation of the elastic parameters of the skull is developed and investigated. The joint reconstruction (JR) problem is solved by use of a proximal optimization method that allows constraints and non-smooth regularization terms. The proposed method is evaluated by use of large-scale three-dimensional (3D) computer-simulation studies that mimic transcranial PACT experiments.

DIC Measurement on Stress Wave Propagation and Strain Field Distribution Induced by Deep Rock Blasting

Abstract An ultra-high-speed digital image correlation system was applied in a blasting experiment that simulates the blasting response of deep rock under high ground stress. The full field strain evolutionary process of the specimen and the strain time histories of certain gauges were analyzed. Under a static stress field (simulating high ground stress), stress concentration occurs within three times the radius of the blasthole, and then, according to the region of stress concentration, the specimen plane was divided into near zone and far zone of the blasthole. There was no significant difference between deep and superficial formation in the law of explosive stress wave propagation in the blasthole far zone, which was based on the blasting compression zone, crack zone, and vibration zone, and elastic mechanics theory. Through nonlinear fitting, the explosive stress wave attenuation function between the maximum principal strain and the distance from the blasthole was obtained quantitatively, namely, by εmax=697+718·e−0.166·s. In addition, the strain value of the blasthole far zone caused by the combined action of the blasting stress field and the static stress field was equal to the linear superposition of the strain values caused by these two fields separately.

The mode transformation of a T(0,1) guided wave in an elbow pipe and its influence on defect location

To correct the inaccurate location of elbow pipe defects, our study established an experimental platform for magnetostrictive T(0,1) guided wave detection. The experimental platform was used to detect circumferential grooving defects with the same specifications, which were present at three different locations, i.e., the front straight pipe segment of the elbow, the elbow segment, and the back straight pipe segment of the elbow. The echo signals were analyzed. We found that the echo signals of the first two defects were normal, and the defect location could be recognized accurately, while two defect echoes occurred continuously in the straight pipe segment behind the elbow. To determine the causes of the abnormal defect signals, we selected a pitch-catch detection sensor to collect the guided wave transmission signal of the straight section after the elbow. The finite element numerical model extracted the guided wave propagation time-domain signal, and then, snapshots of the wavefield propagation were generated. The analysis results suggest that T(0,1) guiding will gradually resolve with a new mode signal when it propagates to the straight section behind the elbow. Through the theoretical calculation and analysis of the dispersion curve, the signal was identified as an F(1,2) flexural guided wave because its group velocity was less than that of the T(0,1) guided wave. The former defect echo wave packet is the T(0,1) guided wave, and the latter is the F(1,2) guided wave. The orientation of the defects should be subject to the position of the T(0,1) guide wave.

Spatially correlated polarization and non-paraxial propagation of electromagnetic wave fields

The theoretical description of the spatially correlated polarization of electromagnetic wave fields and its non-paraxial propagation is discussed in terms of pure spatially correlated polarization states. They are characterized by the spatial correlation of polarization matrix and the non-local Stokes parameters, thus formalizing the tendency of specific scalar and vector features of the electromagnetic wave field to take on similar values at two distant points in space. Non-paraxial interference and diffraction are modelled by representing optical devices and spatial correlation areas by transmission matrices and polarization domains respectively. It gives new insight for the (scalar) spatial coherence as well as for the (vector) correlation of polarization of electromagnetic wave fields. Some numerical examples illustrate the capabilities of the proposed model as simulation tool for the design and development of optical devices for applications in small scale optics.

Rock Fracture Monitoring Based on High-Precision Microseismic Event Location Using 3D Multiscale Waveform Inversion

Microseismic (MS) source location can help us obtain the fracture characteristics of a rock mass under a thermal-hydraulic-mechanical (THM) coupling environment. However, the commonly used ray-tracing-based location methods are easily affected by the large picking errors, multipath effects of travel time, and focusing and defocusing effects of rays in wavefield propagation, which are caused by the strong three-dimensional (3D) heterogeneity in mining areas. In this paper, we will introduce the rapidly developed waveform inversion-based location method into a mine MS field study. On this basis, the wavefields were modeled by utilizing a high-resolution 3D velocity model, a fractional-order Gaussian wavelet source-time function, and spectral element method (SEM) wavefield modeling. In order to reduce the computation cost of wavefield modeling, the 3D ray-shooting method based on a coarse grid was adopted to obtain an approximate MS event location. Based on this initial location, the multiscale waveform inversion strategy (from coarse to fine grids) and the L-BFGS iteration optimization algorithm were separately jointly selected to improve wavefield modeling speed efficiency and iterative convergence rate. Then, the IMS MS monitoring system set in the Yongshaba mine (China) and its tomographic 3D velocity model were used to conduct the synthetic test and application study. Results show that the source-time function based on the fractional-order Gaussian function wavelet can better fit complex recording waveforms compared with the conventional Ricker wavelet-based source-time function, and the waveform misfit during the L-BFGS iteration decreased rapidly. Furthermore, the multiscale waveform inversion method can obtain a similar location accuracy compared with the waveform inversion based on a single fine grid, and it can significantly decrease the iteration times and wavefield modeling computational cost. The average location error of the eight premeasured blasting events by the proposed approach is only 17.6 m, which can provide a good data research basis for analyzing MS event location and rock mass fracture characteristics in a mine.

Adaptively accelerating FWM2DA seismic modelling program on multi-core CPU and GPU architectures

This paper presents work done towards porting of FWM2DA, an open source program, on multi-core CPU and GPU architectures. FWM2DA is a Fortran90 sequential program which performs acoustic wave propagation of single source location for the 2D subsurface earth model using finite difference time domain modelling. We have reproduced this program using C programming language and upgraded its functionality for performing acoustic wave propagation of multiple source locations and allowing different grid spacing in x and z direction for the subsurface earth model. Performance of the upgraded version is improved by implementing inter-node and intra-node parallelization. Inter-node parallelization is implemented using MPI for efficiently utilizing the distributed memory while intra-node parallelization focuses on efficient utilization of underlying architecture’s resources. Outcome of these programs are compared with that of the original FWM2DA program for Sigsbee2a model and found similar thus establishing the correctness of implementation done. The developed programs are tested using two layer subsurface earth model of 5000 X 5000 grid dimension on PARAM Shreshta system having Intel Xeon Gold 6148F Skylake CPU and NVIDIA Tesla V100 GPU. Ported programming models are evaluated for execution time for wavefield propagation of single source location using two layer subsurface earth model. Performance gain of 8.6X for OpenMP, 83.22X for OpenACC and 107.77X for CUDA C implementation are recorded over the sequential C program. The multi-core CPU program is further optimized and overall 29.37X performance is achieved with respect to the sequential C program. Performance of CUDA C program is also improved by making use of shared memory in GPU and 1.18X speedup is recorded with respect to the baseline CUDA C program. The numerical experiments demonstrate the effectiveness and robustness of the developed programs with high scalability and efficiency on multi-core CPU and GPU based HPC system.

The mode‐conversion coefficient of ELF wave propagation due to land‐to‐sea transition

AbstractThe mode‐conversion coefficient is studied to investigate the ELF wave propagation over a mixed land‐to‐sea path. As partition by the consideration of reflection influence from the ionosphere layer, we assume the propagation can be regarded as being subjected to two different models over mixed paths, in terms of the propagation distance in the range of ELF far‐field and near‐field regions, respectively. Both of the mentioned stratified models can be represented as cascaded transmission networks at the abrupt junctions. In conformity with previous study to formulate the far‐field propagation as a cascaded terrestrial waveguide with abrupt height and ground impedance changes, the presented study proposed an equivalent cascaded network to exploit the concept of mode‐conversion for near‐field propagation across discontinuity. Representative parameters of ground types in contrast are supportive to demonstrate the interference of abrupt impedance‐change at ELF band. The presented analysis provide with computational schemes to obtain synthetic fields of ELF wave propagation, which could be extended to more realistic model over multi‐segmental mixed paths.

Lensless In-Line Holographic Microscopy With Light Source of Low Spatio-Temporal Coherence

Lensless microscopy with coherent or partially coherent light sources is a well known imaging technique, commonly referred as digital in-line holographic microscopy. In the established methods, both the spatial and temporal coherence of light play a crucial role in determining the resolution of reconstructed object. We report lensless microscopy with a spatially extended white LED, a light source of low spatial and very low temporal coherence. The wave-field propagation between two parallel planes can be obtained using a convolution operation, where the convolution kernel depends on the object-sensor distance and the characteristics of the light source. For a light source of unknown characteristics, this kernel is an unknown function. In the proposed reconstruction method, we decompose an unknown convolution kernel of very large size (128 X 128) into a small unknown light-source-specific kernel (size 9 X 9) and a known light-source-independent kernel (size 128 X 128). This drastically reduces the number of parameters to be estimated at the system identification step, which has been performed here by one time imaging of the known microscopic objects. Final unknown object estimation has been performed using the upper-bound constrained deconvolution. A lateral resolution of ~1-2 micrometer has been demonstrated.

Modelling of sound propagation in the ocean using the matrix propagator

The problem of sound propagation in an oceanic waveguide is considered. Attention is concentrated on properties of a wavefield propagator that governs transformation of an arbitrary wavefield in course of propagation. Using the basis of normal modes, we can represent the propagator in the matrix form. If horizontal inhomogeneity of a waveguide is weak, the propagator can be calculated by means of the first-order perturbation theory. In the case of random inhomogeneity, the apparatus of random matrix theory can be exploited. We demonstrate methods of propagator construction for realistic models of waveguides, including waveguides with adiabatic inhomogeneities and shallow-sea waveguides. A scheme of experimental measurement of a propagator in a shallow-sea waveguide is proposed.

Turbulent exchanges between near-inertial waves and balanced flows

Abstract