Parallel Algorithm with Modulus Structure for Simulation of Seismic Wave Propagation in 3D Multiscale Multiphysics Media

Anisotropy is widely-used nowadays in seismic processing as it may characterize fractured reservoirs, pre-stressed state of formations etc. However, numerical simulation of seismic wave propagation in anisotropic media requires the use of advanced, computationally-intense algorithms. Meanwhile anisotropic formations take relatively small part, several percents, of the model. In this situation it is reasonable to develop a finite-difference algorithm coupling the anisotropy-oriented scheme with efficient standard staggered grid, or Virieux, scheme. So, that the computationally-intense algorithm is used only inside the anisotropic formations, while the Virieux scheme is used in the major isotropic part of the model. The coupled scheme may be almost as efficient as Virieux scheme but providing full detailed knowledge about wave propagation in anisotropic formations.

Accurate simulations of seismic wave propagation in complex geological structures with great and rapid variations of topography are of primary interest for environmental and industrial applications. Unfortunately, difficulties arise for such complex environments, due essentially to the existence of shadow zones, head waves, diffractions and edge effects. Usually, methods and codes are tested against "validated" ones, but one might wonder which method/code ultimately approaches the "real" solution. An original approach for seismics is to compare synthetic seismic data to controlled laboratory data for a well-described configuration, in order to analyze the respective limitations of each method/code. This is one of the objectives of the BENCHIE project, which brings together laboratories in France, Norway and Russia. In this presentation we will present some preliminary results provided by both laboratory experiments conducted in a tank and numerical simulations of wave propagation. The laboratory data have been obtained by zero-offset acquisitions at different ultrasonic frequencies on the Marseille model which is made up of anticlines, fault and truncated pyramid. The numerical results have been obtained by two methods: the Spectral-Element Method and the Tip-Wave Superposition Method.

We investigated the development of a distinct later phase observed at stations near the Japan Trench associated with shallow, outer-rise earthquakes off the coast of Sanriku, northern Japan based on the analysis of three-component broadband seismograms and FDM simulations of seismic wave propagation using a heterogeneous structural model of the Japan Trench subduction zone. Snapshots of seismic wave propagation obtained through these simulations clearly demonstrate the complicated seismic wavefield constructed by a coupling of the ocean acoustic waves and the Rayleigh waves propagating within seawater and below the sea bottom by multiple reflections associated with shallow subduction zone earthquakes. We demonstrated that the conversion to the Rayleigh wave from the coupled ocean acoustic waves and the Rayleigh wave as they propagate upward along the slope of seafloor near the coast is the primary cause of the arrival of the distinct later phase at the station near the coast. Through a sequence of simulations using different structural models of the Japan Trench subduction zone, we determined that the thick layer of seawater along the trench and the suddenly rising sea bottom onshore of the Japanese island are the major causes of the distinct later phase. The results of the present study indicate that for realistic modeling of seismic wave propagation from the subduction zone earthquakes, a high-resolution bathymetry model is very crucial, although most current simulations do not include a water column in their simulation models.

Realistic 3D seismic wave simulations and inversions have recently enjoyed tremendous advances, partly due to the development of innovative numerical algorithms, partly due to the availability of cost‐effective high‐performance computer clusters.Harnessing such hardware, the spectral‐element method has enabled the accurate and efficient simulation of seismic wave propagation in 3D acoustic, (an)elastic and poroelastic Earth models. We present migration images of the SEG/EAGE salt dome model obtained by combining spectral‐element and adjoint methods, starting from 2D examples and moving towards 3D simulations. Possible iterative inversion strategies are motivated by these experiments.

Simulation of seismic wave propagation has been very important way to study the relation between a specific condition of earth medium and seismogram recorded during a seismic event such as an earthquake. In this study, a numerical modelling of P-SV wave propagation in elastic heterogeneous medium has been done using fourth order finite-difference method. The medium model was created based on topography profile of selected line intersecting Mount Merapi, where 200 meters thick low-velocity layer has been added. The computation was performed using an NVIDIA CUDA-enabled graphics card. Synthetic seismogram was recorded at three receiver stations and was obtained by using a deep seismic source and a shallow seismic source located within the volcano. Results shows significant differences of wave propagation in presence of topography and low-velocity layer, while compared to the homogeneous version of the model which excludes the low-velocity layer. The formation of surface wave is also proved to significantly affect the recorded seismogram. Topography, low-velocity layer located at near-surface, and generated surface wave are suspected to be responsible for the complexity of the recorded seismogram. Compared to computation by using only CPU, usage of NVIDIA graphics processing unit proved to be successful to accelerate the execution time by 23 times.

We present a scattering attenuation model based on the statistical wave propagation theory in random media. It is suitable for the weak wavefield fluctuation regime and has practically no restriction in the frequency domain. The presented formulas allow to quantify scattering attenuation in complex geological regions using simple statistical estimates from well-log data. This knowledge is important for further petrophysical interpretations of reservoir rocks. To test our theory we perform numerical simulations of seismic wave propagation in 3-D elastic random media using a finite-difference solution of the elastodynamic wave equation. From the synthetic seismograms we determine the scattering attenuation (Q −1) with help of spectral decay methods. We find good agreement of the frequency-dependent Q values and the theoretical predictions.

ABSTRACTNumerical modelling plays an important role in helping us understand the characteristics of seismic wave propagation. The presence of spurious reflections from the boundaries of the truncated computational domain is a prominent problem in finite difference computations. The nearly perfectly matched layer has been proven to be a very effective boundary condition to absorb outgoing waves in both electromagnetic and acoustic media. In this paper, the nearly perfectly matched layer technique is applied to elastic isotropic media to further test the method's absorbing ability. The staggered‐grid finite‐difference method (fourth‐order accuracy in space and second‐order accuracy in time) is used in the numerical simulation of seismic wave propagation in 2D Cartesian coordinates. In the numerical tests, numerical comparisons between the nearly perfectly matched layer and the convolutional perfectly matched layer, which is considered the best absorbing layer boundary condition, is also provided. Three numerical experiments demonstrate that the nearly perfectly matched layer has a similar performance to the convolutional perfectly matched layer and can be a valuable alternative to other absorbing layer boundary conditions.

Summary Nowadays the seismic survey technology is widely used for the oil and gas fields exploration. In connection with the recent discovery of unconventional deposits, the task of improving its methods and approaches is important. Mathematical modeling may allow us to calculate seismic responses from the geological medium with a given structure in the reasonable time. Due to the increase of the computational power of HPC systems, more and more complex mathematical models can be used: acoustic, elastic, averaged fractured, etc. In this paper the process of the seismic wave propagation in fluid-saturated geological media is investigated. The Dorovsky model is used, which takes into account the porosity and other properties of the elastic skeleton and the saturating fluid. The authors expanded the scope of the numerical grid-characteristic method, previously well-proven in problems of seismic wave propagation in acoustic, elastic and fractured media. A two-dimensional formulation of the seismic exploration problem is considered. Formulas for the interior points of the integration domain were obtained, as well as the boundary condition on the “day surface”, in explicit form. Calculations illustrating the differences in the wave fields when using acoustic, elastic and fluid-saturated models for describing geological media were carried out.

The problem of tsunami warning and the use of the grid-characteristic method developed for studying wave processes in heterogeneous media is addressed. A multilayer geological model with curved boundaries and contrasting elastic parameters is considered. Various seismic survey methods, as well as different geometries of the boundaries, different values of rock densities, and various longitudinal and shear wave velocities, are examined. The boundary value problem is numerically solved jointly for the elastic and acoustic wave equations (seismic wave propagation in rocks and water layer, respectively). We use the numerical grid-characteristic method with combined structured curvilinear and regular computational grids. The wave velocity fields (velocity as derivative of displacement) and stress fields are calculated and analyzed. Synthetic seismograms are calculated for the coastal zone. It is found that some specific features of seismograms and some wave modes can be used for tsunami warning. The optimal parameters of seismic surveying are determined. Numerical simulation of wave propagation effects is used for these purposes. The proposed numerical grid-characteristic method can be used in forward numerical modeling in order to interpret seismograms recorded in the coastal zone.

Theory of elastic waves layered homogeneous medium or even medium for the study can not meet the actual demand for seismic exploration, especially for fine rock to construct reservoirs for the study, had to consider small-scale heterogeneity of seismic wave propagation effects. In this thesis, multi-scale model of a complex medium, in ensuring the premise to further improve simulation accuracy simulation efficiency issue, the introduction of a variable grid numerical simulation techniques, and were analyzed for different types of grid difference, establish a different media model simulation results verify the validity of simulation and analyzes its efficiency and accuracy problems.

Wavefront construction methods allow for efficient simulation of seismic wave propagation in anisotropic media using ray theory. This approach models an individual wavefront as a mesh that is adaptively refined as the wave travels through an earth model. The algorithm, implemented here for quasi-compressional waves, provides an effective tool for modeling and analyzing a large vertical seismic-profile data set from the Gulf of Mexico. Seismic velocities in this region generally increase linearly with depth, but simulations show that an isotropic vertical-gradient model cannot accurately reproduce traveltimes of first arrivals. However, a simple velocity-analysis inversion based on the wavefront-construction method allows a straightforward estimation of improved isotropic and transversely isotropic models that significantly reduce the misfit between computed traveltimes and the observations. The goal of this analysis is to produce a simple model suitable for use as a starting point for migrations and for assessing the importance of anisotropy in the field site. In fact, the final anisotropic model is much more consistent with background geologic information than the best isotropic model, which also has a larger rms traveltime error. The results strongly support the presence of measurable anisotropy.

Parallel computing is widely used for large scale three-dimensional simulation of seismic wave propagation. One particularity of most of these simulations is to consider a finite computing domain whereas the physical problem is unbounded. Additional numerical conditions are then required to absorb the energy at the artificial boundaries, which introduces a different formulation and a load-imbalance. In the context of finite difference method, we study the use of thread overloading approach to alleviate the imbalance. We introduce a mixed-hybrid parallel implementation based on a classical cartesian partitioning at the MPI level and a self-scheduling algorithm at the thread level to handle more than 700 threads on 8 processors. We demonstrate the efficiency of our methodology on an example of regional modeling performed on 80 processors.

A hybrid method combining finite element and 4th-order finite difference techniques is developed to model SH and P-SV seismic wave propagation in a 2D elastic medium with irregular surface topography. Both the classic staggered grid finite difference scheme and the partially staggered grid scheme are tested. The accuracy of the hybrid method is studied by comparison with a semi-analytical and another numerical method. Subsequently, to study the amplification, numerical simulations of seismic wave propagation in a series of hills are carried out and compared with the single-hill case. Depending on the position of the source in relation to the topography, the ratio between the heights and lengths of the hills or the ratio between the lengths of the hills and the wavelength, the presence of several hills as opposed to a single one can increase the amplification effect due to topography. This study highlights the fact that, when evaluating topographic site effects, surrounding topography must be taken into account in addition to local topography.

We review the application of the discrete wave number method to problems of scattering of seismic waves formulated in terms of boundary integral equation and boundary element methods. The approach is based on the representation of the diffracting surfaces and interfaces of the medium by surface distributions of sources or by boundary source elements, the radiation from which is equivalent to the scattered wave field produced by the diffracting boundaries. The Green's functions are evaluated by the discrete wave number method, and the boundary conditions yield a linear system of equations. The inversion of this system allows the calculation of the full wave field in the medium. We investigate the accuracy of the method and we present applications to the simulation of surface seismic surveys, to the diffraction of elastic waves by fractures, to regional crustal wave propagation and to topographic scattering.

Finite difference simulation of seismic wave propagation in 2D solids with spatial distribution of discrete fractures