scholarly journals Computation of ray-Born seismograms using isochrons

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. T245-T256 ◽  
Author(s):  
Martin Sarajaervi ◽  
Henk Keers
Keyword(s):  
Finite Difference ◽  
Frequency Domain ◽  
Heterogeneous Media ◽  
Acoustic Wave Equation ◽  
Seismic Modeling ◽  
Time Step ◽  
Velocity Models ◽  
Modeling Methods ◽  
Acoustic Media ◽  
The Time Domain

Seismic modeling in heterogeneous media is accomplished by using either approximate or fully numerical methods. A popular approximate method is ray-Born modeling, which requires the computation of 3D integrals. We have developed an integration technique for accurate and, under certain circumstances, efficient evaluation of the ray-Born integrals in the time domain. The 3D integrals are split into several 2D integrals, each of which gives the wavefield at a certain time, so that the waveform at each time step is computed independently of all other times. We compute seismograms for 3D heterogeneous acoustic media using this technique and compare these seismograms with seismograms computed using two other modeling methods: frequency-domain ray-Born modeling and finite-difference modeling of the acoustic wave equation. Our method can also be applied to elastic ray-Born modeling. Velocity models with smooth scatterers and the SEG/EAGE overthrust model are used for comparison. The ray-Born seismograms computed using the time- and frequency-domain ray-Born modeling methods are identical, as expected. The comparison between the ray-Born modeling and the finite-difference-modeling method indicates that the waveforms are similar for both types of velocity models. We evaluate the discrepancies in terms of multiple scattering and multipathing.

Efficient Two-dimensional Acoustic Wave Finite-Difference Numerical Simulation in Strongly Heterogeneous Media Using the Adaptive Mesh Refinement (AMR) Technique

Geophysics ◽  
2021 ◽  
pp. 1-76
Author(s):  
Chunli Zhang ◽  
Wei Zhang
Keyword(s):  
Finite Difference ◽  
Acoustic Wave ◽  
Adaptive Mesh Refinement ◽  
Heterogeneous Media ◽  
Mesh Refinement ◽  
Adaptive Mesh ◽  
Grid Spacing ◽  
Time Step ◽  
Velocity Models ◽  
The Stability

The finite-difference method (FDM) is one of the most popular numerical methods to simulate seismic wave propagation in complex velocity models. If a uniform grid is applied in the FDM for heterogeneous models, the grid spacing is determined by the global minimum velocity to suppress dispersion and dissipation errors in the numerical scheme, resulting in spatial oversampling in higher-velocity zones. Then, the small grid spacing dictates a small time step due to the stability condition of explicit numerical schemes. The spatial oversampling and reduced time step will cause unnecessarily inefficient use of memory and computational resources in simulations for strongly heterogeneous media. To overcome this problem, we propose to use the adaptive mesh refinement (AMR) technique in the FDM to flexibly adjust the grid spacing following velocity variations. AMR is rarely utilized in acoustic wave simulations with the FDM due to the increased complexity of implementation, including its data management, grid generation and computational load balancing on high-performance computing platforms. We implement AMR for 2D acoustic wave simulation in strongly heterogeneous media based on the patch approach with the FDM. The AMR grid can be automatically generated for given velocity models. To simplify the implementation, we employ a well-developed AMR framework, AMReX, to carry out the complex grid management. Numerical tests demonstrate the stability, accuracy level and efficiency of the AMR scheme. The computation time is approximately proportional to the number of grid points, and the overhead due to the wavefield exchange and data structure is small.

A hybrid method applied to a 2.5D scalar wave equation

2008 ◽  
Vol 45 (12) ◽  
pp. 1517-1525
Author(s):  
P. F. Daley ◽  
E. S. Krebes ◽  
L. R. Lines
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Heterogeneous Medium ◽  
Integral Transform ◽  
P Wave ◽  
Acoustic Wave Equation ◽  
Seismic Modeling ◽  
Subsurface Structures ◽  
Spatial Dimensions ◽  
Finite Integral

The 3D acoustic wave equation for a heterogeneous medium is used for the seismic modeling of compressional (P-) wave propagation in complex subsurface structures. A combination of finite difference and finite integral transform methods is employed to obtain a “2.5D” solution to the 3D equation. Such 2.5D approaches are attractive because they result in computational run times that are substantially smaller than those for the 3D finite difference method. The acoustic parameters of the medium are assumed to be constant in one of the three Cartesian spatial dimensions. This assumption is made to reduce the complexity of the problem, but still retain the salient features of the approach. Simple models are used to address the computational issues that arise in the modeling. The conclusions drawn can also be applied to the more general fully inhomogeneous problem. Although similar studies have been carried out by others, the work presented here is new in the sense that (i) it applies to subsurface models that are both vertically and laterally heterogeneous, and (ii) the computational issues that need to be addressed for efficient computations, which are not trivial, are examined in detail, unlike previous works. We find that it is feasible to generate true-amplitude synthetic seismograms using the 2.5D approach, with computational run times, storage requirements, and other factors, being at reduced and acceptable levels.

scholarly journals ONE-STEP EXTRAPOLATION METHOD USING CHEBYSHEV’S RECURRENCE RELATION APPLIED TO SEISMIC MODELING

2016 ◽  
Vol 34 (4) ◽  
Author(s):  
Laura Lara Ortiz ◽  
Reynam C. Pestana
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Difference Scheme ◽  
Chebyshev Polynomials ◽  
Finite Difference Scheme ◽  
Acoustic Wave Equation ◽  
Seismic Modeling ◽  
First Order ◽  
One Step

ABSTRACT. In this work we show that the solution of the first order differential wave equation for an analytical wavefield, using a finite-difference scheme in time, follows exactly the same recursion of modified Chebyshev polynomials. Based on this, we proposed a numerical...Keywords: seismic modeling, acoustic wave equation, analytical wavefield, Chebyshev polinomials. RESUMO. Neste trabalho, mostra-se que a solução da equação de onda de primeira ordem com um campo de onda analítico usando um esquema de diferenças finitas no tempo segue exatamente a relação de recorrência dos polinômios modificados de Chebyshev. O algoritmo...Palavras-chave: modelagem sísmica, equação da onda acústica, campo analítico, polinômios de Chebyshev.

Adaptive 27-point finite difference frequency domain method for wave simulation of 3D acoustic wave equation

Geophysics ◽  
2021 ◽  
pp. 1-39
Author(s):  
Wenhao Xu ◽  
Bangyu Wu ◽  
Yang Zhong ◽  
Jinghuai Gao ◽  
Qing Huo Liu
Keyword(s):  
Wave Equation ◽  
Finite Difference ◽  
Acoustic Wave ◽  
Frequency Domain ◽  
Difference Frequency ◽  
Lookup Table ◽  
Acoustic Wave Equation ◽  
Wave Simulation ◽  
Finite Difference Frequency Domain ◽  
Point Stencil

The finite-difference frequency-domain (FDFD) method has important applications in the wave simulation of various wave equations. To promote the accuracy and efficiency for wave simulation with the FDFD method, we have developed a new 27-point FDFD stencil for 3D acoustic wave equation. In the developed stencil, the FDFD coefficients not only depend on the ratios of cell sizes in the x-, y-, and z-directions, but we also depend on the spatial sampling density (SD) in terms of the number of wavelengths per grid. The corresponding FDFD coefficients can be determined efficiently by making use of the plane-wave expression and the lookup table technique. We also develop a new way for designing an adaptive FDFD stencil by directly adding some correction terms to the conventional second-order FDFD stencil, which is simpler to use and easier to generalize. Corresponding dispersion analysis indicates that, compared to the optimal 27-point stencil derived from the average-derivative method (ADM), the developed adaptive 27-point stencil can reduce the required SD from approximately 4 to 2.2 points per wavelength (PPW) for a cubic mesh and to 2.7 PPW for a general cuboid mesh. Numerical examples of a 3D homogeneous model and SEG/EAGE salt-dome model indicate that the developed stencil is more accurate than the ADM 27-point stencil for cubic and general cuboid meshes, while requiring similar CPU time and computational memory as the ADM 27-point stencil for direct and iterative solvers.

An optimal frequency-domain finite-difference operator with a flexible stencil and its application in discontinuous-grid modeling

Geophysics ◽  
2021 ◽  
pp. 1-41
Author(s):  
Na Fan ◽  
Xiao-Bi Xie ◽  
Lian-Feng Zhao ◽  
Xin-Gong Tang ◽  
Zhen-Xing Yao
Keyword(s):  
Finite Difference ◽  
Frequency Domain ◽  
Waveform Inversion ◽  
Uniform Grid ◽  
Optimal Method ◽  
Velocity Models ◽  
Full Waveform ◽  
Rotationally Symmetric ◽  
Grid Points ◽  
Coarse To Fine

We develop an optimal method to determine expansion parameters for flexible stencils in 2D scalar wave finite-difference frequency-domain (FDFD) simulation. The proposed stencil only requires the involved grid points to be paired and rotationally symmetric around the central point. We apply this method to the transition zone in discontinuous-grid modeling, where the key issue is designing particular FDFD stencils to correctly propagate the wavefield passing through the discontinuous interface. The proposed method can work in FDFD discontinuous-grid with arbitrary integer coarse-to-fine gird spacing ratios. Numerical examples are presented to demonstrate how to apply this optimal method for the discontinuous-grid FDFD schemes with spacing ratios 3 and 5. The synthetic wavefields are highly consistent to those calculated using the conventional dense uniform grid, while the memory requirement and computational costs are greatly reduced. For velocity models with large contrasts, the proposed discontinuous-grid FDFD method can significantly improve the computational efficiency in forward modeling, imaging and full waveform inversion.

NON LINEAR ANALYSIS OF SHIP MOTIONS AND LOADS IN LARGE AMPLITUDE WAVES

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
G Mortola ◽  
A Incecik ◽  
O Turan ◽  
S.E. Hirdaris
Keyword(s):  
Frequency Domain ◽  
Time Domain ◽  
Large Amplitude ◽  
Linear Time ◽  
Ship Motions ◽  
Wave Loads ◽  
Time Step ◽  
Strip Theory ◽  
Non Linear ◽  
The Time Domain

A non linear time domain formulation for ship motions and wave loads is presented and applied to the S175 containership. The paper describes the mathematical formulations and assumptions, with particular attention to the calculation of the hydrodynamic force in the time domain. In this formulation all the forces involved are non linear and time dependent. Hydrodynamic forces are calculated in the frequency domain and related to the time domain solution for each time step. Restoring and exciting forces are evaluated directly in time domain in a way of the hull wetted surface. The results are compared with linear strip theory and linear three dimensional Green function frequency domain seakeeping methodologies with the intent of validation. The comparison shows a satisfactory agreement in the range of small amplitude motions. A first approach to large amplitude motion analysis displays the importance of incorporating the non linear behaviour of motions and loads in the solution of the seakeeping problem.

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