Accurate seabed modeling using finite difference methods

Abstract

Finite difference is the most widely used method for seismic wavefield modeling. However, most finitedifference implementations discretize the Earth model over a fixed grid interval. This can lead to irregular model geometries being represented by 'staircase' discretization, and potentially causes mispositioning of interfaces within the media. This misrepresentation is a major disadvantage to finite difference methods, especially if there exist strong and sharp contrasts in the physical properties along an interface. The discretization of undulated seabed bathymetry is a common example of such misrepresentation of the physical properties in finite-difference grids, as the seabed is often a particularly sharp interface owing to the rapid and considerable change in material properties between fluid seawater and solid rock. There are two issues typically involved with seabed modeling using finite difference methods: firstly, the travel times of reflections from the seabed are inaccurate as a consequence of its spatial mispositioning; secondly, artificial diffractions are generated by the staircase representation of dipping seabed bathymetry. In this paper, we propose a new method that provides a solution to these two issues by positioning sharp interfaces at fractional grid locations. To achieve this, the velocity The Unconventional Natural Gas Institute, China University of Petroleum (Beijing), Beijing 102249, China model is first sampled in a model grid that allows the center of the seabed to be positioned at grid points, before being interpolated vertically onto a regular modeling grid using the windowed sinc function. This procedure allows undulated seabed bathymetry to be represented with improved accuracy during modeling. Numerical tests demonstrate that this method generates reflections with accurate travel times and effectively suppresses artificial diffractions.

Multi-Directional Viscous Damping Absorbing Boundary in Numerical Simulation of Elastic Wave Dynamic Response

“…Numerical seismic wave field simulation based on the elastic wave equation is important to study the kinematics and dynamics characteristics of seismic wave propagation in geologic bodies, which is widely used in seismic design [1], geologic survey [2], and non-destructive structure detection [3]. Currently, the numerical seismic wave field simulation methods include the finite element method (FEM) [4,5], the finite difference method (FDM) [6,7], and the boundary element method (BDM) [8,9]. The FEM has become the most commonly used method for numerical seismic wave field simulation in geotechnical engineering due to its advantages in discretizing the mesh and free boundary treatment of irregular geological structures [10,11], and a variety of commercial software programs have been developed based on the FEM, such as ABAQUS (https: //www.3ds.com/products/simulia/abaqus), COMSOL (https://www.comsol.com/), and ANSYS (https://www.ansys.com/) (all accessed on 1 March 2024).…”

Eliminate Time Dispersion of Seismic Wavefield Simulation with Semi-Supervised Deep Learning

“…Researchers have developed wave-equation-based imaging methods such as reverse-time migration [2,3] and full-waveform inversion [4][5][6]. The finite-difference (FD) scheme is the most basic and often used method to solve the wave equation [7][8][9]. However, the FD approximations of time and space derivatives lead to numerical dispersion when the sample interval is large, even if it satisfies the stable condition [10,11].…”