2D finite‐difference viscoelastic wave modelling including surface topography

Abstract

We have pursued two‐dimensional (2D) finite‐difference (FD) modelling of seismic scattering from free‐surface topography. Exact free‐surface boundary conditions for the particle velocities have been derived for arbitrary 2D topographies. The boundary conditions are combined with a velocity–stress formulation of the full viscoelastic wave equations. A curved grid represents the physical medium and its upper boundary represents the free‐surface topography. The wave equations are numerically discretized by an eighth‐order FD method on a staggered grid in space, and a leap‐frog technique and the Crank–Nicholson method in time. In order to demonstrate the capabilities of the surface topography modelling technique, we simulate incident point sources with a sinusoidal topography in seismic media of increasing complexities. We present results using parameters typical of exploration surveys with topography and heterogeneous media. Topography on homogeneous media is shown to generate significant scattering. We show additional effects of layering in the medium, with and without randomization, using a von Kármán realization of apparent anisotropy. Synthetic snapshots and seismograms indicate that prominent surface topography can cause back‐scattering, wave conversions and complex wave patterns which are usually discussed in terms of inter‐crust heterogeneities.

Sub-basalt seismic imaging using optical-to-acoustic model building and wave equation datuming processing

“…This internal heterogeneity and the existence of rough surfaces can severely distort and scatter the seismic wavefield. The role of wave scattering in seismic imagery is well documented in the literature (Gibson and Levander, 1998;Martini et al, 2001;Martini and Bean, 2002a;Pullammanappallil et al, 1997) as well as the effect of irregular interfaces on wave propagation (Hestholm and Ruud, 2000;Bean, 2002a,b, Paul andCampillo, 1988;Purnell et al, 1990). This scattering can be both coherent, where waves reverberate within individual layers, and incoherent, producing 'random noise' through which deeper sub-basalt reflections are difficult to identify (Martini and Bean, 2002a,b).…”

Local time–space mesh refinement for simulation of elastic wave propagation in multi-scale media

“…Full-scale simulation can be used to study the peculiarities of wave propagation in complex models, such as anisotropic [1,2], viscoelastic [1], and poroelastic models [3,4], and models with irregular topography [5][6][7], etc. Moreover, numerical simulation is an essential element in seismic imaging procedures such as Reverse Time Migration and Full Waveform Inversion [8].…”

A linearized Euler finite-difference time-domain sound propagation model with terrain-following coordinates

“…Since then the use of terrainfollowing coordinates with height, pressure or entropy as the vertical coordinate, is the standard method to include the effect of hilly or mountainous terrain in meteorological numerical simulations and numerical weather prediction. Coordinate transformations were also used in seismic wave propagation modeling to consider the topography ͑Hestholm and Ruud, 1994;Hestholm, 1999͒. With respect to acoustical modeling, but not with the focus on outdoor sound propagation, Botteldooren ͑1994͒ proposed a FDTD model which uses a quasi-Cartesian grid to incorporate the effects of tilted and curved boundaries.…”