A staggered-grid high-order finite-difference modeling for elastic wave field in arbitrary tilt anisotropic media

The paper presents a staggered-grid any even-order accurate finite-difference scheme for two-dimensional (2D), three-component (3C), first-order stress-velocity elastic wave equation and its stability condition in the arbitrary tilt anisotropic media; and derives a perfectly matched absorbing layer (PML) boundary condition and its stag- gered-grid any even-order accurate difference scheme in the 2D arbitrary tilt anisotropic media. The results of nu- merical modeling indicate that the modeling precision is high, the calculation efficiency is satisfactory and the absorbing boundary condition is better. The wave-front shapes of elastic waves are complex in the anisotropic media, and the velocity of qP wave is not always faster than that of qS wave. The wave-front triplication of qS wave and its events in both reflected domain and propagated domain, which are not commonly hyperbola, is a common phenomenon. When the symmetry axis is tilted in the TI media, the phenomenon of S-wave splitting is clearly observed in the snaps of three components and synthetic seismograms, and the events of all kinds of waves are asymmetric.

PML Absorbing Boundary Condition for Seismic Numerical Modeling by Convolutional Differentiator in Fluid-Saturated Porous Media

The perfectly matched layer（PML） was first introduced by Berenger as an absorbing boundary condition for electromagnetic wave propagation.In this article,a method is developed to ex-tend the PML to simulating seismic wave propagation in fluid-saturated porous medium.This non-physical boundary is used at the computational edge of a Forsyte polynomial convolutional differenti-ator（FPCD） algorithm as an absorbing boundary condition to truncate unbounded media.The incor-poration of PML in Biot＇s equations is given.Numerical results show that the PML absorbing bound-ary condition attenuates the outgoing waves effectively and eliminates the reflections adequately.

Poroelastic finite-difference modeling for ultrasonic waves in digital porous cores

Scattering attenuation in short wavelengths has long been interesting to geophysicists. Ultrasonic coda waves, observed as the tail portion of ultrasonic wavetrains in laboratory ultrasonic measurements, are important for such studies where ultrasonic waves interact with smallscale random heterogeneities on a scale of micrometers, but often ignored as noises because of the contamination of boundary reflections from the side ends of a sample core. Numerical simulations with accurate absorbing boundary can provide insight into the effect of boundary reflections on coda waves in laboratory experiments. The simulation of wave propagation in digital and heterogeneous porous cores really challenges numerical techniques by digital image of poroelastic properties, numerical dispersion at high frequency and strong heterogeneity, and accurate absorbing boundary schemes at grazing incidence. To overcome these difficulties, we present a staggered-grid high-order finite-difference （FD） method of Biot＇s poroelastic equations, with an arbitrary even-order （2L） accuracy to simulate ultrasonic wave propagation in digital porous cores with strong heterogeneity. An unsplit convolutional perfectly matched layer （CPML） absorbing boundary, which improves conventional PML methods at grazing incidence with less memory and better computational efficiency, is employed in the simulation to investigate the influence of boundary reflections on ultra- sonic coda waves. Numerical experiments with saturated poroelastic media demonstrate that the 2L FD scheme with the CPML for ultrasonic wave propagation significantly improves stability conditions at strong heterogeneity and absorbing performance at grazing incidence. The boundary reflections from the artificial boundary surrounding the digital core decay fast with the increase of CPML thick- nesses, almost disappearing at the CPML thickness of 15 grids. Comparisons of the resulting ultrasonic coda Qsc values between the numerical and experimental ultrasonic S waveforms for a cylindrical rock sample demonstrate that the boundary reflection may contribute around one-third of the ultrasonic coda attenuation observed in laboratory experiments.