Numerical Modeling of Seismic Wave Propagation at the Micro-Scale in Digitized Sandstone
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Author(s)
Zhang, Yang
Song, Fuxian
Toksoz, M. Nafi
Date Issued
2007
Publisher
Massachusetts Institute of Technology. Earth Resources Laboratory
Series/Report no.
Earth Resources Laboratory Industry Consortia Annual Report;2007-12
Abstract
In this paper, we first examine the relationship between the relative particle motions of fluids and solids
and the seismic signal received when compressional waves propagate through saturated porous materials.
We use a rotated-staggered-grid finite difference modeling scheme to simulate elastic wave phenomena in a
digitized 2D structural model obtained from micrographs of a loose beach sand. When considering
ultrasonic wave propagation wave in models with explicit inclusion of granular structure, the
heterogeneities of quartz and pores in size and shape lead to frequency-dependent seismic phenomena. By
comparing the numerical results from models where three sources with different frequencies were used, we
saw that (1) strong particle motions concentrate mostly in fluid; (2) significant variations in pressure are
observed in the fluid; (3) during the dynamic process of wave propagation, relative particle motion of the
fluid and solid phases induces stress concentration on the sharp tips and corner of grains; (4) coherent
particle motion is generated by sources with low frequency content, while sources with higher frequencies
induce disordered particle motions. Corresponding to these particle motions, less scattered energy is
observed in cases with more coherent particle motion, and strong scattering is generated by disordered
particle motion.
Then we extend our work to a 3D digitized Fontainebleau sandstone sample. Though the size of the sample
is small, we still consider a relative broad source frequency band (100 kHz – 20 MHz) so as to study the
frequency dependent behavior of this sample. We notice a velocity minimum occurring at some “critical
frequency” (750 kHz). Above this “critical frequency”, the velocity increases with frequency; while below
this frequency, velocity goes to a low frequency value – effective medium value. The transition from low
frequency to high frequency behavior can be viewed as going from wave-like to ray-like propagation. We
then study the fluid effect by saturating the pores with non-viscous and viscous brine and oil. The
velocities for samples saturated with fluids are generally larger than those of dry sample at frequencies
below the critical one, which shows the significant effect of the compressibility of fluids. While the
velocities become smaller than those of dry sample at frequencies above the critical one, which shows that
the density of fluids comes into play a significant role. We see little effect of viscosity of fluids on
velocity. To investigate the scale effect, we first compare the result from dynamic modeling for case with
source frequency of 100 kHz to that from static modeling by using finite element method on a sub-cube
selected from the original sample. Then we elongate the 3D sample in one direction by repeating the
original sample five times, and compare the result from this elongated one to that from the original one at
source frequency of 100 kHz. Velocities for these three cases are close to each other. Smaller velocity
from static modeling might be due to the higher porosity of the selected sub-cube sample.
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