Anisotropic finite-difference algorithm for modeling elastic wave propagation in fractured coalbeds

摘要

The simulation of wave propagations in coalbeds is chal-lenged by two major issues: (1) strong anisotropy resulting from high-density cracks/fractures in coalbeds and (2) nu-merical dispersion resulting from high-frequency content (the dominant frequency can be higher than 100 Hz). We present a staggered-grid high-order finite-difference (FD) method with arbitrary even-order (2L) accuracy to overcome the two difficulties stated above. First, we derive the formulae based on the standard Taylor series expansion but given in a neat and explicit form. We also provide an alternative way to calculate the FD coefficients. The detailed implementations are shown and the stability condition for anisotropic FD mod-eling is examined by the eigenvalue analysis method. Then, we apply the staggered-grid FD method to 2D and 3D coalbed models with dry and water-saturated fractures to study the characteristics of the 2D/3C elastic wave propagation in ani-sotropic media. Several factors, like density and direction of vertical cracks, are investigated. Several phenomena, like S-wave splitting and waveguides, are observed and are con-sistent with those observed in a real data set. Numerical re-sults show that our formulae can correlate the amplitude and traveltime anisotropies with the coal seam fractures.