Numerical simulation of seismic waves in 3-D orthorhombic poroelastic medium with microseismic source implementation

Abstract

SUMMARY We have carried out microseismic forward modelling in orthorhombic poroelastic medium. The seismic response to isotropic (ISO) source, double couple (DC) source and compensated linear vector dipole (CLVD) source was solved by finite-difference algorithm in time domain, respectively. We used analytical solution to test our numerical algorithm and find that the match between the analytical solutions and numerical solutions is sufficiently close. We then designed several different models to calculate the seismic response and analyse the effect of medium parameters and source mechanism on the propagation of seismic waves. We observed from the modelling results that ISO source excites two kinds of waves in isotropic medium, which are fast longitudinal wave and slow longitudinal wave, while the DC and CLVD sources excite three kinds of waves in isotropic medium, including a transverse wave in addition to the fast and slow longitudinal waves. All of these three kinds of sources generate four kinds of seismic waves in orthorhombic poroelastic medium. These are two separable transverse waves in addition to the fast and slow longitudinal waves. The fluid viscosity and medium tortuosity has an effect on the propagation of the slow longitudinal wave. The slow longitudinal wave appears in propagating mode under the effect of low fluid viscosity and appears at the source location in a static mode under the effect of high fluid viscosity. The wavefield snapshot of the slow longitudinal wave has a circular shape when the tortuosity is isotropic, whereas it has an oval shape when the tortuosity is anisotropic. As far as the anisotropic parameters are concerned, the anisotropy of the fast longitudinal wave is more sensitive to the value of $\varepsilon ( {{\varepsilon _1},{\varepsilon _2}} )$, while the value of ${\rm{\delta }}( {{{\rm{\delta }}_1},{{\rm{\delta }}_2},{{\rm{\delta }}_3}} )$ has more effect on the anisotropic behaviour of the two separable transverse waves.