Viscoacoustic wave propagation simulation in the earth

Abstract

Anelasticity of earth materials produces significant changes in the amplitude and phase spectra of seismic waves. The anelastic properties of real materials, particularly of porous rocks, are described using the theory of linear viscoelasticity based on Boltzmann’s superposition principle. Wave‐propagation simulation with this model requires implementing the convolutional relation in the equation of motion. The choice of a viscoacoustic constitutive relation based on a spectrum of relaxation mechanisms allows a realistic description of the anelastic effects, and the introduction of memory variables obviates storing the entire strain history required by the time convolution. A pseudospectral time‐integration technique is used to solve the equation of motion. Applications of viscoacoustic modeling suggest the need for considering the correct attenuation‐dispersion effects for various fundamental seismic problems in anelastic earth models. Comparison of acoustic and viscoacoustic synthetic seismograms shows differences in the amplitudes and arrival times of the wave fields which are enhanced for particular combinations of anelastic and geometrical effects.