Synthesis of scalar-wave envelopes in two-dimensional weakly anisotropic random media by using the Markov approximation

Due to the Earth's inhomogeneity, seismogram envelopes increase in duration and decrease in amplitude with increasing travel distance. Those features have been explained on the basis of the forward scattering in random media using the Markov approximation. Since the conventional studies assumed isotropic random media, they were not realistic enough to represent the anisotropic lithosphere characterized by long horizontal and short vertical correlation distances. Using the Markov approximation, the present study formulates the envelope synthesis in 2-D weakly anisotropic random media characterized by Gaussian and von Kármán-type autocorrelation functions (ACF). Also, wave propagation is numerically simulated with the finite-difference (FD) method; 2 Hz Ricker wavelets propagate through the random media characterized by 4 km s⁻¹ average velocity and the Gaussian ACF with 5 km horizontal correlation distance, 2.5 km vertical correlation distance, and 5 per cent rms fractional velocity fluctuation. We find a good coincidence between the envelopes of the Markov approximation and those of the FD simulations, which supports the reliability of the synthesis method using the Markov approximation. The envelopes of the Markov approximation are scaled by using a characteristic time, which is a function of propagation direction and other model parameters. It predicts that envelopes increase in duration and decrease in maximum amplitude more rapidly in the horizontal propagation than in the vertical when the media are characterized by long horizontal and short vertical correlation distances. In the case of the vertical wave propagation, the envelope of the anisotropic random media has shorter duration and larger maximum amplitude than those of the isotropic random media. It means that the intensity of the inhomogeneity is underestimated when one analyses seismogram envelopes of deep events considering anisotropic lithosphere as isotropic random media.