Simulating the Envelope of Scalar Waves in 2D Random Media Having Power-Law Spectra of Velocity Fluctuation

Abstract

During propagation through random media, impulsive waves radiated from a point source decrease in amplitude and increase in duration with increasing travel distance. The excitation of coda waves is prominent at long lapse time. We use a finite-difference method to numerically simulate scalar waves that propagate through random media characterized by a von Karman autocorrelation function. The power spectral density function of fractional velocity fluctuation for κ -th order von Karman-type random media obeys a power law at large wavenumbers. Such media are considered to be appropriate models for the random component of the structure of the Earth's lithosphere. The average of the square of numerically calculated wave traces over an ensemble of random media gives the reference envelope for the evaluation of envelope simulation methods. The Markov approximation method gives reliable quantitative predictions of the entire envelope for random media that are poor in short wavelength components of heterogeneity ( κ = 1.0), while it fails to predict the coda envelope for random media that have rich short-wavelength components ( κ = 0.1). The radiative-transfer theory reliably predicts the coda excitation for κ = 0.1 when the momentum-transfer scattering coefficient is used as the effective isotropic scattering coefficient. Replacing the direct term of the radiative-transfer solution with the envelope of the Markov approximation, we propose a new method for simulating the entire envelope from the direct arrival through the coda. The method quantitatively explains the whole envelope for κ = 0.1. For the case of κ = 0.5, however, our method predicts too much coda excitation. In such a case, the method can explain whole envelopes by using the effective scattering coefficient estimated from coda excitation. Manuscript received 10 April 2002.