This study presents stochastic methods to simulate wave envelopes in layeredrandom media. High-frequency Seismograms of small earthquakes are so complexdue to lithospheric inhomogeneity that seismologists often analyz...This study presents stochastic methods to simulate wave envelopes in layeredrandom media. High-frequency Seismograms of small earthquakes are so complexdue to lithospheric inhomogeneity that seismologists often analyze wave envelopesrather than wave traces to quantify the subsurface inhomogeneity. Since thestatistical properties of the inhomogeneity vary regionally, it is important to developand examine direct envelope simulation methods for non-uniform random media. Asa simple example, this study supposes planewave propagation through two-layer randommedia in 2-D composed of weak and strong inhomogeneity zones. The characteristicspatial-scale of the inhomogeneity is supposed to be larger than the wavelength,where small-angle scattering around the forward direction dominates large-angle scattering.Two envelope simulation methods based on the small-angle scattering approximationare examined. One method is to solve a differential equation for the twofrequencymutual coherence function with the Markov approximation. The other isto solve the stochastic ray bending process by using the Monte Carlo method basedon the Markov approximation for the mutual coherence function. The resultant waveenvelopes of the two methods showed excellent coincidence both for uniform and fortwo-layer random media. Furthermore, we confirmed the validity of the two methodscomparing with the envelopes made from the finite difference simulations of waves.The two direct envelope simulation methods presented in this study can be a mathematicalbase for the study of high-frequency wave propagation through randomlyinhomogeneous lithosphere in seismology.展开更多
文摘This study presents stochastic methods to simulate wave envelopes in layeredrandom media. High-frequency Seismograms of small earthquakes are so complexdue to lithospheric inhomogeneity that seismologists often analyze wave envelopesrather than wave traces to quantify the subsurface inhomogeneity. Since thestatistical properties of the inhomogeneity vary regionally, it is important to developand examine direct envelope simulation methods for non-uniform random media. Asa simple example, this study supposes planewave propagation through two-layer randommedia in 2-D composed of weak and strong inhomogeneity zones. The characteristicspatial-scale of the inhomogeneity is supposed to be larger than the wavelength,where small-angle scattering around the forward direction dominates large-angle scattering.Two envelope simulation methods based on the small-angle scattering approximationare examined. One method is to solve a differential equation for the twofrequencymutual coherence function with the Markov approximation. The other isto solve the stochastic ray bending process by using the Monte Carlo method basedon the Markov approximation for the mutual coherence function. The resultant waveenvelopes of the two methods showed excellent coincidence both for uniform and fortwo-layer random media. Furthermore, we confirmed the validity of the two methodscomparing with the envelopes made from the finite difference simulations of waves.The two direct envelope simulation methods presented in this study can be a mathematicalbase for the study of high-frequency wave propagation through randomlyinhomogeneous lithosphere in seismology.
