Synthesis of vector wave envelopes on the free surface of a random medium for the vertical incidence of a plane wavelet based on the Markov approximation

Abstract

[1] In short-period seismograms of earthquakes, we often observe the broadening of apparent duration of P and/or S waves and the excitation of the transverse component especially for P waves as travel distance increases. Such phenomena are well explained by scattering caused by random velocity fluctuation in the lithosphere. The Markov approximation is known as one of the powerful stochastic methods for the direct synthesis of wave envelopes. We extend the method to synthesize vector wave envelopes on the free surface of a random medium since seismic observation is usually done on the ground surface. We evaluate the mean square (MS) envelope on the free surface by multiplying the amplification factor on the free surface to the angular spectrum in an infinite random medium. We synthesize MS envelopes for the vertical incidence of an impulsive plane P or S wavelet into a 3-D random medium characterized by a Gaussian autocorrelation function with typical parameters of the lithosphere. As a result, the vertical and horizontal component MS envelopes show different amplification rates on the free surface; however, we may say that "a factor of 4" is a good approximation for the amplification rate for both components. Finally, we numerically confirm the validity of our direct envelope syntheses by the comparison with finite difference simulations of waves in 2-D random media. The Markov approximation is accurate when the wavelength is shorter than the correlation distance and the fractional fluctuation is much smaller than the ratio of the correlation distance to the propagation distance.Citation: Emoto, K., H. Sato, and T. Nishimura (2010), Synthesis of vector wave envelopes on the free surface of a random medium for the vertical incidence of a plane wavelet based on the Markov approximation,

Seismic Wave Propagation and Scattering in the Heterogeneous Earth : Second Edition

“…Emoto et al (2010) examined how the free surface affects the wave envelope of each vector component after the propagation through a random medium for the vertical incidence of a plane wavelet. Emoto et al (2010) examined how the free surface affects the wave envelope of each vector component after the propagation through a random medium for the vertical incidence of a plane wavelet.…”

“…Emoto et al (2010) examined how the free surface affects the wave envelope of each vector component after the propagation through a random medium for the vertical incidence of a plane wavelet. Emoto et al (2010) made a comparison of Markov envelopes and FD envelopes on the free surface of random media. In this case, multiplying the free-surface amplification factor for plane waves, which includes conversion between P-and S-waves, by the angular spectrum just beneath the free surface, and integrating it over ray angles, they calculate each displacement vector-component envelope on the free surface, where the excitation of surface waves is neglected.…”

Measurement of intrinsic and scattering attenuation of shear waves in two sedimentary basins and comparison to crystalline sites in Germany

“…(4) with C = 1 is valid for the full space. Because most stations are deployed on the surface, a free surface correction is introduced with a factor C = 4 (Emoto et al 2010). f can usually be approximated by the difference between upper and lower corner frequency depending on the filter design.…”

OpenSWPC: an open-source integrated parallel simulation code for modeling seismic wave propagation in 3D heterogeneous viscoelastic media

“…The planewave incidence uses a solution of the up-going wave of the 1D wave equation in a homogeneous medium as an initial condition of the velocity and stress components at the bottom of the model (e.g., Emoto et al 2010). A bell-like-shaped spatial distribution corresponding to the source time function (Fig.…”

“…The numerical simulation of seismic wave propagation is a fundamental tool for seismological studies such as estimation of the heterogeneous velocity structure (e.g., Tape et al 2009;Chen and Lee 2015), the study of seismic source processes (e.g., Lee et al 2006;Imperatori and Gallovič 2017), wave propagation in the heterogeneous Earth (e.g., Frankel and Clayton 1986;Emoto et al 2010) and hazard assessment (e.g., Graves et al 2010;Maeda et al 2016). Significant improvements in numerical simulation techniques, high-resolution velocity structure models and high-performance computer systems have enabled the use of 3D numerical simulations as a practical tool for regular data processing studies with currently available parallel computers.…”