Nonlinear Transformations of Seismic Waves in Soil Layers, High-order Spectra and Coherences as Characteristics of Nonlinearity

As shown in the previous chapters, the behavior of subsurface soft soils in the near-fault zones of strong earthquakes can be substantially nonlinear, and we may estimate the degree of nonlinearity in numerical experiments with models of soil behavior. Nonlinear transformations of seismic waves propagating in subsurface soils—nonlinear media—include changes in their waveforms and spectra. These changes are often clearly seen in strong motion records. Nonlinear effects in seismic wave fields can be considered as the results of changes of the medium properties caused by propagating waves and affecting both the propagation of the waves themselves (self-action) and the propagation of other seismic waves (interaction). In this chapter, we discuss the evolution of seismic waves in a nonlinear medium, nonlinear wave processes accompanying the propagation of intense seismic waves, and quasi-stationary shape of the spectrum of seismic motion on the surface. Nonlinearity of the soil response differently influences the ranges of low- and high- seismic frequencies, because it depends on the generation of combinational-frequency harmonics, mechanisms of decay instability regulated by Manley-Rowe relations, nonlinear hysteretic absorption and some other nonlinear mechanisms. As a result of the cumulative action of these mechanisms, spectrum of motion on the surface tends to take a quasi-stationary form E(f) ~ f −k. Nonlinear effects of modulation instability of seismic waves propagating in subsurface soils are studied in numerical experiments. Self-modulation and generation of sub-harmonics of the main (basic) frequencies are observed in intense seismic wave fields in cases of resonant amplification of seismic waves in soil layers; it precedes the stage of chaotization that occurs at further increase of the wave amplitudes. Analysis of high-order spectra and coherences is described, which allows us to identify and estimate nonlinear components of soil response based on seismic records. High-order spectra and coherencies (HOS and HOC) are used in system analysis to study the properties of nonlinear systems. In geophysics, mainly bispectrum and bicoherency are used; however, in order to detect nonlinear components in seismic signals, tricoherency and coherencies of higher odd orders should be more informative, because soils possess mainly odd-order nonlinearities.