L. Margerin

Correlation of random wavefields: An interdisciplinary review

This paper presents an interdisciplinary review of the correlation properties of random wavefields. We expose several important theoretical results of various fields, ranging from time reversal in acoustics to transport theory in condensed matter physics. Using numerical simulations, we introduce the correlation process in an intuitive manner.We establish a fruitful mapping between time reversal and correlation, which enables us to transpose many known results from acoustics to seismology. We show that the multiple-scattering formalism developed in condensed matter physics provides a rigorous basis to analyze the field correlations in disordered media. We discuss extensively the various factors controllingandaffectingtheretrievaloftheGreen’sfunction of a complex medium from the correlation of either noise or coda.Acousticimagingofcomplexsamplesinthelaboratory and seismic tomography of geologic structures give a glimpse of the promising wide range of applications of the correlationmethod.

Empirical synthesis of time‐asymmetrical Green functions from the correlation of coda waves

[1]xa0We demonstrate the existence of long-range field correlations in the seismic coda of regional records in Alaska. The cross correlations between the different components of coda records at two points are measured for a set of distant earthquakes. Remarkably, while individual correlations have a random character, the correlations averaged over source and time exhibit deterministic arrivals that obey the same symmetry rules as the Green tensor between the two points. In addition, the arrival times of these waves coincide with propagating surface waves between the two stations. Thus we propose to identify the averaged correlation signals with the surface wave part of the Green tensor. We observe the causal and anticausal parts of the Green function. However, we find experimentally that amplitudes at positive and negative times are not equal. We explain this observation by the long-lasting anisotropy of the diffuse field. We show that the flux of energy coming from the source can still dominate the late coda and result in nonsymmetric cross correlations when the distribution of earthquakes is not isotropic around the stations. The extraction of Green functions from coda waves allows new types of measurements with seismic waves along paths between stations that could not be obtained with the waves produced by earthquakes.

Multiple scattering of high‐frequency seismic waves in the deep Earth: PKP precursor analysis and inversion for mantle granularity

mantle scattering models reproduce with reasonable accuracy the time dependence of precursors, in agreement with previous findings. Exponential correlations predict a spatial rate of decay of the precursor amplitude which is much faster than observed. Thus we are led to propose a new model of mantle heterogeneity, richer in small-scale than exponential media, that fits uniformly the data. An analytic form of the correlation function and power spectrum of our new model is given explicitly. It is shown that the precise length scale of heterogeneities is fundamentally unresolvable because of the limited range of observations. The perturbations in P wave velocities required to fit the data are only of order 0.1–0.2%, which is more than 1 order of magnitude less than found in previous studies. INDEX TERMS: 7203 Seismology: Body wave propagation; 7207 Seismology: Core and mantle; 7260 Seismology: Theory and modeling; KEYWORDS: multiple scattering, radiative transfer, heterogeneity, power spectrum, lower mantle, D 00 layer

Nonstationary Stochastic Simulation of Strong Ground Motion Time Histories Including Natural Variability: Application to the K-Net Japanese Database

Physical models that can be used to obtain realistic accelerograms usually require a thorough knowledge of the source, path, and site effects. In addition, the computational resources needed might be expensive. Thus, empirical models still represent a good alternative for simulating strong ground motion. In this work, we modify and improve the model developed by Sabetta and Pugliese (1996). This new method models the time-domain accelerogram based on the assumption that the phase is random and that the time envelope can be represented by the so-called average instantaneous power. This is, in turn, described as a lognormal distribution for P and S waves combined with an algebro-exponential function representing the envelope of coda waves. In addition, the frequency content of the signal is nonstationary and follows a modified ω -square model. The method depends on four common indicators in earthquake engineering: peak ground acceleration, strong-motion duration, Arias intensity, and central frequency. These indicators are empirically connected to a given database by means of ground-motion prediction equations. In this study we calibrate the model using Japanese data recorded by the K-net array, which has high-quality digital accelerograms and station-site conditions characterized by geotechnical measurements. In addition, this technique permits the inclusion of the uncertainty of the model parameters to take into account the ground-motion natural variability in the stochastic generation of the time histories. The main goal of this work is to provide the earthquake engineering community with a flexible tool to generate realistic accelerograms for dynamic studies.

The Energy Partitioning and the Diffusive Character of the Seismic Coda

Following recent theoretical developments of the radiative transfer the- ory of elastic waves, we propose to use the ratio R of energies of curl and divergence part of the ground displacement to distinguish between the different possible domi- nant scattering regimes in the lithosphere. A consequence of the diffusion regime is the partitioning of the energy between different vibrational modes, which is inde- pendent of time. It results in the stabilization of R. This behavior is not expected if low-order diffraction (such as single scattering) is dominant. We apply our technique to seismograms recorded by a small-aperture seismic array operated during June- August 1997 in Guerrero (Mexico). We estimate the energy ratio R in the coda of 13 earthquakes recorded by the array. We find it to be very stable in the coda window, while the energy level itself changes by several orders of magnitude. The value of R is 7 1, independent of the earthquake location and the magnitude. The observed stabilization of R is a strong indication of the diffusive regime of the seismic coda.

Passive retrieval of Rayleigh waves in disordered elastic media.

When averaged over sources or disorder, cross correlation of diffuse fields yields the Greens function between two passive sensors. This technique is applied to elastic ultrasonic waves in an open scattering slab mimicking seismic waves in the Earths crust. It appears that the Rayleigh wave reconstruction depends on the scattering properties of the elastic slab. Special attention is paid to the specific role of bulk to Rayleigh wave coupling, which may result in unexpected phenomena, such as a persistent time asymmetry in the diffuse regime.

Introduction to Radiative Transfer of Seismic Waves

We present a detailed introduction to radiative transfer in seismology. Starting from the well-known phenomenological approach for acoustic waves, the theory is then generalized to elastic waves, including the treatment of polarization and mode conversions. The last part of the paper presents a first-principle derivation of the acoustic transfer equation. The fundamental quantities of transport theory such as the specific intensity and the mean free path are then rigorously defined in terms of the statistical properties of the medium and wavefield. Some applications of the theory are discussed.

Effect of Absorption on Energy Partition of Elastic Waves in the Seismic Coda

The stabilization of the ratio of P to S energy in the multiple scattering regime was first predicted theoretically by Weaver (1982) and has been recently observed in the high-frequency coda of earthquakes by Shapiro et al. (2000). The goal of this note is to extend previous theoretical results to the case where anelasticity is present in the medium. Our study demonstrates that even if there is preferential absorption of one of the modes ( P or S ), a stabilization occurs in the multiple scattering regime. The new equilibrium ratio is shifted in favor of the mode that is least absorbed but rarely differs by more than 15% from the ratio predicted for purely elastic media.

Coherent backscattering of elastic waves: Specific role of source, polarization, and near field

Calculation of coherent backscattering of elastic waves in an infinite isotropic random medium is presented. Despite the simplicity of this geometry, this calculation highlights several specific aspects for seismic detection: near field detection, polarization, and the symmetry of the source. Line profiles and enhancement factors are seen to be time independent and are calculated for kinetic, shear, and compressional energy.

Phase Statistics of Seismic Coda Waves

We report the analysis of the statistics of the phase fluctuations in the coda of earthquakes recorded during a temporary experiment deployed at Pinyon Flats Observatory, California. The observed distributions of the spatial derivatives of the phase in the seismic coda exhibit universal power-law decays whose exponents agree accurately with circular Gaussian statistics. The correlation function of the phase derivative is measured and used to estimate the mean free path of Rayleigh waves.