Cross-correlation of 1 month of ambient seismic noise recorded at USArray stations in California yields hundreds of short-period surface-wave group-speed measurements on interstation paths. We used these measurements to construct tomographic images of the principal geological units of California, with low-speed anomalies corresponding to the main sedimentary basins and high-speed anomalies corresponding to the igneous cores of the major mountain ranges. This method can improve the resolution and fidelity of crustal images obtained from surface-wave analyses.

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High-resolution surface-wave tomography from ambient seismic noise.

SUMMARY Ambient noise tomography is a rapidly emerging field of seismological research. This paper presents the current status of ambient noise data processing as it has developed over the past several years and is intended to explain and justify this development through salient examples. The ambient noise data processing procedure divides into four principal phases: (1) single station data preparation, (2) cross-correlation and temporal stacking, (3) measurement of dispersion curves (performed with frequency‐time analysis for both group and phase speeds) and (4) quality control, including error analysis and selection of the acceptable measurements. The procedures that are described herein have been designed not only to deliver reliable measurements, but to be flexible, applicable to a wide variety of observational settings, as well as being fully automated. For an automated data processing procedure, data quality control measures are particularly important to identify and reject bad measurements and compute quality assurance statistics for the accepted measurements. The principal metric on which to base a judgment of quality is stability, the robustness of the measurement to perturbations in the conditions under which it is obtained. Temporal repeatability, in particular, is a significant indicator of reliability and is elevated to a high position in our assessment, as we equate seasonal repeatability with measurement uncertainty. Proxy curves relating observed signal-to-noise ratios to average measurement uncertainties show promise to provide useful expected measurement error estimates in the absence of the long time-series needed for temporal subsetting.

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Processing seismic ambient noise data to obtain reliable broad-band surface wave dispersion measurements

[1] We demonstrate that the coherent information about the Earth structure can be extracted from the ambient seismic noise We compute cross-correlations of vertical component records of several days of seismic noise at different pairs of stations separated by distances from about one hundred to more than two thousand kilometers Coherent broadband dispersive wavetrains clearly emerge with group velocities similar to those predicted from the global Rayleigh-wave tomographic maps that have been constrained using ballistic surface waves Those results show that coherent Rayleigh waves can be extracted from the ambient seismic noise and that their dispersion characteristics can be measured in a broad range of periods This provides a source for new types of surface-wave measurements that can be obtained for numerous paths that could not be sampled with the ballistic waves and, therefore, can significantly improve the resolution of seismic images

/pdf/emergence-of-broadband-rayleigh-waves-from-correlations-of-2lpry85w2t.pdf

Emergence of broadband Rayleigh waves from correlations of the ambient seismic noise.

The late seismic coda may contain coherent information about the elastic response of Earth. We computed the correlations of the seismic codas of 101 distant earthquakes recorded at stations that were tens of kilometers apart. By stacking cross-correlation functions of codas, we found a low-frequency coherent part in the diffuse field. The extracted pulses have the polarization characteristics and group velocities expected for Rayleigh and Love waves. The set of cross-correlations has the symmetries of the surface-wave part of the Green tensor. This seismological example shows that diffuse waves produced by distant sources are sufficient to retrieve direct waves between two perfectly located points of observation. Because it relies on general properties of diffuse waves, this result has potential applications in other fields.

https://science.sciencemag.org/content/sci/299/5606/547.full.pdf

Long-range correlations in the diffuse seismic coda.

The Green's function of waves that propagate between two receivers can be found by cross-correlating multiply scattered waves recorded at these receivers. This technique obviates the need for a source at one of these locations, and is therefore called "passive imaging." This principle has been explained by assuming that the normal modes of the system are uncorrelated and that all carry the same amount of energy (equipartitioning). Here I present an alternative derivation of passive imaging of the ballistic wave that is not based on normal modes. The derivation is valid for scalar waves in three dimensions, and for elastic surface waves. Passive imaging of the ballistic wave is based on the destructive interference of waves radiated from scatterers away from the receiver line, and the constructive interference of waves radiated from secondary sources near the receiver line. The derivation presented here shows that the global requirement of the equipartitioning of normal modes can be relaxed to the local requirement that the scattered waves propagate on average isotropically near the receivers.

/pdf/extracting-the-green-s-function-from-the-correlation-of-coda-47o1qpn8yf.pdf

Extracting the Green's function from the correlation of coda waves: A derivation based on stationary phase

A diffuse acoustic field is shown to have correlations equal to the Green’s function of the body. Simple plausibility arguments for this assertion are followed by a more detailed proof. A careful version of the statement is found to include caveats in regard to how diffuse the field truly is, the spectrum of the diffuse field, and the phase of the receivers. Ultrasonic laboratory tests confirm the assertion. The main features of the direct signal between two transducers are indeed recovered by cross correlating their responses to a diffuse field generated by a third transducer. The quality of the recovery improves with increased averaging and the use of multiple sources. Applications are discussed.

On the emergence of the Green's function in the correlations of a diffuse field

Noise generated in an ultrasonic receiver circuit consisting of transducer and amplifier is usually ignored, or treated as a nuisance. Here it is argued that acoustic thermal fluctuations, with displacement amplitudes of 3 fm, contain substantial ultrasonic information. It is shown that the noise autocorrelation function is the waveform that would be obtained in a direct pulse/echo measurement. That thesis is demonstrated in experiments in which direct measurements are compared to correlation functions. The thermal nature of the elastodynamic noise that generates these correlations is confirmed by an absolute measurement of their strength, essentially a measurement of the sample temperature.

Ultrasonics without a source: thermal fluctuation correlations at MHz frequencies.

On the emergence of the Green's function in the correlations of a diffuse field: pulse-echo using thermal phonons.

As is now well known, the relation between diffuse field correlations and the Green’s function follows directly from a definition of a diffuse field as an uncorrelated smooth spectral superposition of normal modes. Such a definition is, however, inapplicable in most open structures, the earth in particular. A preferable definition might be that of room acoustics: a diffuse field is an uncorrelated isotropic superposition of plane waves. But that definition is inapplicable to heterogeneous structures, or near boundaries. Here, a definition of a local diffuse field applicable to open heterogeneous systems is proposed. A local diffuse field is taken to be one in steady‐state equilibrium with the field in a homogeneous region having an uncorrelated isotropic superposition of incident plane waves. This definition is applicable to both heterogeneous and open systems, and is shown using a reciprocity argument to lead to the familiar identity between the local Green’s function of the structure and the diffuse fields correlations.

Diffuse fields in open systems and the emergence of the Green’s function (L)

We study the temperature dependence of diffuse reverberant ultrasound in elastic bodies. Transient wave forms are found to undergo an almost pure dilation of 0.0277% per degree, related to the temperature dependence of wave speeds. The wave forms also suffer a distortion that, we argue, depends on the rate of conversion between the dilatational (P) and shear (S) waves. Distortion is found to scale in a manner consistent with theoretical arguments but also appears to be a function of the degree of ray chaos in the body, indicating that the mixing rates are slower in more regular bodies.

Oleg I. Lobkis

Papers

On the emergence of the Green's function in the correlations of a diffuse field

Ultrasonics without a source: thermal fluctuation correlations at MHz frequencies.

On the emergence of the Green's function in the correlations of a diffuse field: pulse-echo using thermal phonons.

Diffuse fields in open systems and the emergence of the Green’s function (L)

Coda-wave interferometry in finite solids: recovery of P-to-S conversion rates in an elastodynamic billiard.