Peter Gerstoft

Surface wave tomography from microseisms in Southern California

Received 5 April 2005; revised 23 May 2005; accepted 9 June 2005; published 26 July 2005. [1] Since it has already been demonstrated that point-topoint seismic propagation Green Functions can be extracted from seismic noise, it should be possible to image Earth structure using the ambient noise field. Seismic noise data from 148 broadband seismic stations in Southern California were used to extract the surface wave arrival-times between all station pairs in the network. The seismic data were then used in a simple, but densely sampled tomographic procedure to estimate the surface wave velocity structure within the frequency range of 0.1–0.2 Hz for a region in Southern California. The result compares favorably with previous estimates obtained using more conventional and elaborate inversion procedures. This demonstrates that coherent noise field between station pairs can be used for seismic imaging purposes. Citation: Sabra, K. G., P. Gerstoft, P. Roux, W. A. Kuperman, and M. C. Fehler (2005), Surface wave tomography from microseisms in Southern California, Geophys. Res. Lett., 32, L14311, doi:10.1029/2005GL023155.

Seismic interferometry—turning noise into signal

Turning noise into useful data—every geophysicists dream? And now it seems possible. The field of seismic interferometry has at its foundation a shift in the way we think about the parts of the signal that are currently filtered out of most analyses—complicated seismic codas (the multiply scattered parts of seismic waveforms) and background noise (whatever is recorded when no identifiable active source is emitting, and which is superimposed on all recorded data). Those parts of seismograms consist of waves that reflect and refract around exactly the same subsurface heterogeneities as waves excited by active sources. The key to the rapid emergence of this field of research is our new understanding of how to unravel that subsurface information from these relatively complex-looking waveforms. And the answer turned out to be rather simple. This article explains the operation of seismic interferometry and provides a few examples of its application.

Inversion of seismoacoustic data using genetic algorithms and a posteriori probability distributions

The goal of many underwater acoustic modeling problems is to find the physical parameters of the environment. With the increase in computer power and the development of advanced numerical models it is now feasible to carry out multiparameter inversion. The inversion is posed as an optimization problem, which is solved by a directed Monte Carlo search using genetic algorithms. The genetic algorithm presented in this paper is formulated by steady‐state reproduction without duplicates. For the selection of ‘‘parents’’ the object function is scaled according to a Boltzmann distribution with a ‘‘temperature’’ equal to the fitness of one of the members in the population. The inversion would be incomplete if not followed by an analysis of the uncertainties of the result. When using genetic algorithms the response from many environmental parameter sets has to be computed in order to estimate the solution. The many samples of the models are used to estimate the a posteriori probabilities of the model parameters. T...

P‐waves from cross‐correlation of seismic noise

Received 13 June 2005; revised 19 August 2005; accepted 31 August 2005; published 6 October 2005. [1] We present results from the cross-correlations of seismic noise recordings among pairs of stations in the Parkfield network, California. When performed on many station pairs at short ranges, the noise correlation function (NCF) is the passive analog to a shot gather made with active sources. We demonstrate the presence of both a P-wave and a Rayleigh wave in the NCF. A time-frequency analysis allows us to separate the two wave packets that are further identified through their polarization. Arrival times were estimated from the NCF and they compared favorably with predictions using ray tracing in a regional velocity model and with the velocity gradient across the San Andreas Fault. Citation: Roux, P., K. G. Sabra, P. Gerstoft, W. A. Kuperman, and M. C. Fehler (2005), P-waves from crosscorrelation of seismic noise, Geophys. Res. Lett., 32, L19303,

Ocean acoustic inversion with estimation of a posteriori probability distributions

Inversion methods are applied in ocean acoustics to infer parameters which characterize the environment. The objective of this paper is to provide such estimates, and means of evaluating the inherent uncertainty of the parameter estimates. In a Bayesian approach, the result of inversion is the a posteriori probability density for the estimated parameters, from which all information such as mean, higher moments, and marginal distributions can be extracted. These are multidimensional integrals of the a posteriori probability density, which are complicated to evaluate for many parameters. Various sampling options are examined and it is suggested that “importance sampling” based on a directed Monte Carlo method, such as genetic algorithms, is the preferred method. The formulation of likelihood functions and maximum-likelihood objective functions for multifrequency data on a vertical array is discussed. A priori information about the parameters may be used in the formulation. Shallow-water acoustic data obtain...

Global P, PP, and PKP wave microseisms observed from distant storms

Microseisms are the continuous background vibrations of the Earth observed between earthquakes. Most microseism studies have focused on low frequency energy (0.05–0.5 Hz) propagating as surface waves, but in the microseism spectrum there is also energy that propagates as body waves (P-waves). Using array analysis on southern California stations we show that these body waves are generated in the ocean from distant storms and propagate deep within the Earths mantle and core as P, PP and PKP phases. Comparisons with ocean wave hindcast data identify several distinct source regions in both the northern and southern hemispheres. Analyses of these body waves demonstrate that microseisms often have a strong P-wave component originating from distant locations.

Green's functions extraction and surface-wave tomography from microseisms in southern California

We use crosscorrelations of seismic noise data from 151 stations in southern California to extract the group velocities of surface waves between the station pairs for the purpose of determining the surface-wave velocity structure. We developed an automated procedure for estimating the Green’s functions and subsequent tomographic inversion from the 11,325 station pairs based on the characteristics of the noise field. We eliminate specific events by a procedure that does not introduce any spurious spectral distortion in the band of interest, 0.05–0.2 Hz. Further, we only used the emerging arrival structure above a threshold signal-to-noise ratio. The result is that mostly station pairs with their axes oriented toward the sea are used, consistent with the noise having a microseism origin. Finally, it is the time derivative of the correlation function that is actually related to the Green’s function. The emergence of the time-domain Green’s function is proportional to the square root of the recording time and inversely proportional to the square root of the distance between stations. The tomographic inversion yields a surface-wave velocity map that compares favorably with more conventional and elaborate experimental procedures.

Inversion of broad-band multitone acoustic data from the YELLOW SHARK summer experiments

Integral geoacoustic properties of the sea bottom were determined from full-field inversion of broad-band, water-borne, acoustic propagation data. The data were obtained during the YELLOW SHARK 94 experiment along a 15-km mildly range-dependent transect at a shallow water site in the western Mediterranean. Seven tones from 200 Hz to 800 Hz were transmitted simultaneously by a mid-depth acoustic projector, bottom-moored at different ranges from a vertical array that spanned the water column below the thermocline. Extensive oceanographic and geophysical information were obtained in situ to support and validate the inversion. Matched-field processing was applied to the received pressure fields for each tone frequency. Optimization of the environmental parameters was performed simultaneously across all propagated frequencies. A maximum-likelihood objective function included the linear (Bartlett) cross correlator at the individual frequencies. Genetic algorithms searched for the global minimum of this objective function. The convergence and accuracy of the inversion were determined from statistical analysis of the a posteriori distribution of the candidate environmental models produced by the search algorithm. The following conclusions were drawn from this study. 1) For a fixed source-vertical array configuration broad-band tomographic measurements were a sine qua non to obtain meaningful inversion results. 2) The broad-band inversion provided considerable stability and robustness with respect to volume and bottom variabilities. 3) Corresponding single-frequency inversions performed under the exact same conditions produced erratic results. 4) Integral geoacoustic properties of the bottom were effectively determined within the constraints imposed by the bottom parameterization. 5) More detailed and accurate properties were obtained by including the range dependence of ocean sound-speed profile in the forward modeling. 6) The broad-band-inverted sound-speed profile, attenuation, density, and thickness of the top clay layer, and sound speed of the underlying silt layer, were in close agreement with the independent geophysical measurements.

Inversion for geometric and geoacoustic parameters in shallow water: Experimental results

Experimental results on the estimation of both geometric and geoacoustic parameters in shallow water are presented. Genetic algorithms are used for estimation of the forward model parameters; the estimated parameters are then used by a standard Bartlett processor for source localization. A stationary source at a range of 5.6 km and a moving source at ranges from 5.8–7.7 km were successfully localized in range and depth using a single frequency Bartlett processor. The results indicate that global estimation of the forward model parameters significantly improves source localization performance.

Inversion of acoustic data using a combination of genetic algorithms and the Gauss–Newton approach

An inversion procedure for obtaining speeds, attenuation, densities, and thicknesses for a layered medium is described. The inversion is carried out using the least‐squares technique and the forward modeling is based on SAFARI. The optimization is a hybrid method combining the global genetic algorithms and the local Gauss–Newton method. This is done by taking several gradient steps between each update of the object function for each ‘‘individual’’ in the population. The gradients for the Gauss–Newton method are computed analytically; this makes the computation faster and more stable than computing the gradients by numerical differentiation. The combination of a global and a local method makes the hybrid method faster and it gets closer to the global minimum than a pure global method. Examples based on both real and synthetic data in wave‐number‐frequency and range‐frequency domains show that the method works well.