Karim G. Sabra

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.

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,

Emergence rate of the time‐domain Green’s function from the ambient noise cross‐correlation function

It has been demonstrated experimentally and theoretically that an estimate of the Green’s function between two receivers can be obtained from the time derivative of the long‐time average cross correlation of ambient noise between these two receivers. The emergence rate of these deterministic coherent arrival times of the cross‐correlation function (i.e., the Green’s function estimate) from the recordings of an isotropic distribution of random noise sources is derived by evaluating the amplitude of the variance of the cross‐correlation function. The knowledge of the emergence rate of NCF is essential for practical applications. To the first order, the variance is equal to the ratio of the product of the recorded energy by both receivers and the time–bandwidth product of the recordings. The variance of the time derivative of the correlation function is shown to have a similar dependency. These simple analytic formulas show a good agreement with the variance determined experimentally for the correlation of ocean ambient noise recorded in shallow water at a depth of 21 m, in the frequency band [300–530 Hz] for receiver separation up to 28 m and averaging time from 1 to 33 min.

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.

Using ocean ambient noise for array self-localization and self-synchronization

Estimates of the travel times between the elements of a bottom hydrophone array can be extracted from the time-averaged ambient noise cross-correlation function (NCF). This is confirmed using 11-min-long data blocks of ambient noise recordings that were collected in May 1995 near the southern California coast at an average depth of 21 m in the 150-700 Hz frequency range. Coherent horizontal wavefronts emerging from the time derivative of the NCF are obtained across the arrays aperture and are related to the direct arrival time of the time-domain Greens function (TDGF). These coherent wavefronts are used for array element self-localization (AESL) and array element self-synchronization (AESS). The estimated array element locations are used to beamform on a towed source.

Using cross correlations of turbulent flow-induced ambient vibrations to estimate the structural impulse response. Application to structural health monitoring

It has been demonstrated theoretically and experimentally that an estimate of the impulse response (or Greens function) between two receivers can be obtained from the cross correlation of diffuse wave fields at these two receivers in various environments and frequency ranges: ultrasonics, civil engineering, underwater acoustics, and seismology. This result provides a means for structural monitoring using ambient structure-borne noise only, without the use of active sources. This paper presents experimental results obtained from flow-induced random vibration data recorded by pairs of accelerometers mounted within a flat plate or hydrofoil in the test section of the U.S. Navys William B. Morgan Large Cavitation Channel. The experiments were conducted at high Reynolds number (Re > 50 million) with the primary excitation source being turbulent boundary layer pressure fluctuations on the upper and lower surfaces of the plate or foil. Identical deterministic time signatures emerge from the noise cross-correlation function computed via robust and simple processing of noise measured on different days by a pair of passive sensors. These time signatures are used to determine and/or monitor the structural response of the test models from a few hundred to a few thousand Hertz.

Blind deconvolution in ocean waveguides using artificial time reversal

Sound that travels through the ocean from a source to a receiver is commonly distorted by multipath acoustic propagation. The severity and details of this distortion are determined by the sound channel’s characteristics, which may not be known. However, recovery or reconstruction of undistorted signals from recordings made in unknown complex multipath environments—a process commonly referred to as blind deconvolution—is advantageous in many applications of underwater acoustics. This paper presents a simple and robust means to achieve blind deconvolution in unknown sound channels with an array of receiving transducers. The technique, artificial time reversal (ATR), can be effective when there is a linear relationship between frequency and the phase of the low-order propagating modes of the sound channel. Broadband simulations of ATR in a generic shallow ocean sound channel show that the maximum correlation between the original signal and the reconstructed signal may approach 100% for signal pulses having a 258 Hz bandwidth and a 500 Hz center frequency. Application of ATR to ocean sound-propagation measurements produces original-to-reconstructed signal correlations from 80% to 95%. Possible extensions and improvements of ATR are discussed.

Broadband time-reversing array retrofocusing in noisy environments.

Acoustic time reversal is a promising technique for spatial and temporal focusing of sound in unknown environments. Acoustic time reversal can be implemented with an array of transducers that listens to a remote sound source and then transmits a time-reversed version of what was heard. In a noisy environment, the performance of such a time-reversing array (TRA) will be degraded because the array will receive and transmit noise, and the intended signal may be masked by ambient noise at the retrofocus location. This article presents formal results for the signal-to-noise ratio at the intended focus (SNRf) for TRAs that receive and send finite-duration broadband signals in noisy environments. When the noise is homogeneous and uncorrelated, and a broadcast power limitation sets the TRAs electronic amplification, the formal results can be simplified to an algebraic formula that includes the characteristics of the signal, the remote source, the TRA, and the noisy environment. Here, SNRf is found to be proportional to the product of the signal bandwidth and the duration of the signal pulse after propagation through the environment. Using parabolic-equation propagation simulations, the formal results for SNRf are illustrated for a shallow water environment at source-array ranges of 1 to 40 km and bandwidths from several tens of Hz to more than 500 Hz for a signal center frequency of 500 Hz. Shallow-water TRA noise rejection is predicted to be superior to that possible in free space because TRAs successfully exploit multipath-propagation.

Broadband performance of a time reversing array with a moving source

The automatic spatial and temporal focusing properties of a time-reversing array (TRA) make it an attractive technology for active and passive sonar systems that may be deployed in unknown multipath environments. However, in these and other potential underwater applications of TRAs, either the source, the array, or both are likely to be moving. In this paper we present broadband-signal TRA performance predictions that include the influence of the Doppler effect on the time-reversal process for broadband signals transmitted from an arbitrarily moving source to a stationary vertical TRA through a shallow ocean environment. Here, the impact of source motion on TRA performance is predicted from analysis and numerical simulations using a formulation of the Doppler shifted field based on Fourier superposition of stationary but spatially distributed time-harmonic sources. Quantitative results for the size and location of the TRA’s retrofocus are presented as well as the correlation of the TRA retrofocus signal with the time-reversed original signal for various source motions in range-independent and range-dependent shallow water sound channels. Overall, source motion is predicted to have little effect on TRA operations with source speeds less than 20 m/s for signals having a center frequency of 500 Hz at source–array ranges of a few kilometers.

Passive invivo elastography from skeletal muscle noise

Measuring the in vivo elastic properties of muscles (e.g., stiffness) provides a means for diagnosing and monitoring muscular activity: muscles typically become ‘‘harder’’ during contraction occurring through physiological changes. Standard elastography imaging techniques estimate soft tissue (e.g., skeletal muscle, breast) stiffness using propagating shear waves in the human body generated by an external active source (e.g., indentation techniques, ultrasonic radiation force). We demonstrated a passive in vivo elastography technique without an active external radiation source. This technique instead uses cross‐correlations of contracting skeletal muscle noise recorded with skin‐mounted sensors. The coherent arrivals emerge from a correlation process that accumulates contributions over time from noise sources whose propagation paths pass through both sensors successively. Each passive sensor becomes a virtual in vivo shear wave source. The results point to a low‐cost, noninvasive technique for monitoring ...