Pierre Gouédard

Estimation of the effect of nonisotropically distributed energy on the apparent arrival time in correlations

Correlations of random seismic noise are now widely used to retrieve the Green’s function between two points. Whereas this technique provides useful results in tomography and monitoring studies, it is mainly limited by an uneven distribution of noise sources. In that case, theoretical requirements are not completely fulfilled and we may wonder how reliable the reconstructed signals are, in particular for the purpose of estimating traveltime from correlations. This study finds a way to quantify effects of a nonisotropic noise field by estimating the arrival-time error resulting from a particular nonisotropic distribution of recorded wave intensity. Our study is based on a theoretical prediction of this bias and we successfully test the theory by comparing the theoretical expectation to real measurements from seismic-prospecting data. In particular, we distinguish between the effects of source distribution and the effects of medium heterogeneity between the sources and the region of receivers. We find relat...

Convergence of the two-point correlation function toward the Green's function in the context of a seismic-prospecting data set

When considering direct waves in the correlation process, the Green’s function is reconstructed when using an even distribution of seismic sources or when the source distribution is restricted to the direction close to the alignment of the sensors. On the other hand, when considering records of coda waves, the convergence is achieved for any source distribution, as expected theoretically. We extract the expected amplitude decay along a seismic profile from the correlation functions when an even distribution of sources is considered or when the time window includes scattered waves.

Imaging along‐strike variations in mechanical properties of the Gofar transform fault, East Pacific Rise

A large part of global plate motion on mid-ocean ridge transform faults (RTFs) is not accommodated as major earthquakes. When large earthquakes do occur, they often repeat quasiperiodically. We focus here on the high slip rate (∼14 cm/yr) Gofar transform fault on the equatorial East Pacific Rise. This fault is subdivided into patches that slip during Mw 5.5–6 earthquakes every 5 to 6 years. These patches are separated by rupture barriers that accommodate slip through swarms of smaller events and/or aseismic creep. We performed an imaging study to investigate which spatiotemporal variations of the fault zone properties control this segmentation in mechanical behavior and could explain the specific behavior of RTFs at the global scale. We adopt a double-difference approach in a joint inversion of active air gun shots and microseismicity recorded for 1 year. This data set includes the 2008 Mw 6 Gofar earthquake. The along-strike P wave velocity structure reveals an abrupt transition between the barrier area, characterized by a damaged fault zone of 10–20% reduced Vp and a nearly intact fault zone in the asperity area. The importance of the strength of the damage zone on the mechanical behavior is supported by the temporal S wave velocity changes which suggest increased damage within the barrier area, during the week preceding the Mw 6 earthquake. Our results support the conclusion that extended highly damaged zones are the key factor in limiting the role of major earthquakes to accommodate plate motion along RTFs.

Correction of Ocean-Bottom Seismometer Instrumental Clock Errors Using Ambient Seismic Noise

Abstract Very accurate timing of seismic recordings is critical for modern processing techniques. Clock synchronization among the instruments constituting an array is, however, difficult without direct communication between them. Synchronization to Global Positioning System (GPS) time is one option for on‐land deployments, but not for underwater surveys as electromagnetic signals do not propagate efficiently in water. If clock drift is linear, time corrections for ocean‐bottom seismometer (OBS) deployments can be estimated through GPS synchronization before and after the deployment, but this is not sufficient for many applications as the nonlinear component of the drift can reach tens to hundreds of milliseconds for long‐duration experiments. We present two techniques to retrieve timing differences between simultaneous recordings at ocean‐bottom instruments after deployment has ended. Both techniques are based on the analysis of the cross correlation of ambient seismic noise and are effective even if clock drift is nonlinear. The first, called time symmetry analysis, is easy to apply but requires a proper illumination so that the noise cross‐correlation functions are symmetric in time. The second is based on the doublet analysis method and does not have this restriction. Advantages and drawbacks of both approaches are discussed. Application to two OBS data sets shows that both can achieve synchronization of recordings down to about five milliseconds (a few percent of the main period used).

Small-scale seismic inversion using surface waves extracted from noise cross correlation

Greens functions can be retrieved between receivers from the correlation of ambient seismic noise or with an appropriate set of randomly distributed sources. This principle is demonstrated in small-scale geophysics using noise sources generated by human steps during a 10-min walk in the alignment of a 14-m-long accelerometer line array. The time-domain correlation of the records yields two surface wave modes extracted from the Greens function between each pair of accelerometers. A frequency-wave-number Fourier analysis yields each mode contribution and their dispersion curve. These dispersion curves are then inverted to provide the one-dimensional shear velocity of the near surface.

Source depopulation potential and surface-wave tomography using a crosscorrelation method in a scattering medium

We use seismic prospecting data on a 40 � 40 regular grid of sources and receivers deployed on a 1 km � 1 km area to assess the feasibility and advantages of velocity analysis of the shallow subsurface by means of surface-wave tomography with Green’s functions estimated from crosscorrelation. In a first application we measure Rayleigh-wave dispersion curves in a 1D equivalent medium. The assumption that the medium is laterally homogeneous allows using a simple projection scheme and averaging of crosscorrelation functions over the whole network. Because averaging suppresses noise, this method yields better signal-to-noise ratio than traditional active-source approaches, and the improvement can be estimated a priori from acquisition parameters. We find that high-quality dispersion curves can be obtained even when we reduce the number of active sources used as input for the correlations. Such source depopulation can achieve significant reduction in the cost of active source acquisition. In a second application we compare Rayleigh-wave group velocity tomography from raw and reconstructed data. We can demonstrate that the crosscorrelation approach yields group velocity maps that are similar to active source maps. Scattering has an importance here as it may enhance the crosscorrelation performance. We quantify the scattering properties of the medium using mean free path measurements from coherent and incoherent parts of the signal. We conclude that for first-order velocity analysis of the shallow subsurface, the use of crosscorrelation offers a cost-effective alternative to methods that rely exclusively on active sources.

Surface-wave eikonal tomography in a scattering environment

Surface waves are of increasing interest in seismic prospecting. Traveltime tomography based on dispersion measurements is often used to process surface-wave data, but it has limitations due to the a priori information it requires. The surface-wave eikonal tomography proposed here does not require such a priori information. In complex scattering environments, picking arrivals is difficult because the waveforms are complicated. Working in narrow frequency bands makes it even more difficult as it spreads arrivals in time and introduces overlap. We present here a neighborhood-based cross-correlation picking method that overcomes this difficulty, which then allows for reliable calculation of 2D phase-velocity variation through the eikonal equation.

Reflection and time-reversal of ultrasonic waves in the vicinity of the Rayleigh angle at a fluid-solid interface

When sending a plane ultrasonic wave toward a fluid-solid interface, the reflected wave is affected, depending on the incident angle. Around the Rayleigh angle the reflection coefficient has a strong and rapidly varying imaginary part. This has the effect of distorting the reflected wave front. If this reflected wave is time-reversed and sent back toward the interface, the reflected wave of this time-reversed wave should not present any distortion, as the time-reversal process restores the original phases. A theoretical and experimental study of these phenomena has been done. The distortion of the reflected waves around the Rayleigh angle is observed and as expected this distortion is canceled by the time-reversal process. However a significant loss of energy in the time-reversed signal is observed for incident angles around the Rayleigh angle, as part of the energy contained in the Rayleigh wave escapes the time-reversal mirror and is lost for the time-reversal process. In a second part, it is shown by s...

Experimental study of the convergence of two‐point cross‐correlation toward the Green's Function

Cross‐correlation of seismic noise recorded at two points yields the Greens Function (GF) between the two points when seismic noise is spatially and temporally diffuse. Seismic events yield the same result (1) when direct waves are cross‐correlated from sources that are azimuthally distributed or (2) when coda waves are cross‐correlated whatever the source distribution. In this work, the question of convergence toward the GF is investigated with real data. From a high‐resolution survey with dense arrays of geophones and sources, we select different sets of sources and time windows to compute the cross‐correlation between two receivers. We compare correlations derivative with the actual GF, and show the influence of source locations and scattering on the GF reconstruction. For direct waves, sources located in the endfire lobes of the receiver pair have an essential contribution. With sources located outside the endfire lobes, the GF can nevertheless be retrieved using coda waves.

Dispersion curves and small‐scale geophysics using noise cross‐correlation techniques

It has been demonstrated, both theoretically and experimentally, that the Green’s function between two receivers can be retrieved from cross‐correlation of isotropic noise records. Since surface waves dominate noise records in geophysics, tomographic inversion using noise correlation techniques have been performed from Rayleigh waves so far. However, very few numerical studies implying surface waves have been conducted to confirm the extraction of the true dispersion curves from noise correlation in a complicated sedimentary ground model. In this work, synthetic noise has been generated in a small‐scale (<1 km) numerical realistic environment and classical processing techniques are applied to retrieve the phase velocity dispersion curves in the medium, first step toward an inversion. We compare results obtained from SPAC (spatial auto‐correlation method) and noise correlation techniques on a ten‐element array. Two cases are presented in the (1–20 Hz) frequency bandwidth that corresponds to an isotropic or a directional wavefield noise.