New Advances in Seismic Imaging for Exploration and Solid Earth Geophysics I
Presiding: N Shapiro, Department of Physics, University of Colorado at Boulder; K Wapenaar, Department of Applied Earth Sciences, Delft University of Technology
S31A-01 INVITED 08:30h
Diffuse Field Correlations in Open Systems
Recent theoretical progress in understanding diffuse field correlations is reviewed with a view towards applications in seismology. As is now well known, an identity between diffuse field correlations and the Green function follows from a definition of a diffuse field as an uncorrelated smooth 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 this is inapplicable to heterogeneous structures or near boundaries. It is shown here that an alternative definition, of a locally diffuse field, applies to open heterogeneous structures like the earth. The field is taken to be one in equilibrium with an incident field consisting of an uncorrelated isotropic superposition of incident plane waves. This definition is applicable to both heterogeneous and open systems. It is shown, using a reciprocity argument, to lead to the familiar identity between the diffuse field's correlations and the local Green's function of the structure including all local reflections and scatterings. Applications of these ideas to Seismology have successfully recovered the ballistic surface wave part of the Green function. Other parts of the Green function have not been retrieved. One presumes their amplitudes lie below the remaining fluctuations in the correlograms, but theory has so far not addressed the issue. Here we take a model of diffuse fields in open structures as that resulting from a Gaussian random distribution of sources spread over all space. It is found that this model lends itself to calculations of the variance of R, and thus to estimates of the degree to which an R calculated using finite amounts of data will conform to the Green function. The model indicates that such conformation is strongest at low frequencies. Ray arrivals are detectable only if sufficient data has been collected; the amount of data needed scales with the square of the frequency, and for surface (bulk) waves with the (square of the) source-receiver separation. Thus, long distance high frequency rays will be most difficult to retrieve. The result is consistent with seismological examples.
http://www.tam.uiuc.edu/faculty/weaver/publications/OpenFlucts.pdf
S31A-02 08:45h
A Physical Interpretation of "Passive Imaging" With Correlations of Scattered Wave Fields
Many recent works in seismology, underwater acoustics or ultrasound have shown that the correlation of a scattered wavefield recorded at two points A and B could be used to estimate the Green's function (or at least its first arrivals) between A and B, even though none of these points actually acts as a source. This led to the idea of "passive imaging" of a heterogeneous medium such as the earth's crust. Here we argue that the space- and time-correlation that is performed is more than a signal analysis trick: it has a deep physical interpretation. The correlation can be analysed in terms of time-reversed propagation of a scattered wave field inside the medium to be imaged. One advantage of this approach is that all the results that have been derived about time-reversed propagation in complex media can be fruitfully applied to passive imaging. The time-reversal approach can tell us in what circumstances the Greens function can or cannot be actually retrieved from correlations. We emphasize the role of several crucial points: the spatial distribution of the sources, the role of disorder and multiple scattering, the frequency bandwidth, and the advantage of performing one-bit correlations. The argument will be sustained by numerical simulations as well as experimental results, and its implication for imaging and detection purposes will be discussed.
S31A-03 INVITED 09:00h
Imaging the Earth Structure From Long Distance Time Correlations of the Seismic Noise
The field to field correlation of diffuse waves has been shown to allow the reconstruction of the Green function between the two points of measure. This property is related to the property of equipartition of diffuse waves. An averaging over a set of distant sources is nevertheless required when dealing with data of finite duration as seismograms. The emergence of Green function from correlation of coda waves from large earthquakes can be observed for periods up to 50 s. At longer period, the scattering is less efficient to produce isotropic, equipartitioned wave-field. In absence of scattering, an almost perfect azimuthal coverage of source is required to reconstruct the Green function by correlation. These properties are illustrated by numerical, seismological and ultrasound experiments. Consequently, the possibility of using seismic ambient noise to reconstruct Green functions depends on the actual sources of the noise, which spatial distribution is still an open problem, and on the presence of scattering. When averaged over long time series, we expect at the first order the distribution of noise sources to randomize. This assumption does not need to be strictly fulfilled when scattering in the earth participate in randomizing the wave field. We present examples showing that long period surface waves can be reconstructed from seismic noise. At period between 5 and 100 seconds, the expected time symmetry of the correlation is often broken, an effect that we interpret as a mark of a net flux of energy resulting from a non-isotropic distribution of sources and an incomplete equipartition. The cross-correlation of records from a series of couples of stations can be used simply to determine the back-azimuth of the dominant source of noise without the restrictive conditions of array processing. We apply this approach with data from Europe and North America to investigate the main source regions. Finally, we present examples of tomographic images produced from surface wave measurements obtained from noise correlations.
S31A-04 09:15h
Interferometric techniques in seismic reflection imaging and the principle of stationary phase
Interferometric imaging where the Green's function is constructed using the correlation of complex wavefields recorded at two receivers is a rapidly emerging field. The methodology has been justified based on assumptions of equiparitioning of the normal modes of the system, as well as on various versions of the representation theorem applied to time-reversed waves. I will present another point of view that is based on stationary phase arguments. This complementary formulation of interferometric imaging gives insight in the physics of the emergence of the Green's function, and of the limitations that are encountered when applying this technique to data. Issues that will be covered are the relation between ensemble averaging and time averaging, and interferometric imaging of reflected waves. This example is of particular interest for exploration seisology since it shows that interferometric imaging may introduce spurious multiple reflections. I will show that these "multiples" have a clear physical interpretation and do not form a problem in seismic imaging.
S31A-05 09:30h
Green Function Retrieval Versus Interferometric Imaging
In the past couple of years it has been shown by various authors that the cross-correlation of wave fields observed at two receiver points yields the Green function between these two points. Several quite distinct derivations exist for this phenomenon. On the one end of the spectrum is the theory pioneered by Weaver and Lobkis (PRL, JASA, 2001), in which the main assumption is that the wave field is diffuse; the diffusivity can be due to the irregularity of the enclosure or to the presence of random scatterers. On the other end there is the approach based on the Rayleigh reciprocity theorem for an arbitrary inhomogeneous open configuration (Wapenaar et al., SEG, 2002; GJI, PRL, 2004). Here the main assumption is that there are sufficient independent sources, which emit either transient signals that are well separated in time or noise signals which are mutually uncorrelated. The reconstructed Green function contains the ballistic wave as well as the coda due to multiple scattering in the inhomogeneous medium. Once the Green functions are retrieved for a sufficient range of receiver positions at the surface of the earth, they can be used to form an image of the subsurface, using any standard seismic reflection imaging algorithm. Schuster (EAGE, 2001; GJI, 2004) coined this interferometric imaging. Intuitively one would expect that the same assumptions should be fulfilled as for Green function retrieval, however, a more careful analysis proves this wrong. Consider the subsurface of the earth as a fully deterministic open configuration and assume that there is only one noise source present in this subsurface. Although for this situation it is not possible to reconstruct accurate Green functions as an intermediate result, it can be shown that interferometric imaging still maps the primary reflection response (i.e., the ballistic wave) to its correct scattering origin in depth as long as the specular reflection point at the surface lies within the array of receivers. Hence, compared with the theories for Green function retrieval, interferometric imaging is less restrictive with respect to the assumptions about diffusivity or the distribution of sources. On the downside, interferometric imaging requires a background velocity model; moreover, it incorrectly handles multiple reflections, which are mapped as unwanted ghost images.
S31A-06 09:45h
Surface wave tomography in Southern California using seismic ambient noise
It has been demonstrated experimentally that an estimate of the Green's tensor between two seismic stations can be obtained from the long-time average of the cross-correlation of ambient noise at the two stations. This result provides a means to image Earth structure using the ambient noise field only, without the use of active seismic sources or earthquakes. 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 in the frequency band 0.05-0.4 Hz. In this frequency band, ambient noise (originating from ocean microseisms) propagating over long distances is typically dominated by surface waves. A record section of the waveforms as a function of increasing receiver separation shows clearly that the recovered signals are propagating wavetrains. The seismic data were then used in a simple, but densely sampled tomographic procedure to estimate the surface wave velocity structure 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 ambient noise between station pairs can be used for seismic imaging purposes.
http://www.mpl.ucsd.edu/people/gerstoft/