S23D-01 INVITED
Seismic interferometry by multidimensional deconvolution as a means to compensate for anisotropic illumination
It is well-known that under specific conditions the crosscorrelation of wavefields observed at two receivers yields the impulse response between these receivers. This principle is known as 'Green's function retrieval' or 'seismic interferometry'. Recently it has been recognized that in many situations it can be advantageous to replace the correlation process by deconvolution. One of the advantages is that deconvolution compensates for the waveform emitted by the source; another advantage is that it is not necessary to assume that the medium is lossless. The approaches that have been developed to date employ a 1D deconvolution process. We propose a method for seismic interferometry by multidimensional deconvolution and show that under specific circumstances the method compensates for irregularities in the source distribution. This is an important difference with crosscorrelation methods, which rely on the condition that waves are equipartitioned. This condition is for example fulfilled when the sources are regularly distributed along a closed surface and the power spectra of the sources are identical. The proposed multidimensional deconvolution method compensates for anisotropic illumination, without requiring knowledge about the positions and the spectra of the sources.
S23D-02
Chicken or Egg? Turning Earthquakes Into Virtual Seismometers
The global array of permanent seismometers that record seismic energy is confined almost exclusively to
accessible and secure, land-based sites, while the spatial distribution of global earthquakes is highly
heterogeneous and is often most dense beneath the ocean margins. This limits the resolution of subsurface
images, and results in relatively few local measurements from areas of great geological and tectonic interest
(mid-ocean ridges, the Tibetan and Andean plateaus, subduction zones). While standard seismic
interferometry allows the Earth to be imaged using ambient seismic energy recorded at seismometers, the
current and planned future global seismometer distribution will remain a serious cause of bias in our
knowledge of the subsurface.
Here we show that a different form of interferometry can be used to construct an artificial or 'virtual' sensor
from any well-recorded energy source. We demonstrate this by turning two earthquakes in south-west USA
into virtual seismometers located beneath the Earth's surface. Such sensors inherit the spatio-temporal
response function from the radiation pattern of the original energy source; since earthquakes impart strain,
the virtual seismometers are strain sensors. By definition earthquakes are located within the Earth's solid
interior, so virtual seismometers can be located non-invasively inside solid bodies. Earthquakes occur
precisely within many tectonically active areas of most interest in which there are often no real seismometers;
their corresponding virtual seismometers provide local windows into such geological phenomena.
http://www.geos.ed.ac.uk/homes/acurtis
S23D-03
The two Faces of Equipartition
Equipartition is good. Beyond its philosophical implications, in many instances of statistical physics it implies that the available kinetic and potential elastic energy, in phase space, is distributed in the same fixed proportions among the possible "states". There are at least two distinct and complementary descriptions of such states in a diffuse elastic wave field u(r,t). One asserts that u may be represented as an incoherent isotropic superposition of incident plane waves of different polarizations. Each type of wave has an appropriate share of the available energy. This definition introduced by Weaver is similar to the room acoustics notion of a diffuse field, and it suffices to permit prediction of field correlations. The other description assumes that the degrees of freedom of the system, in this case, the kinetic energy densities, are all incoherently excited with equal expected amplitude. This definition, introduced by Maxwell, is also familiar from room acoustics using the normal modes of vibration within an arbitrarily large body. Usually, to establish if an elastic field is diffuse and equipartitioned only the first description has been applied, which requires the separation of dilatational and shear waves using carefully designed experiments. When the medium is bounded by an interface, waves of other modes, for example Rayleigh waves, complicate the measurement of these energies. As a consequence, it can be advantageous to use the second description. Moreover, each spatial component of the energy densities is linked, when an elastic field is diffuse and equipartitioned, to the component of the imaginary part of the Green function at the source. Accordingly, one can use the second description to retrieve the Green function and obtain more information about the medium. The equivalence between the two descriptions of equipartition are given for an infinite space and extended to the case of a half-space. These two descriptiosn are equivalent thanks to the relationship of average autocorrelations with the imaginary part of Green function at the source. Preliminary results are displayed in data sets from Chilpancingo, Mexico, and the Tautona Gold Mine, South Africa, that strongly suggest that equipartition, that guarantees the diffuse nature of seismic fields, has more than one face. Acknowledgements. Partial supports from DGAPA-UNAM, Project IN114706, Mexico; from Proyect MCyT CGL2005-05500-C02/BTE, Spain; from project DyETI of INSU-CNRS, France, and from the Instituto Mexicano del Petróleo are greatly appreciated.
S23D-04
Passive Sensor Imaging Using Cross Correlations of Noisy Signals in a Scattering Medium
It is well known that the travel time or even the full Green's function between two passive sensors can be estimated from the cross correlation of recorded signal amplitudes generated by ambient noise sources. It is also known that the direction of the energy flux from the noise sources affects the estimation of the travel time. Using the stationary phase method we show here that the travel time can be effectively estimated when the ray joining the two sensors continues into the noise source region. We extend this analysis to passive sensor imaging of reflectors with different ambient noise source configurations by suitably migrating the cross correlations. If in addition there is multiple scattering in the medium then reflectors can be imaged with passive sensor networks or arrays by migrating suitable fourth-order cross correlations. Fourth-order cross correlations can also be used with auxiliary passive sensors in order to enhance travel time estimation in a scattering medium.
S23D-05 INVITED
Green's function extraction for general linear systems
The extraction of the Green's function from field fluctuations has found numerous applications in seismology. We show that the Green's function can be extracted for a wide class of linear systems that are described either by scalar fields or by vector fields. Geophysically relevant examples of such systems include the pore pressure in reservoir or aquifers, or the propagation of low-frequency electromagnetic waves in the conductive subsurface. (The latter technique forms the basis of the now popular CSEM measurements.) We show for systems that are invariant for time-reversal that the sources of the field fluctuations can be confined to a closed surface around the receivers. In contrast, for attenuating or diffusive systems those sources must distributed throughout the volume. This requirement can be an impediment to practical applications. As an alternative to the, by now, traditional correlation method, we propose multidimensional deconvolution as an alternative that does not require sources throughout the volume. Wapenaar, K., E. Slob, and R. Snieder, Unified Green's function retrieval by cross-correlation, Phys. Rev. Lett., 97, 234301, 2006 Snieder, R., K. Wapenaar and U. Wegler, Unified Green's function retrieval by cross-correlation; connection with energy principles, Phys. Rev. E, 75, 036103, 2007 Wapenaar, K., E. Slob, and R. Snieder, Seismic and electromagnetic controlled-source interferometry in dissipative media, Geophys. Prosp., 56, 419-434, 2008
S23D-06
Method of Second Cross-Correlation
In a high frequency band above 1 Hz, the Noise Cross-Correlation method works because of multiple scattering but in a lower frequency band, say below 0.2 Hz, it works mainly because of wide distribution of sources as effects from multiple scattering are much smaller. As noise-source locations change seasonably, seasonal variations are often seen in the correlated seismograms (first correlogram). In Southern California, weaker signals are seen in summer because of weaker ocean waves. Source distribution also introduces another problem; near the coast, it is often found that the paths perpendicular to the coast show good signal in correlograms but the paths parallel to the coast do not necessarily contain good signals. This is directly related to the source locations, i.e., ocean waves in low frequency bands. This feature does harm in tomographic studies, especially for the recovery of azimuthal anisotropy, as measurements from all azimuths are the key to its success. One method to circumvent this problem is the method of Second Cross-Correlation. This method computes cross-correlations of Greens function that have been obtained by the noise cross-correlation method. We call it here as Second Cross-Correlation and refer to correlated seismograms as second correlograms. Campillo et al. (2008) showed an application to coda in Greens functions for the first time but in this study we focus on the entire waveforms. We present theoretical analysis of this method with some examples from Southern California. It works for a relatively dense array of network only, but such dense arrays are available in many parts of the world now. We extend our theoretical analysis in Tanimoto (2008) for first correlograms which was a full normal-mode- theory version of theories developed by Snieder (2004), Roux et al. (2005) and Wapenaar (2004). There are some distinct features in second correlograms; for example, while an ordinary (first) correlogram depends on f**2, where f is the source spectra, the second correlogram depends on f**4, leading to narrower frequency band for the dominant energy. For the same reason with first correlograms, calculation of synthetic seismograms is difficult, as we do not know f. Note that f may change with time, as sources are often ocean waves. On the other hand, the formula does not contain extra phase perturbation and thus phase velocity can be obtained. For some paths, we can recover good surface wave signals in the second correlogram even though the first correlogram does not contain good signals.
S23D-07
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,
however, 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 Earth's 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 have a strong P-wave
component originating from anywhere on the Earth.
http://www.mpl.ucsd.edu/people/gerstoft/
S23D-08
Two 70-km Long Pseudo-Reflection Profiles from Seismic Ambient Noise Interferometry: Implications in Regional Geology and Active Tectonics
As part of an effort in using seismic ambient noise to assess local site effects of strong ground motion caused by potential earthquakes, microtremor measurements on two profiles were acquired in summer 2007 in Beijing area. Each of these two profiles is about 70-km long, with site spacing of 200 meters. One profile runs northwest to southeast and the other runs roughly orthogonal to the first one, from northeast to southwest. We used an array of 30 short-period 3-component seismometers to acquire the data. At each site the observation duration was at least one hour with a sampling rate of 50 Hz. We have applied seismic interferometry procedure to the data set. When cross-correlation is applied to microtremor records from two adjacent sites it forms a trace of 'pseudo-reflection' record. A collection of the pseudo-reflection traces sequentially from all site pairs forms a 'pseudo-reflection' profile. The most pronounced reflector on the profiles appears to be coincident with the quaternary/tertiary interface in Beijing area. Meanwhile, interruptive changes in reflector depth and loss of reflector continuities appear to be associated with active faults in this area. This conclusion was supported by the 'ground truth' from the borehole logging data close to the profiles, the existing geological mapping, as well as the quaternary sediment thickness estimation from the horizontal to vertical spectral ratio (HVSR) method applied to the same data set. Upon further confirmation, seismic ambient noise interferometry may find another application in regional tectonics investigation with great economical advantages.