S21D-01 INVITED 08:00h
Phase and Correlation in Random Seismic Fields and the Reconstruction of Green Function
This paper was strongly influenced by Aki's works on the interpretation of the energy decay of coda waves and on the array processing of seismic noise. We first present a summary of recent results on coda interpretation. We emphasize the observation of the stabilization of P to S energy ratio indicating the modal equipartition of the wave field. This property attests that the coda waves are in the regime of multiple scattering. We use numerical solutions of the elastic radiative transfer equation to illustrate the evolution of the wave-field towards P to S energy stabilization, and asymptotically to complete isotropy. The energy properties of the coda have been widely studied but the phase properties have often been neglected. The recently observed coherent backscattering spot, an expression of the so-called `weak localization', demonstrates that phase effects, as interferences, still persist for multiply diffracted waves. Another manifestation of the persistence of the phase is the possibility to reconstruct the Green function between two stations by averaging the cross-correlation of coda waves produced by distant earthquakes and recorded at those two stations. This reconstruction is directly related to the properties of reciprocity and time reversal of any wave-field. Using broad-band coda waves, we show that the dominant phases of the Green function in the band 10sec-2sec, namely Rayleigh and Love waves, are reconstructed. At higher frequencies, absorption reduces the length of the records available for processing and it is difficult to detect the body waves. However, their amplitude is expected to be small with respect to surface waves for source and receiver at the free surface. We analyse the time symmetry of the cross correlation and shows how the level of symmetry evolves with the isotropization of the diffuse field with lapse time. Similarly we investigate the correlation in continuous ambient noise records. Whereas the randomness of the coda results from multiple scattering on randomly distributed scatterers, we assume that the seismic noise is random mostly because of the distribution of sources at the surface of the Earth. We show that surface waves can be extracted from long time series., We computed the dispersion curves of Rayleigh waves from the correlations. On paths where direct measurements are available, we show that they are in good agreement with those deduced from noise correlation. The measurement of correlation along paths crossing different crustal structures allows to differentiate them, opening the way for a `passive imaging' of the Earth structure.
S21D-02 08:30h
Monitoring with Coda Wave Interferometry
Aki has been a pioneer in monitoring the subsurface with coda waves and with guided waves. His analysis of temporal and spatial variations in coda Q has proven to be a powerful tool for monitoring purposes. We have extended his technique in new method called coda wave interferometry where changes in the full waveforms of coda waves are used to monitor changes in the subsurface. We have developed and implemented the theory to use this technique to monitor the following changes: a change in the seismic velocity, a change in scatterer locations, and a change in the location of earthquakes. As shown by Aki, the seismic coda is dominated by shear waves. Therefore our technique is primarily sensitive to changes in the S-velocity. Aki also worked on wave propagation in volcanoes. We have used coda wave interferometry to monitor two active volcanoes, Arenal (Costa Rica) and Mt. Erebus (Antarctica). I will give several examples to illustrate how coda waves can be used for monitoring purposes.
S21D-03 08:45h
Synthesis of Plane Vector Wave Envelopes in 2D Random Elastic Media based on the Markov Approximation and Comparison with Finite Difference Simulations
High-frequency seismograms mainly consist of incoherently scattered waves. Their envelopes are a stable measure exhibiting characteristic features like peak amplitude decay and envelope broadening with increasing travel distance which can be used to infer stochastic parameters of the heterogeneous Earth. As a simple model we study the propagation of plane P- and S-waves through a 2D random elastic medium. If wavelength is smaller than correlation distance and medium inhomogeneity is weak, conversion scattering can be neglected, and a stochastic parabolic wave equation for potential field is derived. By solving the master equation for the two-frequency mutual coherence function we obtain the temporal change of the mean squared envelope at fixed distance. From the angular spectrum the distribution of energy between longitudinal and transverse components is calculated. For the case of a Gaussian autocorrelation function this solution is completely analytical. The theoretical envelopes are compared to the results of 2D elastic finite-difference simulations. For a stable estimate of mean squared envelopes the squared FD traces from different receiver positions and several realizations of the random medium have been averaged. The theoretical curves well explain the delay of the peak arrival from the onset and the broadening of envelopes with increasing propagation distance. Also the transverse component amplitude for P-wave incidence and the longitudinal component amplitude for S-wave incidence is precisely explained by the theory. These components start to exceed the original components as lapse time increases. The time integral of mean squared transverse component for P-wave incidence and of mean squared longitudinal component for S-wave incidence linearly increases with travel distance. The linear coefficient is a measure of the ratio between mean squared fractional fluctuation and correlation distance. The successful validation of the Markov approximation against numerical wavefield simulations encourages us to extend the method to more realistic cases like point sources with nonisotropic source radiation and 3D problems.
S21D-04 09:00h
Extracting seismic time domain Green's functions from 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 [Shapiro and Campillo, Geophys. Res. Lett., 31, 2004]. This result provides a means to find trace data that can be used to infer Earth structure without the use of active seismic sources or earthquakes. The availability of numerous broadband seismic recording stations throughout the world makes this technique attractive for simulating virtual large dense seismic arrays for continuous sampling of the earth's crust. Cross-correlations have been computed from ambient noise recorded over 150 broadband seismic stations located in California. A simple and straightforward processing yielded hundreds of cross-correlation pairs, for receiver separations of up to 250 km, that clearly exhibit coherent broadband dispersive wavetrains. A record section of the waveforms as a function of increasing receiver separation shows clearly that the recovered signals are propagating wavetrains. The potential use of this passive seismic imaging technique was investigated across 1) the frequency band [5mhz-10Hz], 2) the spatial distribution of the pair of stations (in range and azimuth), 3) averaging time periods of 1 day to 1 month.
S21D-05 09:15h
Spatial Resolution of an Imaging System: Roles of Data-Acquisition Configuration and Imaging Propagators
Spatial resolution of an imaging system is formulated under the general frame of inversion theory. The spatial resolution operator (matrix) and its kernel (resolving kernel) are defined as a special case of the parameter resolution operator and its kernel, respectively. The formulation is derived for a general imaging system, including the data acquisition system and the imaging process. It is shown that there are many factors influencing the spatial resolution, including the acquisition aperture and geometry, overburden structures above the target area, and the accuracy of the propagators used in the imaging process. In the case of spatial resolution, the resolving kernel is reduced to the point spreading function (PSF) of the imaging system. We first discuss the theoretical limit of the resolution, which corresponds to an ideal, perfect reconstruction. In this case, the spatial resolution of the image depends only on the acquisition system configuration. Then we compare the resolutions (PSF) of imaging systems using different propagators in the imaging process: wave-theory based one-way propagators versus ray-theory based propagators (ray-Kirchhoff migration). Numerical examples are shown and compared with theoretical predictions. For imaging in heterogeneous media, such as random media with different scales of heterogeneities, we can clearly see the high-resolution feature of wave-theory based imaging methods compared with ray-theory approximated imaging methods.
S21D-06 09:30h
Changes of seismic velocity around the Karadere-Duzce branch of the north Anatolian fault from coda waves generated by repeating earthquakes
We analyze temporal variations of seismic velocity along the Karadere-Duzce branch of the north Anatolian fault from repeating earthquakes in aftershocks of the 1999 Mw7.4 Izmit and Mw7.1 Duzce earthquakes. We identified about 30 sets of repeating earthquakes, each containing 5-16 events. Relocation of events in each set suggests that most rupture approximately the same fault patch at different times. We use a sliding cross-correlation window technique (Niu et al., 2003) to measure travel time difference and evolving decorrelation in waveforms generated by each set of repeating events relative to the waveform of the first event. We find systematic changes between the early S coda waves generated by events before the Duzce mainshock and those generated after it. The largest co-seismic velocity change is observed at station VO that was deployed inside the rupture zone of the Izmit earthquake and recorded up to 1g ground acceleration during the Duzce mainshock. The amplitude of delay times seems to follow a logarithmic decay after the Duzce mainshock, suggesting a possible recovery from the mainshock damage. The observations are likely to reflect changes of material properties in the shallow structure of the fault zone. Updated results will be presented in the meeting.
S21D-07 09:45h
Quantitative, Calculable, Fluid-Rock Deformation
As a result of stress-aligned fluid-saturated microcracks, seismic shear-wave splitting is seen with similar parameters in almost all rocks from 1% porosity granites to 20% porosity sandstones. These microcracks are the most compliant elements of in situ rock and the response/deformation of microcracked rock can be modeled by Anisotropic Poro-Elasticity (APE). The mechanism is based on the unique correspondence between the distribution of fluid-filled microcracks and the evolving differential stress field in all fluid-saturated rocks. Numerical modeling with APE matches a huge range of phenomena. These include: accurate 3C reflection surveys, where the response to both high- and low-pressure CO2-injections was matched exactly; and monitoring stress-accumulation before earthquakes, where on one occasion the time and magnitude of a M 5 earthquake was successfully stress-forecast in SW Iceland. There are many other important implications. The rock mass is highly compliant and varies spatially and temporally. This means that high-resolution seismic measurements may degrade (by one or two ms) from the moment they are recorded. (The key to achieving such accuracy is using the highly repeatable shear-wave source, the Downhole Orbital Vibrator.) In contrast, if appropriate data are available the response of the rock mass to known changes can be calculated or predicted. Consequently, if changes in conditions are known, the response of in situ rock can be controlled by feedback. Note that the key observable is shear-wave splitting. P-waves are sensitive to many phenomena, but only stress-controlled shear-wave splitting that can monitor the evolution of fluid-saturated microcracked rock. As a result the understanding of shear-wave splitting has advanced substantially in the last few years. Recent papers and preprints can be found at http://www.glg.ed.ac.uk/$\sim$scrampin/opinion/.