S51D-01 INVITED
Envelope Synthesis of High-Frequency Seismic Waves in the Lithospheric Inhomogeneity
High-frequency seismograms of earthquakes are complex and mostly composed of incoherent waves scattered by distributed inhomogeneities in the lithosphere; however, their wave-envelopes are smooth, systematic, frequency dependent, and vary regionally. Therefore, it is useful to analyze bandpass-filtered seismogram envelopes disregarding phase information for the study of medium inhomogeneity. If we focus on seismogram envelopes around the onset and the maximum peak, the envelope broadening and peak delay increase with travel distance increasing; the transverse-component amplitude of P waves and the longitudinal- component amplitude of S waves increase with travel distance increasing. We can interpret these phenomena as the result of multiple scattering around the forward direction by random velocity inhomogeneities. When the wavelength is shorter than the characteristic scale of random media, the Markov approximation, a stochastic extension of the phase screen method for the parabolic wave equation, is a powerful theoretical method for the synthesis of wave envelopes in random media in relation with their power spectrum. We have theoretically developed the envelope synthesis for vector waves in isotropic random elastic media as an extension of that for scalar waves for both plane-and spherical-wave cases. A closed form analytical solution is obtained especially in random media characterized by a Gaussian power spectrum. The developed method well explains how the wave envelope of each vector-component is broadened with travel distance increasing. The envelopes synthesized agree well with ensemble-average wave envelopes calculated from finite difference simulations of the elastic wave equation for a suite of 2-D random media. We also show the vector-wave envelope synthesis in nonisotropic random media, which are appropriate to represent the lithospheric inhomogeneity. The broadening of synthesized vector-wave envelopes with travel distance depends on the ray direction relative to the nonisotropy of randomness. These envelope syntheses will be a mathematical base for the study of lithospheric inhomogeneity from the analyses of local earthquake seismograms and teleseismic records.
S51D-02
Use of coda wave interferometry for estimating the variation in source orientation between double couples
It is shown how a change in source orientation between two identically located double couple events can be estimated from the correlation of their coda waves. The change in orientation is given by the root mean square of the change in strike, Δφs dip, Δδ and rake, Δλ of the double couple. It is not possible to determine Δφs, Δδ or Δλ individually from the cross correlation. Theoretical results are tested using synthetically generated waveforms for source-pairs with differing strike, dip and rake. In each case a cross-over is identified such that the actual change in orientation is within one standard deviation of the coda wave interferometry (CWI) estimates for all rotations below the cross-over. After the cross-over, the CWI estimates provide a lower bound on the change in orientation. Cross-over points of 30°, 62° and 56°, respectively are observed when the strike, dip and rake are varied independently. When all angles are varied simultaneously by the same quantity the cross-over point is 17°. The new theory can be applied in combination with existing coda wave interferometry techniques for estimating source separation It also has potential for joint relative location and focal mechanism determination using coda waves recorded at a single station.
S51D-03
Multiple Scattering and Coda Localization at Merapi Volcano
Due to their eruptive history the cones of strato volcanoes consist of different materials such as hardened lava, tephra, and volcanic ash. Additionally, due to their rough topography, e.g. caused by erosion, deposition is irregular and the volcanic structure cannot be described by a simple 1D layered model. The 3D small scale heterogeneities with large impedance contrast cause multiple scattering of seismic waves and are important features for the modelling of seismic wave propagation in strato volcanoes. Active seismic experiments at Merapi and Vesuvius volcanoes have shown that the transport mean free path of strato volcanoes is as small as some hundreds of meters and, therefore, is about three orders of magnitude smaller than the transport mean free path of usual Earth's crust. Moreover, the transport mean free path is at least one order of magnitude smaller than the characteristic scale length of intrinsic attenuation. Finally, the transport mean free path is in the same order as the inverse of the wave number. This indicates, that in strato volcanoes heterogeneity is so strong that we approach the regime of strong scattering where the classical theories such as radiative transfer and diffusion become invalid. All this makes strato volcanoes a natural laboratory for the application of multiple scattering theories. One important recent observation at Merapi volcano is an abnormal spatial concentration of coda energy in the summit region. This observed coda localization can be interpreted as an indication of Anderson localization, which is a theoretically predicted effect of strong scattering beyond the validity of diffusion theory. We show that the Anderson localization model better fits the data observed at Merapi than a standard half space diffusion model. However, we also show that, alternatively, the observation can also be explained within the classical diffusion approach by assuming leakage of energy from the strongly scattering volcanic edifice into the much more homogeneous underlying earth crust. Similar to Anderson localization the leakage results in an inhomogeneous distribution of energy in space, where the energy is low near the volcano-crust boundary and large inside the strongly scattering volcano far from that boundary. Additionally to the Anderson localization model, we use two classical models to explain coda localization: The first one is based on an analytical solution of the diffusion equation for a scattering cylinder (representing the volcano) embedded in a homogeneous half-space (representing the surrounding crust). The second model is based on a Monte-Carlo simulation of the acoustic equation of radiative transfer. In this simulation we take into account multiple scattering inside the volcanic edifice as well as leakage at the bottom of the volcano into the less heterogeneous crust. Additionally, in this model we also consider the true topography of the volcano by simulating reflections at the free surface, where we use a digital elevation model of the volcano and the Kirchhoff tangent plane method.
S51D-04
Inversion of depth-dependent small-scale heterogeneity spectra in the Earth using transmission fluctuations of logarithmic amplitude and phase data
The transmission fluctuations of log-amplitude and phase data across a seismic array provide sensitive probe for the heterogeneities at depth. The coherence functions formed using these transmission fluctuations can be used to invert for the depth-dependent small-scale heterogeneity spectrum in the context of variable background velocity model whereas the previous theory was formulated with a constant background velocity. Our newly extended theory allows us to apply the method to data collected on the Earth's surface. We investigated the depth sensitivity of the logA and phase coherence functions. The angular coherence function (ACF) and the transverse coherence function (TCF) are two extreme cases of the joint transverse and angular coherence function (JTACF). The phase ACF has sensitivity at shallow depths; the phase TCF has almost uniform sensitivity over all depths; the phase JTACF has focused sensitivity around depth where the paths of the two events intersect. Likewise, the logA TCF and ACF have very poor depth resolution. The depth sensitivity of logA JTACF is similar to that of the phase JTACF. The spectral inversion is formulated as a generalized inversion problem. A lithosphere-asthenosphere model is tested for numerical validation using the finite difference generated seismograms. It shows that using JTACFs with angular separation up to 15°, we were able to recover the heterogeneity spectra of the two-layer model. Our method recovers the heterogeneity spectrum at the high wavenumber end and it is supplementary to the traditional seismic tomography where only the low wavenumber end information is retrieved. We will also show some preliminary results of the heterogeneity spectrum under Japan using the HiNet data.
S51D-05
Diffuse Waves and Energy Densities Near Boundaries
Green function can be retrieved from averaging cross correlations of motions within a diffuse field. In fact, it has been shown that for an elastic inhomogeneous, anisotropic medium under equipartitioned, isotropic illumination, the average cross correlations are proportional to the imaginary part of Green function. For instance coda waves are due to multiple scattering and their intensities follow diffusive regimes. Coda waves and the noise sample the medium and effectively carry information along their paths. In this work we explore the consequences of assuming both source and receiver at the same point. From the observable side, the autocorrelation is proportional to the energy density at a given point. On the other hand, the imaginary part of the Green function at the source itself is finite because the singularity of Green function is restricted to the real part. The energy density at a point is proportional with the trace of the imaginary part of Green function tensor at the source itself. The Green function availability may allow establishing the theoretical energy density of a seismic diffuse field generated by a background equipartitioned excitation. We study an elastic layer with free surface and overlaying a half space and compute the imaginary part of the Green function for various depths. We show that the resulting spectrum is indeed closely related to the layer dynamic response and the corresponding resonant frequencies are revealed. One implication of present findings lies in the fact that spatial variations may be useful in detecting the presence of a target by its signature in the distribution of diffuse energy. These results may be useful in assessing the seismic response of a given site if strong ground motions are scarce. It suffices having a reasonable illumination from micro earthquakes and noise. We consider that the imaginary part of Green function at the source is a spectral signature of the site. The relative importance of the peaks of this energy spectrum, ruling out non linear effects, may influence the seismic response for future earthquakes. 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.
S51D-06
Analysis of Pdiff coda using the axi-symmetric finite difference method
The scattering of seismic waves from small spatial variations of material properties (e.g., density and seismic wave velocity) affects all seismic observables including amplitudes and travel-times and also gives rise to seismic coda waves. A large amount of the seismic energy observed at high frequencies is contained in these coda waves, and is especially evident for the seismic phases P and Pdiff. Analysis of seismic scattering has provided a means to quantify small-scale seismic properties that cannot be determined through travel-time analysis or ray theoretical approaches. Numerical wave propagation techniques, such as Finite Difference (FD) techniques, have been utilized in analyzing the full waveform effects of the scattered wave field, although application of these techniques has been focused on studies in regional distance ranges. We examine the seismic coda of the phases P and Pdiff for events occurring in the Tonga/Fiji and Kermadec Trench regions, recorded at the short period Yellowknife array (YKA) located in northwestern Canada. We model the envelope of the coda wave train using the axi-symmetric finite difference approach PSVaxi. Although, we do not model full 3D scatterer geometries, the 2.5D axi-symmetric approach allows us to reach dominant seismic periods on the order of 3-4 sec. The result of using 2.5D scatterer geometries is that our scattering strength is smaller than suggested by full 3D geometries, thus producing a conservative estimate to the scattering strength. We generate our models of random heterogeneity by application of the Karhunen-Loève Expansion (KLE). The KLE technique is ideal for this application as it works for both isotropic and anisotropic correlation structures on both Cartesian and non-Cartesian grids, and is also capable of producing models with non-stationary correlation structures without introducing first-order discontinuities. The Pdiff phase for the ray path geometry we study passes through the lower mantle in the central Pacific region, an area showing a high degree of lateral heterogeneity. For these ray paths, Pdiff shows strong coda development and also demonstrates strong lateral variability of coda duration. Using this numerical approach is the first attempt at actually synthesizing waveforms for seismic scattering at the global scale and comparing these waveforms with data. We present comparisons of the synthesized waveforms for our best fitting models with our YKA dataset.
S51D-07 INVITED
Using coda waves extracted from microseisms to construct direct arrivals.
The analysis of long range correlations of microseisms has been shown to provide reliable measurements of wave speeds that can eventually be used for seismic imaging.In the case of an even distribution of noise sources, it has been theoretically demonstrated that the correlation is the exact Green function, including all types of waves. In practice this method islimited in its application by the actual source distribution. We present the example of a set of stations in Europe, for which the predominant flux of energy from the northern Atlantic results in a clear azimuthal dependence of the quality of the reconstruction of Rayleigh waves, with a very poor reconstruction in some azimuths. To solve this problem, we use the noise correlations measured on the entire network. Let us consider two stations A and B for which the Rayleigh waves are not efficiently reconstructed by correlation of continuous records. We compute all the correlations between the station A (resp.B) and all the 150 other stations located at regional distances. Theoretically, these correlations must contain direct waves and coda with various signal to noise ratios. We then use these signals as equivalents to seismograms produced by sources acting at station locations and recorded in A and B. We select the time windows corresponding to coda waves and compute the average correlation between virtual seismograms obtained in A and B. As for actual earthquake data (Campillo and Paul, 2003), this correlation function contains the surface wave part of the Green function. We illustrate the efficiency of the reconstruction by comparison with direct measurements. This procedure can be used to perform velocity measurement between stations, even in presence of a very directive and poorly oriented noise. It shows that, in spite of a currently small signal to noise ratio, the cross correlations of microseisms contain more than direct surface waves. Arrivals with complex travel paths as coda waves are also present.