S13A-1779
The 26th December 2004 Sumatra-Andaman mega-event: Observed and synthetic spectra computed with various models
The high quality of the records obtained after the huge Sumatra-Andaman earthquake of December 2004 from the broad-band seismological stations of all FDSN networks offers a good opportunity for studying the free oscillations of the Earth and especially the gravest ones (frequencies lower than 1 mHz). We have studied both frequencies and the quality factor respectively for seventeen and seven modes. Their studying is the best way to determine a density and attenuation profile of the Earth. Our work is mainly based on the analysis of vertical component recordings and some horizontal components. Our results are compared to the theoretical eigenfrequencies and attenuation factor computed with the HOPT method. Our synthetics are computed with the PREM and 1066A models, both taking into account rotation and ellipticity of the Earth, and on top of these one D models, we add the 3D elastic model of the mantle SAW12D, and the 3D attenuation model of the upper mantle QR19. At low frequency, the misfit between our measurements and the theoretical corresponding values point out that some parameters are not constrained enough to explain our observations. A small change in the density profile model or the attenuation profile model may provide new eigenfrequencies and Q values and a better fit with our observations. At larger frequency the lateral heterogeneities of the Earth can also affect the results and we have to discriminate among the different effects. The new catalog of modal eigenfrequencies and attenuation factors provided from the huge Sumatra- Andaman event analysis offers a plethora of perspectives. The two observed datasets (frequencies and quality factors) will be invert in order to determine a density and an attenuation profil of the Earth.
S13A-1780
First estimates of Q quality factors from the individual singlets of the Earth's normal modes from the 26th December 2004 Sumatra-Andaman mega-event
The interest of Earth scientists in the normal modes, particularly the gravest ones or the core sensitive ones,
is mainly due to the key role they play to better constrain Earth's models and to their evident contribution to a
better knowledge of the density profile in the Earth.
The giant Sumatra-Andaman earthquake of December 2004 and the high quality of the numerous recordings
obtained from the broad-band seismological stations of all FDSN networks offer a good opportunity for
studying the free oscillations of the Earth. The clear spheroidal modes splitting observations and the
accurate identification of singlets of some particular modes (gravest modes or outer-core and inner-core split
modes) made possible to study extensively their behaviour. The resolution never obtained from broad-band
seismometers records made their analysis particularly promising.
An efficient technique developed in our group allows to compute the attenuation factors from the apparent
decrease of the amplitude of each singlet with time. The feasibility of such a method applied on individual
singlets is clearly demonstrated.
Some spheroidal modes under observation show a clear identification of the individual well isolated singlet
eigenfrequencies, making possible to determine the corresponding attenuation factors. The results are
compared to the theoretical Q quality factors computed for the PREM-re model, taking into account both
rotation and ellipticity effects of the Earth. We present modal attenuation measurements of some spheroidal
fundamental gravest modes and some particular higher modes, inner-core modes and inner-core
anomalously split modes. Our results correspond to attenuation factors measurements of a few individual
singlets of two rarely observed modes, the 2S1 and 3S1 modes, as well as singlets of core modes, a normal
one 1S2(core mode) and an anomalously split mode such as 3S2 (inner core mode).
This new catalog of modal attenuation factors provided from the Sumatra-Andaman event analysis, in
addition to the catalog of the corresponding eigenfrequencies will allow to build a density (or attenuation)
profile model with a good resolution.
http://www.ipgp.jussieu.fr
S13A-1781
Global teleseismic P wave attenuation
We analyze the variation with epicentral distance (Δ) of the attenuation of teleseismic (30°- 85°) P waves from about 200 deep (> 200 km) earthquakes recorded at 300 broadband global and regional network stations. High quality P wave spectral ratios, measured between 0.03 and 1 Hz, are inverted for the attenuation parameter tP* by least-squares inversion. Our results indicate that tP* increases by less than 0.2 s between 30° and 55° and by about 0.3 s between 55° and 85°. We also observe systematic variations in tP*(Δ) along several highly sampled source- receiver corridors. For South American earthquakes, tP* increases by 0.4 s at stations in eastern North America but only by 0.1 s at stations in western North America. This indicates the presence of large scale Q variations in the North American deep mantle. We compare our global tP* measurements to new measurements of tS* and to global 1D profiles of Q to determine the robustness of our measurements. We also compare tP* and tS* to P and S wave traveltimes which would help towards constraining the physical mechanism of attenuation in the deep mantle.
S13A-1782
Full-3D Waveform Tomography for Crustal and Upper Mantle Seismic Velocity and Attenuation Structure in Eastern Eurasia Based On the Scattering-Integral (SI) Method
The main objectives of this study are to jointly invert for 3-D crustal and upper mantle seismic velocity and attenuation structure for eastern Eurasia, especially focus on shear wave properties. We address this problem by applying a unified full-wave analysis and inversion method to simultaneously infer 3-D seismic velocity and attenuation structures from regional seismic waveforms recorded by broadband 3-component digital seismic stations. Specifically, we analyze broadband body and surface waves from regional earthquakes, recorded on the IRIS Global Seismic Network (GSN) stations, and measure frequency-dependent phase and amplitude residuals of these waveforms with respect to synthetics calculated from a 1-D reference Earth model that represents the eastern Eurasia region. These residuals are inverted for a 3-D tomographic model of shear velocity and shear attenuation quality factor using 3-D sensitivity kernels that fully account for the effects of both elastic and anelastic structure on the amplitude and phase behavior. By jointly inverting for shear velocity along with shear attenuation, we remove much of the uncertainty associated with elastic effects such as focusing/defocusing and large-scale scattering.
S13A-1783
Velocity and Q Structure of the Quaternary Sediment in Bohai Basin, China
Heavily populated by Beijing and Tianjin cities, Bohai Basin is a seismically active Cenozoic basin suffering from huge lost by devastating earthquakes, such as Tangshan earthquake. There have been some studies about three dimensional structure of the lithosphere in this region; however the attenuation (Qp and Qs) of the surfacial quaternary sediment has not been studied at natural seismic frequency (1-10HZ), which is crucial to earthquake hazards study. Borehole seismic records of micro earthquake provide us a good way to study the velocity and Q attenuation of the surfacial structure (0-500m). We found that there are two pulses well separated with simple waveforms while analyzing borehole seismic records from the 2006 Mw4.9 WenAn earthquake sequence. Then we performed waveform modeling with Generalized Ray Theory (GRT) to confirm that the two pulses are direct wave and surface reflected wave, and found that the average Vp and Vs of the top 300m in this region are about 1.83km/s and 0.42km/s while Vp/Vs falls in a high value of 4.4. We also modeled surface reflected wave with Propagating Matrix method to study the value of Qs and the surfacial velocity structure. Our modeling indicates that Qs should be larger than 30, even up to 100, this is quite larger than the typically assumed extremely low Q (~=10) found by Hauksson et al (Hauksson et al, 1987; Blakeslee and Malin, 1991) but much similar to that of Langston (2002). Also, the velocity gradient just beneath the free surface (0-50m) is very large and velocity increases slowly at larger depth. Our modeling demonstrates the value of borehole seismic records in resolving shallow velocity and attenuation structure, and hence their significance in earthquake hazard simulation.
S13A-1784
Velocity Dispersion Effect in a Virgin Heavy Oil Reservoir
In this work we attempt to do a detailed analysis of seismic wave attenuation in a Heavy Oil reservoir before starting oil production. The data we use is a shallow zero offset VSP located in the Athabasca region in Alberta, Canada. Previous work in the area (see Schmitt, 1999) shows velocity differences between the log and the VSP velocities that happen at the reservoir level and can be attributed to velocity dispersion. Batzle and Hofman (2006) argue that this effect is highly possible heavy oil sands. We used common inversion techniques to find the smooth solution for the velocity and the quality factor. Then we computed the misfit to simultaneously find the velocities and quality factors that give the best fitting to the data. The method we are using is based on the spectral ratio technique and we avoid any attempt to compute the reflection coefficients, therefore all of the misfitting analysis is done in the frequency domain. Nonetheless the true amplitudes were not included in the computation of Q we did a careful analysis of the source to avoid any phase change not related to attenuation. Moreover a previous work using trace to trace comparison for computing a Q profile shows the same trend that the results we got by inverting the data. Although this data is very old, the quality of the acquisition including the high density of vertical and time sampling allow us to establish limits for the profile, to use a relatively wide range of frequencies and to relate results to lithology changes. This finding seems to agree with theories of anelasticity due to the high viscosity of the heavy oils and is expected to be more pronounced after production starts. The production of heavy oil involves steam injection that dramatically decreases its viscosity. The work also shows that a detailed computation of Q profiles can be used as starting model for further works with more data, i.e. seismic volumes, this would help to have a better fitting in cases were dispersion is present.
S13A-1785
FD Computation of Seismic Waveform for a Global Earth With Anelastic Attenuation
In order to reveal detailed structure of the Earth's interior, we need to employ waveform inversion. The waveform inversion is the method that determines structures by minimizing the difference between observed waveforms and theoretical seismograms. For the direct comparison between them, employment of realistic attenuation is crucial since it affects amplitudes, traveltimes, and waveforms of observed seismograms. Stress-strain relation in a viscoelastic material is represented as a convolution in the time domain, so incorporation of the anelasticity into time domain methods such as the finite-difference (FD) method had been quite difficult before the so-called memory variable was introduced (e.g., Emmerich & Korn, 1987, Geophysics; Carcione et al., 1988, Geophys. J. R. astr. Soc.). On the other hand, in the field of global seismology, axisymmetric FD modeling (e.g., Igel & Weber, 1995, GRL) has usually been employed to save computational resources. The axisymmetric modeling uses a structure model with rotational symmetry about an axis through a seismic source, and then solves the elastodynamic equation in spherical coordinates. The axisymmetric modeling has been a powerful method especially in global seismology since it can correctly model the 3-D geometrical spreading effects with computational resources comparable to 2-D modeling. Recently we proposed implementation of an arbitrary moment tensor point source into axisymmetric FD scheme (Toyokuni & Takenaka, 2006, EPS). Nevertheless, anelastic attenuation has not been incorporated in the conventional axisymmetric global FD modeling. In this presentation, we employ the anelasticity in the axisymmetric FD scheme through the memory variable, and show some numerical examples.
S13A-1786
Assessing the Accuracy of the Velocity-Memory-Stress Finite-Difference Scheme at the Earth's Surface
The velocity-memory-stress time-domain finite-difference system is a common method of modeling seismic wave propagation in anelastic media. This formulation is based upon the assumption of a standard linear solid rheology which allows the conversion of the original integro-differential system of equations into purely differential equations. Understanding the accuracy of this finite-difference methodology is essential for proper interpretations of simulated waveforms. High-contrasts in material properties across interfaces, such as at the surface of the earth, are well-known to cause problems for traditional finite-difference schemes. One method to circumvent this problem is to define an explicit stress-free surface where one solves a different set of equations than in the interior of the model. These special equations at the free surface are different for elastic and anelastic media and the utilization of the elastic free surface equations for anelastic media, as is sometimes done for expediency, leads to noticeable inaccuracy within a very few wavelengths distance from the source. Another approach to handling the earth's surface is to grade the density slowly from rock to air densities. This allows the same equations to be utilized throughout the model, but it can lead to inaccuracies especially near the interface. We have developed a method for stably and accurately computing finite-difference waveforms for both elastic and anelastic media at high-contrast interfaces, including the air-earth interface. We demonstrate the accuracy of this new methodology for anelastic media especially in the context of surface waves with comparisons to the explicit free-surface case and to a frequency-wavenumber 1-D layered media code. Sandia National Laboratories is a multiprogram science and engineering facility operated by Sandia Corporation, a Lockheed-Martin company, for the US Department of Energy's National Nuclear Security Administration, under contract DE-AC04-94AL85000.
S13A-1787
Poroelastic Attenuation due to Mesoscopic Heterogeneities
Seismic attenuation and dispersion are numerically determined for computer-generated porous materials that contain mesoscopic-scale heterogeneies having an anisotropic shape. The local equations used to determine the poroelastic response within such materials are those of Biot (1962). Upon applying a step change in stress to samples containing mesoscopic-scale heterogeneity, the poroelastic response is determined using finite difference modeling. In this study, we limit our investigations to orthotropic materials, for which the poroelastic properties only vary in the three orthonornal directions of space. In this special case, only nine stiffnesse are nedeed to descibe the wave propagation. The ratio of the imaginary and real parts of these stiffnesses determines the attenuation as a function of frequency associated with the modes of applied stress (pure compression and simple shear). The nine complex stiffnesses and the associated attenuations have been computed for two different families of samples: (1) Samples consisting of ellipsoidal inclusions embedded within a homogeneous matrix; (2) Sample having a random distribution with a Gaussian correlation function of their elastic properties. For both types of samples, our main observation is that the maximum attenuation associated with the different directions of wave propagation is a clean powerlaw of the geometrical aspect ratios of the mesoscale heterogeneities present within the meterial. Speculation on the nature of the exponents in the powerlaws will be provided.
S13A-1788
Recursive formula for maximum amplitude in von Karman type random media with intrinsic absorption on the basis of the Markov approximation
In high frequency range (>1Hz), an impulsive seismic wave radiated from a microearthquake is collapsed and broadened as travel distance increases due to random inhomogeneities and intrinsic absorption. We have investigated spatial distributions of random inhomogeneities by the analyses of the peak delay time that is defined as the time lag from the S-wave onset to the maximum amplitude arrival. Our inversion analyses, for example, revealed that the regions beneath the Quaternary volcanoes show strong inhomogeneities (e.g., Takahashi 2007 IUGG Mtg.). Such results imply that strong inhomogeneities are related to magma-diapir. For detailed discussion on such interpretation, we need to investigate the intrinsic absorption in the lithosphere. In this study, we examine the characteristics of the maximum amplitude attenuation assuming along ray-path variation of random inhomogeneities and intrinsic absorption on the basis of the Markov approximation. Then, we propose a recursive formula for maximum amplitude of seismic envelopes as a tool to investigate the intrinsic Q structures. Seismic envelopes are synthesized by the stochastic ray-path method (e.g., Takahashi et al. 2008, G.J.I.). This method is based on the Markov approximation of parabolic wave equation for spherical waves. The medium is divided into thin spherical shells, and each shell is characterized by von Karman type power spectral density function (PSDF) with intrinsic Q. For the case that random inhomogeneities changes along the ray-path and Q-1=0 for the whole space, the power of the travel distance dependence of maximum amplitude is affected by all of the stochastic parameters of the random media in which waves have propagated. This characteristic is similar to the peak delay time, and cannot be described by the exponential decay with scattering Q. To describe this characteristic, we modify the recursive formula (Takahashi et al. 2008, G.J.I.) for the maximum amplitude. This method successfully predicts the simulation results as long as random inhomogeneities are weakly changed in the space. If we take account of the absorption effect (Q- 1>0), the maximum amplitude can be predicted by the same approach by introducing a correction term, that is for a mean increase of the travel distance due to the increase of the peak delay time. If we use the spatial distribution of random inhomogeneities estimated by the peak delay time analysis, we will be able to investigate the attenuation structure, which does not include the effect of multiple forward scattering.
S13A-1789
Frequency-Dependent Attenuation and Q-band Model for the Earth
Surprisingly, the existing interpretations of frequency-dependent Q(f) still remain equivocal. Revisiting several key observations from whole-Earth oscillations to surface-, body-, Lg, and coda waves shows that the frequency dependence may be an artifact of incompletely compensated, ~10-20% variations in geometrical spreading. For this reason, the use of Q for describing of structural and scattering effects should be discouraged. Using the attenuation coefficient α(f) instead of Q(f) leads to simple, assumption-free and unambiguous descriptions of the observations and provides a consistent basis for interpretation. Despite its simplicity, the α(f) picture often leads to dramatic changes in the interpretations. In all cases considered so far, frequency-independent Q was sufficient to explain the available observations within the entire 10-4 -- 102 Hz frequency band. Therefore, frequency-selective scattering and relaxation rheological mechanisms may not be required. Instead, the data indicate two bands of lower Q within the outer core and upper mantle, and a higher-Q crust.
S13A-1790
Determining the Sensitivity of Phase Velocity Eigenvalues to Perturbations of Elastic Moduli in Anisotropic Media
Inverting for the phase velocities of an elastically anisotropic medium such as finely layered marine sediments, the mantle of the Earth, or single crystals of a mineral, requires the computation of the sensitivities or Frechet derivatives of the phase velocities with respect to perturbations in the elastic moduli. One obvious way to do this is to carry out a numerical computation employing brute force differencing. The Hellman-Feynman Theorem provides a direct analytical method for computing the sensitivity of the phase velocity eigenvalues of the Christoffel equation with respect to the moduli for an elastically anisotropic medium. This does not require computation of the derivatives of the eigenvectors with respect to the moduli. The application of the Feynman-Hellman Theorem to the the problem of determining the Frechet derivatives of the Christoffel equation are discussed, along with some other geophysical applications.
S13A-1791
Role of the Inhomogeneity Angle in Attenuation Analysis
The inhomogeneity angle (the angle between the real and imaginary parts of the wave vector) is seldom taken into account in estimating attenuation coefficients from seismic data. However, wave propagation through the subsurface may result in relatively large inhomogeneity angles ξ, especially for models with significant attenuation contrasts across layer boundaries. Here, we study the influence of the angle ξ on phase and group attenuation in arbitrary anisotropic media using the first-order perturbation theory verified by exact numerical modeling. Application of the spectral-ratio method to transmitted or reflected waves yields the normalized group attenuation coefficient {𝒜}g, which is responsible for the amplitude decay along seismic rays. Our analytic solutions linearized in the anisotropy parameters show that {𝒜}g is close to the normalized phase attenuation coefficient {𝒜} computed for a zero inhomogeneity angle. The coefficient {𝒜}|ξ=0° can then be inverted for the attenuation-anisotropy parameters using the existing formalism developed by Zhu and Tsvankin (2006). In other words, no knowledge of the inhomogeneity angle is required for attenuation analysis of seismic data in isotropic or anisotropic media. This conclusion remains valid even for uncommonly high attenuation with the quality factor Q less than 10 and strong velocity and attenuation anisotropy. We also demonstrate that the velocity function remains practically independent of attenuation for arbitrary values of ξ, while the angle variation of the attenuation coefficients is controlled primarily by the attenuation-anisotropy parameters. The influence of velocity anisotropy on attenuation becomes non- negligible only for strongly attenuative media (Q<5) and large inhomogeneity angles (ξ > 70°). In principle, estimation of the attenuation-anisotropy parameters from the coefficient {𝒜} requires computation of the phase angle, which depends on the anisotropic velocity field. However, for moderately anisotropic models the difference between the phase and group directions does not significantly distort the results of attenuation analysis.
S13A-1792
Seismic Signature of Fault-Opening Motion
Earthquakes are typically assumed to be caused by shear faulting. However, it is also recognized that earthquake ruptures may have motion components normal to the fault. The non-double-mechanism may reflect tensile faulting but it can also be produced by shear faulting in an anisotropic medium and a combination of several different double couples. In this study we aim to find additional seismic signatures of fault-opening motion by performing a theoretical parameter-space study involving analysis of synthetic seismograms generated by sources with fault-opening components using several different receiver configurations. The arrival time, polarity and amplitude information of different seismic phases are systematically examined in order to find robust seismic signatures indicative of fault-opening motions during earthquakes. One interesting characteristic is related to the fact that fault-parallel seismograms recorded close to the fault from a shear dislocation are nearly zero, whereas corresponding seismograms generated by a tensile dislocation record appreciable motion in both the P and S waves. As a result, seismograms at such receiver geometries generated by combined sliding and opening motion may be dominated by signals produced by the fault-opening. In addition, the P and S phases on seismograms across the fault have same or opposite polarities across the fault depending on the type of the component (fault-parallel or fault-normal) and the nature of the source (shear or tensile). Updated results will be presented in the meeting. We are in the process of looking for additional informative signals of opening motion along faults that separate similar and dissimilar solids. Updated results will be presented in the meeting.
S13A-1793
Multidimensional Absorptive-Dispersive Inverse Scattering and Parameter Leakage at the Linear Step
Research is active into the use of inverse scattering to create direct non-linear methods for task-separated imaging, inversion, and Q compensation of primary reflections (Weglein et al., 2008). We will discuss some recent developments within the third of these efforts. First, we will describe an extension of the absorptive inverse scattering equations in multiple dimensions to the case of an absorptive reference medium. This requires a generalized definition of the perturbation as compared to the non-absorptive reference medium case. Second, because of its potential impact on a recently described prototype direct non-linear Q compensation algorithm (Innanen and Weglein, 2005; Innanen and Lira, 2008), we will discuss the issue of leakage of absorptive parameters. Leakage is an inverse phenomenon in which actual variations in one medium parameter lead to variations of the linear estimate of other parameters, especially at large angles and large contrasts. This is a linear issue exclusively; the full non-linear inverse scattering series addresses leakage, and corrects for it. Our prototype non-linear Q compensation algorithm involves the isolated use of some, but not all, of the non-linear terms of the inverse scattering series. The question we wish to address is: does this subset of the full inverse series also manage and correct for leakage, or will it over- or under-compensate at large angles and large contrasts? If the latter, further analysis and collection of inverse series components will likely be indicated. A. B. Weglein, A. C. Ramirez, K. A. Innanen, F. Liu, J. E. Lira and S. Jiang, 'The underlying unity of distinct processing algorithms for (1) the removal of free-surface and internal multiples, (2) Q compensation (without Q) (3) depth imaging, (4) nonlinear AVO, that derive from the inverse scattering series', 2008: Proc. Soc. Expl. Geop. K. A. Innanen and A. B. Weglein, 'Towards non-linear construction of a Q compensation operator directly from measured seismic reflection dataa', 2005; Proc. Soc. Expl. Geop. K. A. Innanen and J. E. Lira, 'Direct non-linear Q compensation of primaries in layered media: theory and synthetic examples', 2008: Proc. Soc. Expl. Geop.