S32A-01
Surface wave tomography: where does ray theory break down on a global scale?
In global seismic tomography, almost all inversions thus far have relied on ray theory. Ray theory is valid at high frequencies where wavelengths are short compared to the size of the heterogeneous structure of the Earth. Particularly for surface waves at longer periods, we need to go beyond this approximation. Born theory is expected to perform well even for heterogeneities of approximately the same size as the wavelength. Today, it has become feasible to apply Born sensitivity kernels in global scale inversions, but it is still unknown how well ray theory and Born theory compare with one another especially for surface wave tomography; a systematic investigation on global-size scales with a realistic source/receiver distribution is lacking. A common way to investigate the resolution of the ill-posed inverse problem consists of conducting a set of different checkerboard tests with the same inverse algorithm. Thus, regions of high and poor resolution can be distinguished. In this study, we focus on phase-velocity inversions of intermediate to long-period surface waves. We use the source/station distribution of a real phase-anomaly measurement database to investigate the resolution limit of ray-theoretical and Born-theoretical inversions. Our synthetic datum is calculated by cross-correlating waveforms obtained numerically from a membrane model which accounts implicitly for all nonlinear propagation effects; it therefore surpasses known problems where synthetic data are computed in a linear model. For this 2-D case, we are also able to iterate the inverse scheme with Born sensitivity kernels calculated in a heterogeneous background Earth via the adjoint wavefield method. Our results show a clear improvement for high harmonic degree when Born theory is used to invert phase-anomaly measurements of long-period surface waves.
S32A-02 INVITED
An Efficient Approach to the Calculation and Storage of Fr{é}chet kernels for Finite-Frequency Tomography
Numerical modeling experiments of wave propagation have shown that the traveltime and amplitude anomalies of a finite-frequency seismic wave are influenced by the heterogeneities in the first Fresnel zone of the wave, a region surrounding its ray path. This leads to the so-called 'banana-doughnut' sensitivity (Fr{é}chet) kernels for finite-frequency waves whose values vary in the first Fresnel zone, rather than concentrate only on the ray path. Therefore, if finite-frequency effect is not taken into account in seismic tomography, the unrealistic sensitivity kernels will limit the resolution to roughly the widths of the first Fresnel zones of the seismic waves, even if all the other aspects are perfect. For the same reason, to realize the full potential of finite-frequency approach in seismic tomography, the spatial sampling in computing the Fr{é}chet kernels and in discretizing the structural model must be sufficiently small so that there are enough sampling points within the width of the first Fresnel zone. This introduces a high demand in computational resources including memory, CPU time, disk storage and the input/output (I/O) operations. To facilitate the practice of finite-frequency high-resolution tomography, we develop an efficient algorithm for computing the Fr{é}chet kernels based on the normal-mode theory in spherically symmetric earth models. The strain Green tensors (SGTs) for a spherically symmetric reference model are computed by normal-mode summation on a dense depth-distance grid by normal-mode summation. This normal-mode SGT database can then be used to calculate all the wavefield quantities needed in seismic studies including synthetic seismograms, partial derivatives with respect to source parameters for the inversion of CMT solutions, and the Fr{é}chet kernels for various kinds of model parameters for the inversions of anelastic and anisotropic structures. The SGT database approach provides the necessary efficiency for calculating the Fr{é}chet kernels with sufficient spatial samples in the first Fresnel zones. To reduce the disk storage and the I/O demands, we also develop an algorithm for the compressions of the SGTs and the Fr{é}chet kernels based on wavelet decomposition. We will compare the orthogonal Haar wavelets with the bi-orthogonal Cohen-Daubechies-Feauveau (CDF) wavelets which are characterized by a higher regularity and thus ensure a higher compression rate.
S32A-03
Investigating the Anisotropic Shear Wave Velocity Structure of the Earth's Mantle
The principal tool by which we learn about the upper part of the mantle (the top 1000 km say) is through the study of surface waves and, importantly, surface wave overtones. In this study we combine a variety of existing databases of surface wave phase velocity measurements into a very large data set consisting of more than 9,500,000 dispersion measurements of fundamental and higher mode (up to the 4th overtone) Rayleigh and Love waves with wave periods between T=35s and T=200s (Visser et al., GRL, 2007; van Heijst and Woodhouse, GJI, 1999; Ekström et al., JGR, 1997). We carry out inversions of this large data set for perturbations in the isotropic S-velocity structure and the anisotropic parameter ζ s=\frac{v2SH-v2SV}{2v2S} in the top 1000 km of the Earth's mantle. The models are parameterised using spherical harmonic basis functions up to degree 20 for the lateral variations and using 21 spline functions for the depth dependence. We carry out a large number of inversions using a variety of damping schemes and we choose the optimal model using the Akaike Bayesian Information Criterion (ABIC) together with a priori information. In a first step, we invert separately the Rayleigh and Love wave data sets for perturbations in the isotropic SV-velocity and SH-velocity structures, respectively. Our 3D isotropic models share the large scale features of previous global tomographic studies. Furthermore, these isotropic models fit well the various existing subsets of dispersion measurements we use, showing that they are quite compatible with each other. We then invert the complete data set of surface wave dispersion measurements for perturbations in purely isotropic S- velocity structure. The estimated model shows well known large scale anomalies and provides a reasonable fit to the data. In a second step, we address the distribution of radial anisotropy, using fully anisotropic sensitivity kernels. Overall, allowing for radial anisotropy improves the data fit by about 2% compared to a purely isotropic inversion. Nevertheless, for certain surface wave modes, the data fit is improved by more than 10% when allowing for radial anisotropy. We investigate what is the smallest significant amount of anisotropy required by the different subsets of data. Finally, we compare our prefered 3D anisotropic model with previous tomographic studies and discuss possible relationships between flow and anisotropy.
S32A-04
Towards Multi-mode Diffractional Tomography in Radially Anisotropic Media
We calculate the three-dimensional (3-D) sensitivities of low-order, multi-mode, surface-wave phase and amplitude measurements to the Earth's lateral heterogeneity in seismic velocity as well as radial anisotropy. The 3-D Born scattering sensitivity kernels are formulated for multi-mode measurements made between the data and mode-summed synthetic seismograms using a surface-wave mode-summation approach that fully accounts for interactions between simultaneous overtone arrivals. We derive sensitivity kernels for cross-spectral multi-taper measurements in radially anisotropic reference earth models. Our calculations of sensitivity kernels show that (1) in the presence of radial anisotropy, SH and SV waves are strongly coupled, and the sensitivities of Rayleigh waves to P wave velocities (PH and PV) become significant, when higher-mode surface-wave energy dominates in the measurement window; and (2) the windowing/tapering processes applied in making measurements have strong effects on the sensitivity kernels, especially for measurements made with short time windows. In general, multi-taper measurements are less sensitive to window selections compared to single-taper (e.g., cosine-taper or boxcar-taper) measurements. This multi-mode surface-wave approach opens the opportunity for imaging high-resolution structure of seismic velocity and radial anisotropy in the top 1000 km of the mantle.
S32A-05
Finite Frequency Upper Mantle Tomography Using the Spectral Element Method
In the past quarter century, global tomography based on ray theory and first-order perturbation methods has imaged long-wavelength velocity heterogeneities of the Earth's mantle. While these models have contributed significantly to our understanding of mantle circulation, the development of higher resolution images of the Earth's interior holds tremendous promise for understanding the nature of the observed heterogeneities. This endeavor confronts us with two challenges. First, it requires extracting a far greater amount of information from the available seismograms than is generally used. Second, the approximate techniques upon which global tomographers have traditionally relied become inadequate when dealing with short-wavelength heterogeneity. We have developed a novel hybrid approach to long-period waveform tomography in which forward-modeling is performed using the Coupled Spectral Element Method (CSEM: Capdeville et al., 2003), which can accurately model seismic wave propagation in a 3D earth with both short and long wavelength structure, while in the inversion step, the sensitivity kernels are calculated using an approximate, non-linear normal mode summation approach (NACT: Li and Romanowicz, 1995). Our dataset consists of complete 3-component time domain seismograms filtered at periods greater than 80 s for 100 earthquakes observed at well over 100 stations of the IRIS/GSN, GEOSCOPE, GEOFON and various regional broadband networks. Modeling is performed in an iterative fashion, and convergence is achieved as long as the sign of the sensitivity kernels is correct. A further advantage of this hybrid approach is that it allows us - for the first time in global tomography - to accurately account for the effects of crustal structure on the observed seismograms. We illustrate these effects and the consequences of common assumptions such as linear crustal corrections. We present a preliminary model of velocity and radial anisotropy variations in the upper 800 km of the mantle, and analyze the consequences of using an accurate 3D forward modeling technique.
S32A-06
Adjoint Tomography of Southern California
Our goal is to improve the present 3D shear and compressional velocity models of southern California. Our approach involves using adjoint methods to compute the gradient of the misfit function, which is a weighted sum of sensitivity kernels --- or Fréchet derivatives --- which represent the sensitivity of seismograms with respect to the model parameters. A tomographic inversion requires the specification of a misfit function, which we take to be frequency-dependent differences in traveltimes. We collect a set of E × R × C data seismograms, where E = 150 is the number of events, R = 200 is the number of broadband receivers, and C = 3 is the number of components, for a total of approximately 100,000 seismograms. We then compute a corresponding set of synthetic seismograms using a 3D spectral-element method (SEM) based upon a 3D southern California reference model. The differences between the data and synthetics are used in constructing a set of adjoint sources, which are placed at each of the receivers for a simulation of the adjoint wavefield. The interaction between the adjoint wavefield and the forward wavefield for each event forms an event kernel. The sum of the event kernels is the gradient of the misfit function, which illuminates the regions of the reference model that give rise to the discrepancy between data and synthetics. We apply an automated measurement algorithm that allows for a rapid, robust selection of time windows suitable for measurements between data and synthetics generated from a 3D reference model. The total number of measurements for a single event kernel is N = R × C × P, where P is the average number of time windows (per time series pair) selected for measurement by the automated procedure. All measurements are used simultaneously in constructing the combined adjoint source. The resultant event kernel requires two simulations, i.e., it is independent of N. We present several examples of event kernels for the 3D southern California velocity model using crustal phases. The event kernels are the building blocks for a gradient-based, iterative inversion to improve the velocity model while reducing the misfit function. We present preliminary results of our new tomographic model.
S32A-07
Seismic waveform tomography in the time-frequency domain with applications to the Australian upper mantle
We present a novel approach to full waveform tomography based on misfits in the time-frequency domain and adjoint methods. Our focus is on theoretical developments and synthetic inversions for heterogeneities in the Australian upper mantle. The centrepieces of our methodology are envelope and instantaneous phase misfits defined on time-frequency transforms of the seismograms. These misfits allow us to extract the maximum robust information from seismograms for the purpose of high-resolution tomography. We derive Fréchet kernels for different definitions of the envelope and phase misfits using adjoint methods. The Fréchet kernels for instantaneous phase measurements agree with those obtained from waveform cross- correlation only in the special - though unrealistic - case of monochromatic waves. Examples of Fréchet kernels for data collected during the SKIPPY project are computed by means of a recently developed spectral element method. With synthetic inversions we demonstrate that lateral heterogeneities can be determined efficiently by using instantaneous phase measurements of S waves and surface wave trains without explicitly dissecting the seismograms. Special attention is given to the following questions relating to the inversion, i.e., the misfit minimisation algorithm: 1) determination of the optimal step length for gradient methods, 2) acceptance/rejection criteria for the updated models and 3) the pre-conditioning of the steepest descent direction. Finally, we examine the possibility of using enevelope or amplitude measurements and their corresponding Fréchet kernels for seismic waveform tomography.
S32A-08
Anisotropy in Crust and Upper Mantle Beneath China Continent and its Adjacent Seas
Using the difference of S wave velocity structures derived respectively from Love and Rayleigh wave, the polarization anisotropy in crust and upper mantle beneath China continent and adjcent seas is studied. The result indicates that the distribution of anisotropy is spatially uneven. (a) The VSH>VSV anisotropy is dominant in the upper 150km, which indicates the horizontal stress in shallower lithosphere and the horizontal mass flow in upper asthenosphere are the leading factors in the formation of polarization anisotropy. In the land area the anisotropy intensity changes markedly with depth. The anisotropy in upper crust and upper mantle lid is widely much weak, while the anisotropy is intense in the rheological intense lower crust and ashenosphere, which indicates the lower crust may decouple in the lithosphere deformation. (b) VSH<VSV anisotropy is the main characteristic of the lower asthenosphere beneath 200km, which reflects the vertical movement of the mantle mass. (c) The overall picture in eastern China continent is: in stable blocks VSH>VSV anisotropy is more prominent in lithosphere and VSH<VSV anisotropy is weaker in asthenosphere, in tectonically active areas it is on the contrary. (d) In western China the anisotropy is apparently related to the subduction of India plate beneath Tibet. The conspicuous VSH>VSV anisotropy is the result of the collision and compression between India plate and Eurasian continents which makes the mantle material recrystalize orientationally.