S23B-1370
Finite-frequency sensitivity of seismic observables to mantle anisotropy based upon adjoint methods
We study the sensitivity of finite-frequency seismic waves to mantle anisotropy based upon kernels calculated by combining adjoint methods with spectral-element modeling of seismic wave propagation. We are mainly interested in surface-wave and SKS-splitting observables since these are the most popular data for studying mantle anisotropy. Anisotropy is described by the 21 elastic parameters naturally involved in asymptotic wave propagation in weakly anisotropic media. Our results illustrate the complexity of wave propagation in anisotropic models and emphasize the importance of full waveform modeling to accurately capture the sensitivity of finite- frequency data. The main characteristic of anisotropic sensitivity is a prominent path-dependence. For surface waves, significant effects due to mode coupling are also observed. They are a major feature for the higher modes. We investigate the sensitivity of SKS splitting through the 'splitting intensity', which characterizes the perturbation of the transverse signal. We show that this observable can efficiently be measured with a cross- correlation technique. SKS-splitting intensity 'senses' mantle anisotropy in a very different way than the surface waves. The sampling region of this observable is mainly confined to the upper mantle beneath the station, and it is sensitive to a much smaller number of elastic parameters.
S23B-1371
Resolving Three-Dimensional Anisotropic Structure with Shear-wave Splitting Tomography
Shear-wave splitting observations are a commonly used tool for inferring seismic anisotropy and deformation within the Earth's interior. We have developed a method for tomographically inverting shear-wave splitting observations for three-dimensional anisotropic structure, and we have tested it with synthetic splitting measurements from local events in subduction zone settings. The mantle is parameterized as a three- dimensional block model of crystallographic orientations with the elastic properties of olivine and orthopyroxene. To efficiently forward calculate splitting, the Christoffel equation is used to progressively split the horizontal components of a synthetic wavelet to account for the anisotropy in each model block, and predicted shear-wave splitting parameters are obtained with an eigenvalue minimization technique. Predictions from this approximate method, in general, compare well with splitting measurements from full waveform, pseudospectral synthetic seismograms. We solve for a best-fitting model of crystallographic orientations using a linearized, damped least- squares inversion that employs numerically calculated partial derivatives. To account for the non-linear behavior of shear-wave splitting, the inversion is applied iteratively and partial derivatives are recalculated after each iteration. We tested the capabilities and limitations of this method with inversions of synthetic data from target structures including lateral and vertical variations in anisotropy in both idealized and real (Nicaragua-Costa Rica) subduction zones. Convergence to accurate and stable solutions is found with widely varying starting models. However, in general the target structures are best retrieved using a starting model that is based on spatial averaging of predicted fast directions and splitting times. With a station spacing of 25 km in an idealized subduction zone containing uniformly spaced events down to 225 km and a slab dip of roughly 60¢ª, both the azimuth and dip of crystallographic axes are resolvable to a depth of 100-150 km, and lateral heterogeneities in anisotropy on a scale of 50 km at arc and fore-arc distances from the trench are easily retrieved. Spatial resolution of anisotropy at scales of 75 km is possible further into the back-arc above 150 km depth. The geometry of stations and observed seismicity in the Nicaragua-Costa Rica subduction zone yields partial resolution at scales of 50-75 km beneath the fore-arc, arc, and limited regions of the back-arc down to 100 km, and resolution at coarser scales is possible in wider regions beneath the back-arc. Given the distributions of seismic sources within many subduction zones and the advances in broadband seismic array deployments, this new method offers a powerful means with which to accurately constrain the orientation of anisotropic fabric in the mantle wedge. http://www.geo.brown.edu/geopeople/grads/abt/CR.htm
S23B-1372
Surface Wave Tomography for Geodynamically Relevant Anisotropic Models
Using seismic data to constrain not only the strength of anisotropy, but the orientation of the best-fitting symmetry axis is important for geodynamic understanding, as this can be ideally related to mantle convection flow patterns. Many recent surface wave models, though, only deal with anisotropy with a vertical axis of symmetry. On the other hand, anisotropic shear velocity models based on body wave measurements such as SKS splitting have traditionally assumed a horizontal axis of symmetry for the material properties, as a purely vertical axis produces negligible shear wave splitting. Recently, however, methods have been developed for using splitting measurements in tomographic inversions for more general symmetry axis orientations (e.g. Chevrot, 2006; Abt and Fischer, 2007). There have also been surface wave studies which model azimuthal dependence of Rayleigh wave velocity through linearized dependence on a horizontal fast axis (e.g Montagner and Tanimoto, 1991; Simons et al, 2002). As the frequency content of body wave splitting measurements and surface wave observations differ greatly, it is essential to have an appropriate finite frequency theory in order to include both in a consistent framework. We derive here nonlinear expressions for 3D finite-frequency surface wave sensitivity to arbitrarily oriented hexagonal symmetric media. We also discuss practical means of inverting for such a model, including combination with the compatible approach of shear wave splitting tomography proposed by Chevrot (2006).
S23B-1373
Using Finite-Frequency SH Wave Traveltimes and Amplitudes to Image Upper Mantle SH Velocity and Attenuation Structure in Western US
In recent mantle tomographic studies, finite-frequency body-wave sensitivity kernels have been used to improve the resolution and the recovery of perturbation amplitude of 3-D heterogeneities. We present a first inversion for SH traveltimes and amplitudes measured in multiple frequency bands. Our data set contains 54294 acceptable traveltimes and amplitudes respectively, measured in 5 frequency bands with center frequencies from 0.025 to 0.4 Hz. In the current data set, about 60% of the data are from US Array and US stations. Data consistency has been confirmed by similar traveltime (amplitude) patterns between close event pairs, and by the correlation between traveltime anomaly pattern and tectonic structures, both globally (in North America and Western Europe) and regionally (along the RISTRA array). The observed traveltime dispersion is on the order of 0.8s. The difference between relative amplitude anomalies (w.r.t. predicted amplitudes) in different frequency bands is on the order of 25%. The multiple-frequency-band data provide higher tomographic resolution because the sensitivity of banana-doughnut kernels is dependent on the frequency content of the waveform. The observed frequency-dependence of the data suggests that some of the heterogeneity is of a length scale comparable to the Fresnel zone. A preliminary inversion result using traveltimes alone shows clearly visible division between slow upper mantle in Western US and higher velocities in Central and Eastern US, though the fact that the data set is limited to teleseismic S waves prevents an accurate depth estimate for high-velocity root. Some details visible in the western US region with dense (US Array) station coverage will be discussed. We also expect to be able to present finite-frequency velocity and attenuation models of the upper mantle in Western US obtained from a simultaneous inversion of traveltime and amplitude data.
S23B-1374
Short-Period Normal-mode Synthetics and Fr{é}chet kernels for Spherically Symmetric Earth Models
Determination of three dimensional multiscale Earth structures requires high-quality seismic data and accurate synthetic waveforms. To extract and interpret the full waveform information from widely available broadband data, we need to be able to calculate complete broadband synthetic seismograms. Normal-mode theory provides the exact solutions to the wave equation in spherically symmetric Earth models, and the efficiency afforded by the usage of precalculated eigenfunction databases makes normal-mode summation the preferred approach for calculating long-period synthetic seismograms in 1-D reference models. In this study, we extend the normal-mode summation to short period by attacking the problems encountered in computing normal-mode eigenfrequencies and eigenfunctions at higher frequencies. Flexible radial sampling scheme based on the WKBJ approximation is adopted to ensure the accuracy of the secular equation when the radial eigenfunctions are highly oscillatory. This allows us to compute accurate normal-mode eigenfunctions up to much higher frequencies (~ 1Hz for Spheroidal and ~ 2Hz for Toroidal modes). Although errors can still be large for certain modes, they are almost all inner-core shear modes, and numerical experiments show that they have no contribution to seismograms on the surface. In contrast, omitting only 0.1% mantle modes at random can lead to noisy synthetics. The capability to compute normal modes up to high frequencies enables us to obtain accurate and complete synthetic seismograms that can be used to both extract waveform information from all seismic phases and to compute their full-wave Fr{é}chet kernels, which opens up possibilities in global and regional high-resolution tomography as well as studies on the seismic structure in the deep mantle and the inner core.
S23B-1375
A Finite-frequency Pdiff Kernel Library for Global Tomography Inversions
We compute finite-frequency Pdiff kernels for 1-D reference model AK135 based upon adjoint methods. Each kernel is generated by the interaction of two wave fields, the regular forward wave field and the `adjoint' wave field produced by using the time-reversed velocity at the receiver as a fictitious source, and both fields are computed numerically based upon the Spectral Element Methods (SEM). These sensitivity kernels show unique elliptical patterns on the CMB, and deviate significantly from the theoretical Pdiff ray path. Taking advantage of the fact that the finite-frequency sensitivity kernels depend only on the distance between the source and the receiver for a 1-D reference model, we compute finite-frequency Pdiff kernel libraries for events with depth between the surface and 700 km, and stations at epicentral distances between 100° and 160 \circ. We also investigate the effect of earthquake source radiation pattern on the sensitivity kernels. We use the finite-frequency Pdiff kernels for global Pdiff measurements in a travel-time tomographic inversion, and compare the tomographic images to ones generated using the theoretical Pdiff ray path. Preliminary results indicate that the models from the two theories are quite similar but the finite-frequency inversion leads to a more stable inversion and larger model amplitudes. Thus, by taking into account the finite-frequency effect of the Pdiff travel-time measurements, we believe we improve our ability to resolve the velocity structure of the earth mantle, in particular the structure near the CMB.
S23B-1376
Synthetic finite-frequency tomography: The optimum coordinate system for traveltime and amplitude observations
Recent advances in the finite-frequency seismic theory have provided more accurate representations of wave propagation. But how to harness the power of the new theories and fully extract the rich information about the earth from three-component broadband seismic records remain a challenge. In this study we carry out synthetic, 3D cross-well tomography using full waveforms simulated in elastic media with a staggered-grid finite-difference code. These controlled experiments allow us to compare the input and recovered structures and quantitatively assess the tomographic resolution in ways that cannot be done with a real data set for an earth structure. Our results show that the choice of the coordinate system in which travel times and amplitude anomalies are measured affects the Fréchet sensitivity kernels and results in significant differences in tomographic resolution. The radial, transverse, and vertical (RTZ) coordinate system has been widely used, because it reflects the intrinsic differences of P-SV and SH systems and therefore provides a direct way to separate the two wave fields. However, this and other fixed coordinate systems are not the optimum for resolving the structure in finite- frequency tomography. For example, in our 3D cross-well tomography experiments, the RTZ system may concentrate the energy of P waves on the radial direction and annihilate the energy on the transverse and vertical directions. In contrast, a variable and rotated coordinate system distribute the arrival evenly on the three components, making it possible to utilize the differences in the sensitivity kernels of the same arrival on the three components for tomography. Compared to a fixed RTZ system, the variable and rotated coordinate system yields much improved resolutions in our synthetic, 3D cross-well tomographic experiments.
S23B-1377
Frechet kernels for wave equation reflection tomography on curvilinear coordinates
We develop a method of wave equation reflection tomography where the misfit criteria are not based on the correlation of waveforms from specific phase arrivals, but on the annihilation of the observed wavefield. Optimization thus uses the redundancy in the data to minimize the difference between images produced at different slownesses. This method, which is a generalization of differential semblance optimization, admits for the formation of caustics. It is established in exploration seismology, and we seek to modify it for application to large scale geological surveys including passive data, e.g. from USArray. In doing so, irregular source and receiver placement and source depth must be taken into account. For higher computational efficiency in dealing with the large volumes of data, migration is carried out by large angle one-way wave propagators which can be based either on finite differencing or generalized screens. One shortcoming of one-way propagators is the requirement that waves must not be allowed to travel horizontally. In order to accommodate situations where turning waves occur, e.g. teleseismic studies or reflection off of tectonic features like lateral faults, we transform to curvilinear coordinates where the wavefront travels nowhere horizontally in the pseudodepth coordinate. By use of the adjoint state method, we develop finite frequency Frechet kernels on curvilinear coordinates which can be used with a variety of optimizations schemes.
S23B-1378
Application of the L-curve in geophysical inverse problems: methodologies for the extraction of the optimal parameter
Inverse problems in Applied Geophysics are usually ill-posed. One way to reduce such deficiency is through derivative matrices, which are a particular case of a more general family that receive the name regularization. The regularization by derivative matrices has an input parameter called regularization parameter, which choice is already a problem. It was suggested in the 1970's a heuristic approach later called L-curve, with the purpose to provide the optimum regularization parameter. The L-curve is a parametric curve, where each point is associated to a λ parameter. In the horizontal axis one represents the error between the observed data and the calculated one and in the vertical axis one represents the product between the regularization matrix and the estimated model. The ideal point is the L-curve knee, where there is a balance between the quantities represented in the Cartesian axes. The L-curve has been applied to a variety of inverse problems, also in Geophysics. However, the visualization of the knee is not always an easy task, in special when the L-curve does not the L shape. In this work three methodologies are employed for the search and obtainment of the optimal regularization parameter from the L curve. The first criterion is the utilization of Hansen's tool box which extracts λ automatically. The second criterion consists in to extract visually the optimal parameter. By third criterion one understands the construction of the first derivative of the L-curve, and the posterior automatic extraction of the inflexion point. The utilization of the L-curve with the three above criteria were applied and validated in traveltime tomography and 2-D gravity inversion. After many simulations with synthetic data, noise- free as well as data corrupted with noise, with the regularization orders 0, 1, and 2, we verified that the three criteria are valid and provide satisfactory results. The third criterion presented the best performance, specially in cases where the L-curve has an irregular shape.
S23B-1379
Multi-scale Finite-Frequency Travel-time Tomography Applied to Imaging 3-D Velocity Structure of the Upper Mantle Beneath the Southwest United States
Seismic tomographic imaging has played a key component to unravel the deep processes that caused the surface morphology and rift magmatism in the southwest United States. Several studies used teleseismic body- wave arrivals recorded by the La Ristra experiment, a dense broadband array of 950-km in length deployed during 1999-2001 and run through the Great Plains, the Rio Grande Rift, and the Colorado Plateau, to construct a 2-D tomographic image of the upper mantle structure beneath this linear array (e.g., Gao et al., 2004). However, because of the inevitable smoothing and damping imposed in the tomographic model, the resulting velocity contrast is too weak to explain distinct P and S waveform changes across the array (Song and Helmberger, 2007). In this study, we include all the data from the La Ristra and available nearby arrays and reexamine finite- frequency travel time delays measured by inter-station cross correlation of waveforms at both high- (0.3-2 Hz for P and 0.1-0.5 Hz for S) and low-frequencies (0.03-0.125 Hz for P and 0.03-0.1 Hz for S). Differing from the previous models that rely on classical ray theory and simple grid parameterization, our inversion considers more realistic 3-D sensitivity kernels for relative travel-time delays and a wavelet-based, multi-scale parameterization that enables to yield robust features with spatially-varying resolutions. Our preliminary P-wave model reveals a prominent low-velocity zone extending from near surface to the depth of 300 km beneath the Rio Grande Rift, while the upper mantle which underlies the Great Plains and the Colorado Plateau is seismically fast. We will demonstrate the difference and improvement of 3-D tomographic models through the use of finite-frequency kernels and multi-scale parameterization.
S23B-1380
Global tomography using finite-frequency kernels in the wavelet domain
Finite-frequency tomographic methods find their origin in the recognition that seismic waves are sensitive to the earth's structure not only on but also in a neighborhood of the ray connecting source and receiver. The sensitivity kernels are therefore nonzero within some positive distance from this ray. Real-life tomographic applications often need to employ a coarse model parameterization to reduce the number of model parameters and make the inversion practical from a computational point of view. This coarse parameterization, however, substantially reduces the benefit in resolution of finite-frequency tomography when compared to classical tomographic methods; standard coarse parameterization effectively turns the finite-frequency sensitivity kernels into 'fat' rays. To overcome this we are developing global-scale finite-frequency tomography in the wavelet domain, where the sparseness of both the sensitivity kernel and the model can be exploited in carrying out the inversion. We work on the cubed sphere to allow us to use wavelet transforms in Cartesian coordinates. This cubed sphere is built through a one-to-one mapping of Cartesian coordinates on each face of the cube to the corresponding "faces of the sphere". At the edges of each of the faces of the cube, the mapping is singular; this induces artifical singularities in the model and kernel, which in the wavelet domain would show up as large coefficients. We avoid these artificially large wavelet coefficients by using domain-adapted wavelets based on the construction of wavelets on the interval. The inversion is based on an l1-norm minimization procedure. We will present some preliminary examples.
S23B-1381
Plumbing the depths of Seattle's basins with noise correlation
Seismic hazard assessments depend heavily on near-surface S-wave velocity models. Local S-wave velocity models have traditionally been constructed from P-wave models using a deterministic relationship between P- wave and S-wave velocity, or by interpolating within widely spaced observations of geologic structure. Direct measurement of local S-wave velocities can be difficult due to a lack of local seismicity and because S-waves are not well excited by active source experiments. Shallow S-wave velocities are determined by near-surface geology, which in the Seattle area is a combination of crystalline rock, glacial till, young alluvium, and artificial fill. Because geology and therefore ground shaking can vary considerably within such an urban area, improving the accuracy and resolution of shallow S-wave models is the key to improving seismic hazard assessments and predictions for ground shaking. Short-period surface-wave noise cross-correlation tomography has the potential to improve S-wave velocity models in urban areas with dense arrays of short period and broadband instruments. We apply this technique to the Seattle area for the purposes of developing a new shallow S-wave model for the region for use in hazard assessment. By using data from the SHIPS array as well as permanent stations from the PNSN, we have inter- station distances as short as a few kilometers. This allows us to extract very short period surface waves, which are sensitive to shallow basin structure. Initial results show that both broadband and short-period stations can yield useable cross-correlations. The mean Rayleigh wave group velocity at a period of 5 seconds is ~2.1 km/s in the basins around Puget Sound, with most velocities falling between 1.6 and 2.6 km/s, in contrast to the 2.8 km/s average velocity measured in central and eastern Washington.
S23B-1382
Global Travel Time Tomography and Earthquake Relocation With a 3-D Reference Model
Aim of this study is to obtain a high-resolution tomography model of the Earth's mantle. This new model helps to get a better understanding of the tectonic and geodynamic evolution of the Earth and can be used to improve travel time prediction and earthquake location. Improvements of our 3-D tomography model compared to previous models are achieved by incorporating new data from stations in Europe and North America in an existing global travel time data set. Furthermore, we advanced the tomographic method to use a 3-D reference model instead of a standard 1-D Earth reference model. The 3-D reference model is based on a combination of tomography models that use travel times and models that use independent observations from surface waves, normal modes and long period body waves. Compared to previous models using a similar method, more detail is seen in the resulting tomography model in the upper 400 km of the mantle due to the new data and additional core phases help to constrain anomalies in the lowermost mantle. The resulting model combines the long wavelength structure as "seen" by long period seismic information contained in the 3-D reference model with the detailed mantle structure obtained from short period data during inversion. Tests with well located events show that the new tomography model predicts, particularly at regional distances, arrival times better than a 1-D velocity model and that the epicenter location errors are reduced. As a final step, the new tomography model has been used to relocate a global earthquake data set with respect to that model. Thereby, earthquake locations are corrected for 3-D Earth structure not taken into account by the original location process using a standard 1-D Earth reference model. In addition a better focusing of earthquakes in narrower clusters is achieved due to the new tomography model, in particular, in the deeper parts of subducted slabs (> 150 km).
S23B-1383
Three-dimensional Surface-wave Group-velocity Tomography of the Southern Korean Peninsula Using Ambient Seismic Noise Cross-correlation
The uppermost crustal velocity structure of the southern Korean peninsula is investigated based on surface-wave group-velocity using the cross-correlation technique of ambient seismic noise. We use seismograms from 91 accelerograph stations in the southern Korean peninsula recorded during August of 2005. From the correlation results of 4095 data pairs, arrival times of Green's functions between pair of stations are measured in discrete bins of frequency band with overlap. The arrival times for each bin of frequency band are inverted in order to obtain two-dimensional tomographic map of Rayleigh wave group-velocity. Then we obtain dispersion curves by extracting group-velocities at each center frequency of the bins for each tomographic cell. Shear-wave velocity to depth inversion of the dispersion curve at each cell produces one-dimensional velocity profile. After aligning each profile at each tomographic cell, we can obtain a three-dimensional uppermost crustal velocity model above about 5 km depth with high resolution in the southern Korean peninsula.
S23B-1384
Finite-Frequency Tomography Using Ambient Seismic Noise in the Presence of Surface Topography
The use of ambient seismic noise to determine the crustal and upper mantle structure has become an established practice in seismology. Compared to the traditional methods that utilize surface waves from earthquakes, it has several advantages, particularly in extending usable waves to short periods and providing detailed constraints at shallow depths. In this study, we calculate the 3D sensitivity kernels for the Green's function derived from the cross-correlation of ambient noise at pairs of stations. Furthermore we assess the effects of surface topography on the sensitivity kernels and their importance in the use of short-period waves. We have developed an implementation of a force source on the surface in a finite-difference method, which has been validated through both the reciprocity theory and a comparison with results from a semi-analytical method. The phase-delay sensitivity kernels for the impulse response between the two vertical components of a pair of station to S-velocity perturbations, for example, are similar to those of Rayleigh waves from earthquakes, as expected. We note that the kernels reach a local minimum value at about one eighteenth wavelength depth below the free surface and have larger values on the free surface. This near surface effect should be taken into account in the seismic wave simulation and we solve this problem by using a non-uniform-grid finite-difference method. To assess the effects of surface topography, we use a boundary-conforming grid in a non-staggered finite-difference method. Surface topography has a strong effect on the distribution of the phase and amplitude sensitivity kernels, particularly for short-period waves. Thus in places with large surface topography, the topographic effects must be taken into account in the use of short-period ambient noise. We will apply these kernels to real data and discuss the resolution and implication of the new method for the crustal and upper mantle structure.
S23B-1385
Applications of a Multivalued Travel Time Solver in two and three Dimensions
In complex media, seismic energy can travel along more than one path between two points. This means that at a given receiver, one might observe a wavetrain containing several different arrivals. Later arrivals provide additional structural information when compared with first arrivals, as they have taken different paths through the medium. The wavefront construction principle is used as the basis of a new scheme for the computation of multivalued travel times that arise from smooth variations in both velocity structure and interface geometry. In two dimensions, the idea is to represent the wavefront as a set of points, and use local ray tracing and interpolation to advance the wavefront in a series of time steps. Performing the wavefront tracking in reduced phase space significantly enhances the methods capability to resolve complex features such as swallowtails. Later arrivals can be used to improve the quality of images obtained by seismic tomography, as they sample different parts of the model compared to the first arrivals traditionally used in tomography. The wavefront tracking scheme proposed here is not limited to local or regional scale problems; it can be used to compute global phases and associated later arrivals generated by lateral velocity or interface anomalies. Another application is to combine the scheme with the Gaussian beam method and calculate the response of a structure beneath a receiver to an incoming plane wave. This could potentially be used in receiver function analysis and would have the advantage that later arrivals arising from lateral heterogeneity could also be modelled. In three dimensions, the wavefront becomes a surface and can be described using a mosaic of triangles. Evolving a complex surface with a given accuracy is a well known problem in the field of computer graphics. Schemes developed in this field for surface refinement and simplification are applied here to a propagating wavefront in order to maintain a fixed density of nodes. This forms the basis of the method, proposed in this work, for tracking wavefronts in the presence of complex three dimensional velocity models. Application of the new scheme to structures containing strong velocity contrasts, including the SEG/EAGE salt dome model, demonstrate it to be robust and efficient for practical application.
S23B-1386
A New Technique for Assessing Velocity Uncertainty in Seismic Refraction Tomography
Travel-time sensitivity testing uses perturbation of the travel-time data to assess the uncertainty in velocities due to error in the data. Current implementations of this technique provide a qualitative assessment of the reliability of velocities in different regions of the model, but do not provide reasonable values to quantitatively assess the velocity uncertainty. Standard techniques assume independence in the travel-time error (i.e., a Gaussian distribution). For this study, we have developed a technique utilizing the properties of a Cauchy distribution, which considers the more likely case of error dependence in first arrival travel-time picks. Our results show that by assuming independence (Gaussian distribution) in the travel-time errors, the RMS differences (i.e., the velocity uncertainty) in our model are, in general, unrealistically small. This suggests that either our model is not sensitive to travel-time errors less than 150 ms or that our assumption of error independence is not appropriate for travel-time errors. By using a Cauchy or "weighted-tail" distribution to generate random travel-time perturbations, we are able to simulate error dependence in our travel-time picks. This allows us to consider the sensitivity in our model to the "worst-case" error in travel-time picking. By considering a 95% confidence interval for the Cauchy distribution, we were able to develop a new "geophysically meaningful" velocity uncertainty model. Using a 95% confidence interval maintains the basic "worst-case" characteristic, while removing the upper 5%, of the Cauchy distribution. This would essentially correspond to not accounting for the "worst" or most uncertain 5% of your travel-time picks. Given that arrivals with the lowest signal-to-noise ratios are generally ignored or not "picked", we can assume that the remaining picks lie within the 95% confidence level of error. When we consider this more realistic, dependent, distribution of error in the travel-time picks, we are able to show a strong correlation between ray coverage and velocity error. In turn, this method provides a valuable new tool for directly assessing the uncertainties in tomographic velocity model.
S23B-1387
Integration of deformable layer tomography and shot gather modeling for pre-stack velocity and Q analysis
Deformable layer tomography is a new layer based tomography method which can be used to integrate forward modeling and inverse approaches of pre-stack analyses of seismic velocity and Q. Traditionally forward modeling generates zero offset synthetic seismic traces based on logging data because such data provide the 1D profiles of reflector depth and rock property. In our work, forward modeling method was integrated with tomographic approach to generate pre-stack synthetic seismic wavelets along certain reflectors. Since the deformable layer tomography is based on layers instead of grids, it can provide 2D geometric information of each reflector and rock property across the reflector to facilitate a comparison with pre-stack seismic traces. We integrate the shot gather modeling with deformable layer tomography at two stages, the pre-inversion stage and post-inversion stage. The pre-inversion stage is to get initial velocity and Q depth models from shot gather modeling based on priori velocity and geology information. This procedure is interactive ¡§C one can select specific layer and then edit the nodes around the layer and rock property inside the layer through graphic user interface to achieve an approximated fit between the observed seismic traces and modeling result. The post- inversion stage is to edit the inverted velocity and Q model based on the difference between the observed seismic traces and the synthetic traces from the inverted depth model. This integration method has been applied to both synthetic and field tests. Those tests show that forward modeling can provide better initial model for the tomography algorithm to stabilize the inversion and shorten the convergent time. In addition, the inverted model can be further edited to get better match between the observed pre-stack seismic traces and the synthetic traces.
S23B-1388
Development of a State-Wide 3-D Seismic Tomography Velocity Model for California
We report on progress towards the development of a state-wide tomographic model of the P-wave velocity for the crust and uppermost mantle of California. The dataset combines first arrival times from earthquakes and quarry blasts recorded on regional network stations and travel times of first arrivals from explosions and airguns recorded on profile receivers and network stations. The principal active-source datasets are Geysers-San Pablo Bay, Imperial Valley, Livermore, W. Mojave, Gilroy-Coyote Lake, Shasta region, Great Valley, Morro Bay, Mono Craters-Long Valley, PACE, S. Sierras, LARSE 1 and 2, Loma Prieta, BASIX, San Francisco Peninsula and Parkfield. Our beta-version model is coarse (uniform 30 km horizontal and variable vertical gridding) but is able to image the principal features in previous separate regional models for northern and southern California, such as the high-velocity subducting Gorda Plate, upper to middle crustal velocity highs beneath the Sierra Nevada and much of the Coast Ranges, the deep low-velocity basins of the Great Valley, Ventura, and Los Angeles, and a high- velocity body in the lower crust underlying the Great Valley. The new state-wide model has improved areal coverage compared to the previous models, and extends to greater depth due to the data at large epicentral distances. We plan a series of steps to improve the model. We are enlarging and calibrating the active-source dataset as we obtain additional picks from investigators and perform quality control analyses on the existing and new picks. We will also be adding data from more quarry blasts, mainly in northern California, following an identification and calibration procedure similar to Lin et al. (2006). Composite event construction (Lin et al., in press) will be carried out for northern California for use in conventional tomography. A major contribution of the state-wide model is the identification of earthquakes yielding arrival times at both the Northern California Seismic Network and the Southern California Seismic Network. These events are critical to the determination of the seismic velocity model in central California, in the former `no-mans-land' between the Northern and Southern California networks. Ultimately, a combination of active-source datasets, composite events, original catalog picks, and differential times from both waveform cross-correlation and catalog picks will be used in a double-difference tomography inversion.
S23B-1389
3-D Local Tomography for the Shallow Crustal Structure of the Gyeongsang Basin in the Southeastern Korean Peninsula
The seismic activities around the Korean Peninsula is much lower than other active areas such as Japanese Islands and the digital seismic stations in South Korea have been operated only for a relatively short period of less than 12 years. Due to limited availability of seismic data, it has been difficult to construct a 3-D tomography around the Korean Peninsula several years ago. We applied 3-D tomographic inversion in this paper to determine the velocity structure at the Gyeongsang Basin in the southeastern part of Korean Peninsula with 3,034 P-wave arrivals from 534 events selected from KIGAM(Korea Institute of Geoscience and Mineral Resources) earthquake catalogs. The initial velocity model is generated by combining KIGAM 1-D model and IASPEI91 model. Using SIMULPS, 3-D velocity inversion and epicenter relocation are carried out simultaneously. The results of the P-wave velocity distribution show that low velocity zones correspond to the location of cretaceous sedimentary layer at the shallow part of Gyeongsang Basin. The distribution of high velocity zones agrees well with locations where cretaceous granitoid basement rocks intrude and outcrop.
S23B-1390
Multi-scale Tomography Of The Pacific Upper Mantle Using Surface Waveform Data
Owing to the abundant circum-Pacific earthquakes and seismic stations, the coverage density of trans-Pacific minor-arc surface waves is highest among the globe, making the region an excellent candidate for the high resolution surface waves tomography. We invert long period waveform of Rayleigh waves in the time domain in the framework of normal-mode-based asymptotic coupling theory [Li and Romanowicz, 1995] for the upper mantle structure underneath the Pacific. In particular, we propose a two-step lateral model parameterization approach, by which both the accuracy in the forward computation and the flexibility in the inversion stage are achieved. In the first step, the initial model is parameterized in terms of spherical harmonics. Spherical harmonics can be simplified to cosine and sine functions in the great circle path connecting the source and receiver, allowing an efficient and accurate analytical solution for the path integral and therefore forward synthetics. In the second step, partial derivative matrices w.r.t. spherical harmonics are mapped onto nodes of the spherical triangle meshes within the selected region. Taking advantage of the orthogonality of spherical harmonics, the above conversion is straightforward. After the mapping, only about 10-15% of nodes receive effective sensitivities. As a result, the computation cost in the stage of inversion is significantly reduced. With the new matrices, we may utilize either the grid-based fixed-scale or the wavelet-based multi-scale inversion technique [eg. Chiao and Liang, 2003] for the regional tomography. The new approach allows us to obtain partial derivative matrices from three different model bases for the same data set, and only one forward computation is required. We present the tomographic results, compare models derived from different model parameterizations, and discuss how the tomographic features are influenced by model parameterizations.
S23B-1391
Seismic Tomography of western North America
We use teleseismic body wave travel time tomography to image the western United States using an unprecedented number of seismometers that have been deployed across the region as part of Earthscope. The resulting high-resolution images of the interior of the earth in this tectonically active zone provide new insight into the structure and interaction between known geologic objects. For example we image the subducted Juan de Fuca plate extending beneath North American. While it reaches more than 500 km beneath Washington there is a hole in the slab at 400 km depth beneath Oregon. The hole could be explained by the arrival of the Yellowstone plume head around 17Ma. The Yellowstone plume today is imaged as a shallow feature extending to around 500 km depth. Beneath California the high velocity Pacific Plate is abuts against the low velocity North America plate along the San Andreas Fault.
S23B-1392
Inversion of body-wave waveform data for elastic and anelastic transition-zone structure in and around Japan
Inversion of body-wave waveform data for elastic and anelastic transition-zone structure in and around Japan Nobuaki Fuji, Kenji Kawai and Robert J. Geller We have developed new methods to invert seismic waveform data for localized seismic structure. We use these methods to invert for the fine structure of the mantle transition zone in and around Japan using broadband data from regional arrays. Our methods use tools we have developed for performing 'static corrections' for the complex crustal structure in and around Japan. We conduct static correction by making a time shift which gives the best correlation coefficient for the first arrival S phase. We also have used other methods for time shifting such as onset pick time shift, but we found that the results of the inversion do not greatly differ. In order to stabilize the inversion we use automated data selection criteria, which limit the amplitude ratio of the synthetic seismogram to the observed seismogram to be between 0.3 and 3.0, and require a value above 0.5 for the correlation coefficient. The amplitude ratios (synthetic/observed) are systematically large for the initial (PREM) anelasticity model, so we invert simultaneously for both Q and elastic structure. We invert the transverse components of long-period (20-200 s) body-wave data from the NIED F-net array. The target regions lie beneath Hokkaido and the Philippines Sea at depths between 200 km and 700 km. The dataset used in this study consists mainly of triplication S phases that sample the mantle transition zone. It is difficult to analyze such data using previous methods, but our methods can handle such data. Models from studies of this type should contribute to improving our knowledge of the thermal state and proportion of water present in the upper mantle.
S23B-1393
Seismic Tomography Of The Caucasus Region
The Caucasus is one of the most active segments of the Alpine-Himalayan collision belt. We used the catalog data of Georgian Seismic Network to calculate the reference 1-D and 3-D P-velocity model of the Caucasus region. The analog recording period in Georgia was quite long and 17,000 events reported in the catalog between 1956 and 1990. We carefully eliminated some arrivals due to ambiguities for analog type data picking and station time corrections. We choose arrivals with comparably low residuals between observed and calculated travel times (<1 sec). We also limited our data to minimum 10 P-arrivals and maximum azimuthal gap of 180 degrees. Finally,475 events were selected with magnitude greater than 1.5 recorded by 84 stations. We obtained good resolution down to 70 km. First, we used 1-D coupled inversion algorithm (VELEST) to calculate the velocity model and the relocations. The same model convergence is observed for the mid and lower crust. The upper layer (0-10km) is observed to be sensitive to the starting model. We used vertical seismic prospecting data from boreholes in Georgia to fix upper layer velocities. We relocated all events in the region using the new reference 1- D velocity model. The 3-D coupled inversion algorithm (SIMULPS14) was applied using the 1-D reference model as a starting model. We observed very large amount of shift at horizontal directions (up to 50 km). We observed clustered events where they are well correlated with query blasts from Tkibuli mining area. We applied the resolution test to estimate the spatial resolution of the tomographic images. The results of the test indicate that the initial model is well reconstructed for all depth slices, though it is badly reconstructed for the shallowest layer (with depth = 5km). The Moho geometry beneath Caucasus has been determined reliably by the previous geophysical studies. It has a relatively large depth variation in this region from 28 to 61 km depth, according to those studies and our tomography result for the uppermost mantle (50 km) reflects this depth variation of the Moho discontinuity.
S23B-1394
Imaging lateral heterogeneity in the northern Apennines from time reversal of reflected surface waves
Seismic surface waves are partially reflected when their phase velocity changes abruptly, which makes reflected surface waves a natural choice to study lateral heterogeneity in the lithosphere. We investigate surface wave reflections at the northern Apennines (Italy), which can be observed as characteristic late wave packages in the intermediate-period coda in near-regional seismograms in the wider Alpine area, a few 100 km north of the Apennines. Forward modelling of the timing and amplitudes of late arrivals suggests that they can be attributed to the combined effects of a Moho discontinuity and different crustal velocities across the mountain chain. Here, we image the northern Apennines' reflector by time reversal of the surface wave coda. We make use of the concept of adjoints, and compute three-dimensional sensitivity kernels numerically by the time correlation between the simulation of the original forward wavefield and the simulation of the corresponding back-propagating adjoint wavefield. Wave propagation is simulated with the spectral element method, and a three-dimensional regional earth model is involved. The sources for the adjoint wavefield are the time-reversed displacement waveforms of the three-component intermediate-period coda applied at the receiver locations, representing the misfit compared to an earth where reflection did not occur. From this set-up, we expect that our sensitivity kernels illuminate lateral heterogeneity. We compute event kernels for five moderate earthquakes in the Southern Alps and up to ten receiver locations. We obtain clear images of the reflectivity associated with the Northern Apennines especially in kernels for density and S-wave speed, consistent with the fact that reflected Love waves represent the most prominent coda arrivals. The kernels show that surface wave reflections originate from the axial zone of the mountain chain. Apart from the Apennines, sensitivity is low, and no other comparable source of coherent surface wave reflections becomes evident.
S23B-1395
Resolving Small Objects Using Seismic Traveltime Tomography
It is often claimed that the first Fresnel zone associated with the dominant frequency represents the spatial resolution limit of traveltime tomography. To test this assertion, synthetic seismic data were generated for traveltime picking and inversion for a single, small velocity anomaly embedded in a homogeneous background velocity. A variety of traveltime picking techniques were tested and compared for their ability to detect the presence of objects smaller than a Fresnel zone. All picking methods produced accurate ray-theoretical (infinite- frequency) picks from noise-free seismic data for objects much smaller than the dominant-frequency Fresnel zone. All methods successfully detected the presence of objects smaller than a wavelength. Picking methods that focus on features along the onset of the first arrival were the most accurate, while cross-correlation with a known wavelet preformed the worst. The inversion of these traveltime picks always recovered the position and shape of the object. The relevant Fresnel zone limit for tomographic resolution is the maximum, not the dominant frequency in the data. For physically realizable causal signals, the maximum frequency is infinite. In practice, noise, instrument response, and sampling can lower the effective maximum frequency. Random noise at a range of signal-to-noise ratios was added to data for a small object. Pick times with different noise realizations are statistically centered on the noise-free pick, not the time that would be recorded in the absence of the object. Trace stacking prior to picking or the averaging of many picks improves the signal-to-noise ratio and can extract signal that is not detected on an individual pick. An averaging of traveltime picks also occurs during tomographic inversion. This inherent signal-to-noise improvement allows tomography to image objects that are undetectable in individual trace picks. Resolution is further improved by dense ray coverage. The resolution of tomography is limited not by the Fresnel zone associated with the dominant frequency, but by the accuracy of the traveltime picks.
S23B-1396
Simultaneous Imaging of Q Structure and Velocity Structure by Full Waveform Inversion
Seismic inversion is a multiparameter problem: the observed waveforms contain information not only on velocity structure, but also on various other parameters, including attenuation and density (and the possibility of anisotropy). Among these parameters, the attenuation (or its inverse, the seismic Q value) is strongly related to useful geological variables such as rheology, fluid flow, pore fluid content and fractures. In this work, we investigate methodologies for obtaining velocity and attenuation images simultaneously. In contrast to ray-based inversions of first arrival times and/or amplitudes, Full Waveform Inversion incorporates scattered, refracted and reflected waves, and consequently improves image resolution and accuracy. In frequency domain implementations, instead of inverting Q values directly, complex valued velocities are estimated using steepest descent algorithms. The real and imaginary parts of the velocity fields, (vr, vi), have differing sensitivities, making the simultaneous inversion of (vr, vi) with steepest descent methods difficult. Although Newton methods may enable a true simultaneous inversion, these are computationally expensive, and the instability of the Hessian matrix remains problematic. A possible solution to the simultaneous inverse problem is the subspace method (a Newton method in a chosen subspace), in which we search for an optimal update direction in a 2D subspace spanned by each of the two model type steepest descent vectors: P-wave velocity and Q values. The proposed 2D subspace method requires only one additional forward modelling over the steepest descent method, and inverting the 2 × 2 projected Hessian is trivial. The off-diagonal terms of the projected Hessian matrix indicate the coupling of data sensitivities to the two model parameter types. In this study, we implemented the subspace method into frequency-domain full waveform inversion, and compared the results to the standard steepest descent method. Because the model parameterization may influence robustness and resolution of the inversion procedure, we also examined several model parameterizations, including (vr, vi), (vr, Q), and their respective inverses.