DI11A-01 INVITED
The Effect of Thin Structural Layers on Seismic Observations with Applications in Seismic Tomography
There is a strong motivation in long period seismology to understand and to account for the effects of perturbations by non-small amounts over thin structural layers, an important example being the effect of crustal structure on normal mode splitting and coupling, on surface wave dispersion and on long-period travel times. The same issue is important in the calculation of seismic wave fields using full numerical codes, e.g. the spectral element technique, in which it is essential to faithfully account for the effects of the crust, while it may be impractical, or too computationally costly, to incorporate a detailed crustal model. Another problem of the same class, for which the relevant formulae are known, is that of a spherical or an aspherical perturbation in the location of internal boundaries, as this can be thought of as the perturbation of the structure by a non-infinitesimal amount over an infinitesimally thin zone. This contribution will discuss the theory relevant to these problems. A striking result for spherical perturbations is that while the seismic observables are not Fréchet-differentiable functionals of the conventional seismic parameters, they are Frechet- differentiable functionals of the so-called Backus parameters. The presentation will explore the applicability of the theory in a number of areas, including surface wave dispersion, normal mode splitting and coupling and the effects on long-period travel times.
DI11A-02
Improving constraints on Earth's long period internal structure using normal mode measurements for recent large earthquakes
The splitting of Earth's free oscillation spectra places important constraints on compressional and shear wave velocity, and potentially, the density structure of the Earth's mantle. Splitting functions are measured from normal mode spectra and used in tomographic modeling, often in combination with shorter period data. Despite these efforts, many fundamental questions regarding the Earth's long period structure remain unanswered. Several large events have occurred since the most recent compilation of normal mode splitting functions, giving us the opportunity to significantly increase the data set. Our new data set contains modal spectra up to 3 mHz for all Mw > 7.7 events from the last 30 years (1978-2008). It includes the the 23 June 2001 Peru event (Mw=8.4), the Sumatra events of 2004 (Mw=9.0) and 2005 (Mw=8.6) and the 2008 Wenchuan, China event (Mw=7.9). The new events provide significant increase of data coverage in previously unsampled regions. In the first instance, we use the data to make robust measurements of splitting functions for some of the longest period normal modes, including 0S2, 0S3 and 1S2. The new data set also allows us to include spectra directly in a full-coupling approach in the development of our tomographic mantle model S40RTS. Combining normal mode with body wave and surface wave data, we hope to address questions regarding the Earth's thermal and compositional heterogeneity.
DI11A-03
Full waveform inversion for upper-mantle structure in the Australasian region
We present the first results from a full seismic waveform inversion for upper-mantle structure in the Australasian region. The tomographic images are based on high-quality data collected over the past 15 years at several temporary arrays and permanent stations. Fundamental- and higher-mode surface waves as well as S body waves and multiple reflections are used. The centrepieces of our methodology are envelope and phase misfits computed from time-frequency transforms of the seismograms. Both misfit measures are applicable to all types of elastic waves and in particular to interfering wave trains. They allow us to extract a large amount of robust information that is quasi-linearly related to Earth structure. These characteristics make the envelope and phase misfits well- suited for high-resolution tomography. We derive Fréchet kernels for the envelope and phase misfits using the adjoint method in conjunction with a recently developed and highly efficient spectral-element code that operates in a spherical section. The tomographic problem itself is solved by iteratively minimising the phase and - to a lesser extent - the envelope misfit. In the course of the iteration we decrease the dominant period from 100 s to 50 s. We reach acceptable results after 10 to 15 iterations. In the upper 100 km of our current tomographic model we observe S wave speed variations of ± 10% that reduce to ± 3.5 % at 600 km depth where the resolution starts to become poor. The principal tectonic features of the Australasian region are clearly visible, but also small-scale variations within them can be distinguished.
DI11A-04
Global Upper Mantle Radially Anisotropic Model Developed Using the Spectral Element Method
Improving the resolution of global upper mantle tomographic models of shear wavespeed and anisotropy is crucial for understanding the nature and morphology of upper mantle heterogeneities. Traditional methods of global tomography that rely on infinite-frequency and first-order perturbation theory become increasingly inadequate as shorter-wavelength heterogeneities are investigated. The spectral element method, on the other hand, permits accurate calculation of wave propagation through highly heterogeneous structures, and is computationally economical when coupled with a normal mode solution and applied to a restricted region of the earth such as the upper mantle (cSEM: Capdeville et al., 2003). Importantly, cSEM allows a dramatic improvement in accounting for the effects of crustal structure. We have implemented a new method for global tomography, which uses cSEM for forward modeling in conjunction with approximate 2D finite frequency kernels for the inversion step, calculated using non-linear asymptotic coupling theory (NACT: Li and Romanowicz, 1995). In order to avoid biasing our results toward existing 3D upper mantle models, we start our iterative inversion procedure with a 1D model. We verify that the use of approximate kernels does not prevent our iterative procedure from converging. With each iteration, we include additional waveforms that would be rejected based on a comparison with the 1D starting model. We obtain the first global model of upper mantle velocity and radial anisotropy developed by applying the SEM to modeling 3-component long- period (corner frequency : 80s) fundamental- and higher-mode waveforms. Our model confirms the large- scale features observed by previous researchers. In particular, we retrieve the relatively shallow, seismically slow velocities beneath volcanic arcs and mid-ocean ridges, the deeper fast roots underlying cratons, slow velocities in the central Pacific below 250km depth, and enhanced fast velocities anomalies consistent with slab locations in the transition zone. We discuss notable features of the model, comparing and contrasting them with models developed using less accurate techniques.
DI11A-05
Toward Recovery of the Earth's High Frequency Elastic Wave Green's Function
Over the past 25 years, great strides have been taken in our understanding of large-scale Earth structure. Much of this understanding has arisen through analysis of either primary-phase traveltimes (i.e. seismic tomography), or scattering of long-period body waves (e.g. mapping of transition zone discontinuities), for which the source signature is particularly simple. Both of these approaches are limited in their resolving capability. For example, they are unable to detect subducting oceanic crust and hence its fate upon descent into the mantle, an issue of key importance in reconciling apparently discrepant observations from seismology and geochemistry concerning mantle circulation. To resolve such fine-scale structure requires the ability to isolate higher frequency, scattered waves from a source signature the complexity of which increases with frequency. Although one well established technique, receiver function analysis, permits approximation of the S-component of the Earth's Green's function at early times, a comprehensive approach affording a more complete reconstruction at high frequencies is desirable. We have examined the multichannel blind deconvolution problem to this end. There are several ways of posing this problem so as to recover or remove a (e.g. source) signal that is common to 2 or more traces. One set of constraints stems from the recovery of a signal from its phase alone, whereas another set can be derived from the commutativity of the convolution operation. Both sets of constraints can be written as linear systems in involving the unknown Green's functions. Since the number of unknowns can approach or exceed 104, it is useful to cast these relations in terms of discrete fourier transforms thereby enabling the use of fast, iterative inversion methods. The systems are ill-posed and we are investigating the effects of different styles of regularization upon fidelity of the recovered response.
DI11A-06
A Global Lithosphere Asthenosphere Boundary
We use scattered waves recorded at permanent seismic stations from 1990-2004 to map a global interface that may be associated with the lithosphere-asthenosphere boundary. We consider stacked P-to-S (Ps) data at stations where crustal structure is relatively simple, the Moho is well-defined, and the data distribution enables easy identification of crustal phases in nine epicentral distance bins at frequencies up to 2 Hz. These restrictions allow us to identify crustal phases and search for conversions that could be associated with the lithosphere-asthenosphere boundary. Data from stations that fit these criteria suggest the presence of sharp negative discontinuities (velocity decreases with depth) in the depth range of 40 to 140 km. S-to-P results also generally confirm the presence of these discontinuities. So far, we see no consistent feature at these depths in back-azimuthally binned SH-component data from corresponding stations, indicating that anisotropy is not the dominant mechanism causing these apparent velocity changes. The persistence of this feature in single-station SV-component data suggests a global discontinuity. Indeed, globally the depth to the boundary correlates with tectonic environment varying from an average of 110 km beneath cratons, thinning to ~80 km at continental margins and to ~50 km at some oceanic island stations. Beneath noncratonic regions the boundary depth is in general agreement with the sharpest part of the velocity gradient in global velocity models. Beneath cratons the boundary is significantly shallower than the base of the seismically fast keels in global surface-wave models. One explanation is that beneath cratons a compositional boundary in depletion and/or hydration exists at shallow depths (80 to 140 km), while a thermally cold root extends to greater depths. The high frequencies inherent to the Ps converted phases image the potentially sharp shallow compositional boundary, but longer-period surface waves image a deeper, thermally-defined craton. In this model, the compositional and thermal boundaries would be coincident beneath noncratonic areas. Alternative explanations are that the discontinuities illuminated by this study beneath continents represent fossil slabs that were originally stacked during the formation of the continents, or the lids of thin melt reservoirs.
DI11A-07
The Earth's outer core: reconciling geodynamics, travel-time modeling, and normal-mode eigenfrequency splitting.
The splitting of the eigenfrequencies of normal modes or free oscillations of the Earth can be explained for the most part by three-dimensional structure of the mantle and anisotropy in the inner core. However, the residual signal has some coherence, especially at spherical harmonic degree 2 and order 2, and some modes sensitive to the outer core are poorly fit. Already in the 1980s, this observation stirred a certain controversy about the possibility of three-dimensional structure in the fluid outer core. In later studies, further support for seismic structure in the outer core came from global measurements of compressional waves: under the assumption of a spherically symmetric outer core, travel times of waves reflected by the core- mantle boundary, and of those that travel through the CMB and the core, provide contrasting images of CMB topography; but this discrepancy disappears if one introduces outer-core heterogeneity. Several authors have explored different mechanisms to explain this unexpected observation; it was soon pointed out that lateral seismic structure within the core cannot be ascribed to density anomalies involved in convective motions: the size of such anomalies must be well below the seismic detection level, otherwise the amplitude of thermal winds in the core would be much larger than it is compatible with the observed secular variation of the magnetic field. On the other hand, outer-core seismic structure can reflect the geometry of surfaces of constant gravitational potential that define its hydrostatic equilibrium: aspherical density anomalies in the mantle, and those caused by topography at the CMB, impose a steady gravitational forcing on the core, resulting in the asphericity of outer core's equipotential surfaces; and to seismic waves, perturbations in the shape of isosurfaces are equivalent to velocity heterogeneities. We present a stable 3D tomographic model of compressional velocity in the Earth's outer core, whose properties can be explained, at least partly, in terms of gravitational forcing from the mantle. We calculate the normal-mode eigenfrequency splitting predicted on the basis of the 3D outer core model, and evaluate how it fits the corresponding eigenfrequency observations.
DI11A-08
Body Tides on a Three-Dimensional Elastic Earth: Toward a Joint Tidal and Seismological Tomography
Seismic tomography models of the Earth's interior are typically based mainly upon body and surface wave data such as travel times and waveforms. These data, however, lack sensitivity to density variations. On the other hand, the lowest frequency data, i.e., the free oscillations or normal modes of the Earth, depend on lateral variations in density as well as elasticity, because for these data the gravitational restoring force is important. The laterally heterogeneous whole mantle density model inferred from normal-mode inversion has little resemblance to either of the two seismic wave models. In fact, the correlation between density and seismic speeds approaches zero as the depth increases towards the core-mantle boundary, suggesting that the density variations estimated by scaling seismic wave speed models may not be accurate. In order to learn more about the density variations within the mantle, we need to turn to data for which the gravitational potential is important. One such data set is the forced oscillations of the Earth reflected in solid Earth tides. The Earth's interior is perturbed by the disturbing tidal potential, therefore the tidal response of the Earth reveals a great deal about its inner structure. We explore the effects of three-dimensional variations in elastic moduli and density on tidal deformation using a finite-volume code. The calculations show that the perturbation in surface deformation is large with contributions from both elastic moduli and density heterogeneity. Furthermore, the differences in tidal signal due to changes in the input density model (scaled shear wave speed model vs. model obtained from normal-mode constraints) are clearly observed. These results suggest that the tidal deformation can be obtained through GPS measurements and that they may provide invaluable data in further constraining deep Earth structure.