Extending shear-wave tomography for the lower mantle using S and SKS arrival-time data

Seismic tomography using S wave travel times faces the difficulty imposed by the interference between S and SKS phases near 83° epicentral distance, as the SKS phase overtakes the S waves in the mantle. If the cross-over is avoided completely by excluding S data beyond 82° then no resolution is available below 2200 km in the lower mantle. A partial solution is to try to pick up the S phase beyond the cross-over which improves coverage and resolution in depth. However, a much larger improvement can be made by following the first arrival with S character and including SKS information with S. Arrival times for both S and SKS phases and the event hypocentres have been taken from the reprocessing of data reported to international agencies. Each event has been relocated, including depth phase information, and later phases re-associated using the improved locations to provide a set of travel times whose variance is significantly reduced compared with the original data catalogues. S travel-time tomography including SKS information out to 105°, provides tomographic images with improved rendition of heterogeneity in the lower mantle. The three-dimensional models of SV wavespeed relative to the ak135 reference velocity model show a significant increase in heterogeneity at the base of the mantle which matches the behaviour seen in results derived from waveform inversion. For most of the mantle there is a considerable similarity between the patterns of heterogeneity in the S wave images and recent P wave tomographic results, but greater differences develop in the lowermost mantle. In the D″ region the SV wavespeed patterns also show some differences from recent SH wavespeed results which mostly correlate with regions of recognised structural complexity

A Semi-classical calculus of correlations

The method of passive imaging in seismology has been developped recently in order to image the earth crust from recordings of the seismic noise. This method is founded on the computation of correlations of the seismic noise. In this paper, we give an explicit formula for this correlation in the "semi-classical" regime. In order to do that, we define the power spectrum of a random field as the ensemble average of its Wigner measure, this allows phase-space computations: the pseudo-differential calculus and the ray theory. This way, we get a formula for the correlation of the seismic noise in the semi-classcial regime with a source noise which can be localized and non homogeneous. After that, we show how the use of surface guided waves allows to image the earth crust.Comment: To appear in a special issue "Imaging and Monitoring with Seismic Noise" of the series "Comptes Rendus G\'eosciences", from the French "Acad\'emie des sciences

Comparing P and S wave heterogeneity in the mantle

From the reprocessed data set of Engdahl and co-workers we have carefully selected matching P and S data for tomographic imaging. We assess data and model error and conclude that our S model uncertainty is twice that of the P model. We account for this in our comparison of the perturbations in P and S-wavespeed. In accord with previous studies we find that P and S perturbations are positively correlated at all depths. However, in the deep mantle systematic differences occur between regions that have undergone subduction in the last 120 million years and those that have not. In particular, below 1500 km depth ∂ln V[subscript s]/∂ln V[subscript p] is significantly larger in mantle regions away from subduction than in mantle beneath convergent margins. This inference is substantiated by wavespeed analyses with random realizations of the slab/non-slab distribution. Through much of the mantle there is no significant correlation between bulk sound and S-wave perturbations, but they appear to be negatively correlated between 1700 and 2100 km depth, which is also where the largest differences in ∂ln V[subscript s]/∂ln V[subscript p] occur. This finding supports convection models with compositional heterogeneity in the lowermost mantle.National Science Foundation (U.S.) (Grant EAR-9905779

Multiple transition zone seismic discontinuities and low velocity layers below western United States

With P-to-S converted waves recorded at seismic stations of the U.S. Transportable Array, we image the fine structure of upper mantle and transition zone (TZ) beneath the western U.S. We map the topographies of seismic discontinuities by stacking data by common conversion points along profiles. Systematic depth and amplitude measurements are performed not only for the well-known “410” and “660” interfaces but also for minor seismic discontinuities identified around 350, 590, and 630 km depths. The amplitude of conversion suggests shear wave velocity (Vs) increase by 4% at the 410 and the 660. The observed 660 velocity contrast is smaller than expected from the 6% in IASP91 but consistent with a pyrolitic model of mantle composition. The Gorda plate, subducted under northern California, is tracked to the TZ where it seems to flatten and induce uplift of the 410 under northern Nevada. Maps of 410/660 amplitude/topography reveal that the TZ is anomalous beneath the geographical borders of Washington, Oregon, and Idaho, with (1) a thickened TZ, (2) a sharp change in depth of the 660, (3) a reduced 410 conversion amplitude in the North, and (4) a positive “630” discontinuity. Such anomalous structure might be inherited from the past history of plate subduction/accretion. A thinned TZ under the Yellowstone suggests higher-than-average temperatures, perhaps due to a deep thermal plume. Both the “350” and the “590” negative discontinuities extend over very large areas. They might be related either to an increased water content in the TZ, a significant amount of oceanic material accumulated through the past 100 Myr, or both.National Science Foundation (U.S.) (VICI grant NWO:VICI865.03.007

One-Way Wave Propagators For Velocity Analysis On Curvilinear Coordinates

Due to present computational limitations, migration by the one-way wave equation remains an integral tool in seismic exploration. For the realistic interpretation of common image point gathers, it is necessary that migration be free from artifacts from caustics and turning waves. In order to permit situations where turning waves occur, we perform our migration on specially chosen curvilinear coordinates where waves do not travel horizontally. We present an implementation of the curvilinear one-way wave equation using a rational approximation and discuss its application in migration velocity analysis, as well as transmission and reflection tomography

Wave-Equation Reflection Tomography: Annihilators and Sensitivity Kernals

In seismic tomography, the finite frequency content of broad-band data leads to interference effects in the process of medium reconstruction, which are ignored in traditional ray theoretical implementations. Various ways of looking at these effects in the framework of transmission tomography can be found in the literature. Here,we consider inverse scattering of bodywaves to develop a method of wave-equation reflection tomography with broad-band waveform data— which in exploration seismics is identified as a method of wave-equation migration velocity analysis. In the transition from transmission to reflection tomography the usual cross correlation between modelled and observed waveforms of a particular phase arrival is replaced by the action of operators (annihilators) to the observed broad-bandwave fields. Using the generalized screen expansion for one-way wave propagation, we develop the Fréchet (or sensitivity) kernel, and show how it can be evaluated with an adjoint state method. We cast the reflection tomography into an optimization procedure; the kernel appears in the gradient of this procedure.We include a numerical example of evaluating the kernel in a modified Marmousi model, which illustrates the complex dependency of the kernel on frequency band and, hence, scale. In heterogeneous media the kernels reflect proper wave dynamics and do not reveal a self-similar dependence on frequency: low-frequency wave components sample preferentially the smoother parts of the model, whereas the high-frequency data are—as expected—more sensitive to the stronger heterogeneity.We develop the concept for acoustic waves but there are no inherent limitations for the extension to the fully elastic case.TOTAL (Firm)National Science Foundation (U.S.) (grant EAR-0409816

Surface-wave eikonal tomography for dense geophysical arrays

Surface-wave tomography often involves the construction of phase (or group) velocity maps through linearized inversion of measured phase (group) arrival times. Such inversions require a priori information about the medium (that is, a reference model) in order to calculate source-receiver paths, which is inaccurate for complex media, and requires regularization. The surface-wave eikonal tomography proposed here bypasses these limitations and has the advantage of being simple to implement and use, with virtually no input parameters. It relies on accurate phase arrival time measurement, which can be challenging for dispersive waves and complex waveforms. We present a measurement method based on the evaluation of phase arrival time diff erences at nearby receivers.We show, using an exploration data set, that the produced Rayleigh-wave velocity maps are in agreement with results from traditional tomography, but the latter have lower resolution due to the need of regularization to accommodate for the heterogeneity of the study area and noise in data. Eikonal tomography requires averaging over results from multiple sources to produce a proper image, and we evaluate this requirement to a 200 m source spacing in the considered scattering environment. In addition, we validate the approach of combining seismic interferometry and eikonal tomography, for the cases where the source coverage is inappropriate.Shell Researc

Source-Indexed Migration Velocity Analysis with Global Passive Data

The reverse-time migration of global seismic data generated by free-surface multiples is regularly used to constrain the crustal structure, but its accuracy is to a large extent determined by the accuracy of the 3-D background velocity model used for wave propagation. To this improve the velocity model and hence the accuracy of the migrated image, we wish to apply the technique of migration velocity analysis (MVA) to global passive data. Applications of MVA in the active setting typically focus on o ffset- or angle-gather annihilation, a process that takes advantage of data redundancy to form an extended image, and then applies an annihilation operator to determine the success of image formation. Due to the nature of regional-scale passive seismic arrays, it is unlikely that the data in most of these studies will be su cient to form an extended image volume for use in annihilation-based MVA. In order to make use of the sparse and irregular array design of these arrays, we turn towards a shot-pro le moveout scheme for migration velocity analysis introduced by Xie and Yang (2008). In the place of extended image annihilation, we determine the success of the migration velocity model by using a weighted image correlation power norm. We compare pairs of images formed by migrating each teleseismic source by image cross-correlation in the depth direction. We look for a suitable background model by penalizing the amount of correlation power away from zero depth shift. The total weighted correlation power between source-pro le images is then used as the error function and optimized via conjugate gradient. We present the method and a proof-of-concept with 2-D synthetic data

Reverse-time migration-based reflection tomography using teleseismic free surface multiples

Converted and multiply reflected phases from teleseismic events are routinely used to create structural images of the crust–mantle boundary (Moho) and the elasticity contrasts within the crust and upper mantle. The accuracy of these images is to a large extent determined by the background velocity model used to propagate these phases to depth. In order to improve estimates of 3-D velocity variations and, hence, improve imaging, we develop a method of reverse-time migration-based reflection tomography for use with wavefields from teleseismic earthquakes recorded at broad-band seismograph arrays. Reflection tomography makes use of data redundancy—that is, the ability to generate numerous structural images of the subsurface with different parts of the wavefield. In exploration seismology (where it is known as migration velocity analysis) reflection tomography typically involves the generation of an extended image (e.g. offset- or angle-gathers), and the fitness of the background model is evaluated through the application of image-domain annihilators. In regional-scale passive source seismology, however, annihilation-based methods are inadequate because the sparse and irregular distribution of teleseismic sources is not likely to produce illumination over a sufficient range of angles. To overcome this problem we turn towards a source-indexed moveout scheme. Instead of extended image annihilation, we determine the success of the tomographic velocity model by cross correlating images produced with multiply scattered waves from different teleseismic sources. The optimal velocity model is the one that minimizes correlation power between windowed images away from zero depth shift. We base our inversion scheme on the seismic adjoint method and a conjugate gradient solver. For each image pair, the update direction is determined by correlations between downgoing wavefields with upgoing adjoint wavefields for both images. The sensitivity kernels used in this method is similar to those found in other forms of adjoint tomography, but their shapes are controlled by the spatial distribution of the error function. We present the method and a proof-of-concept with 2-D synthetic data

Seismological constraints on the density, thickness and temperature of the lithospheric mantle in southwestern Tibet

H. M.-D. thanks H. Fang, D. Forsyth, R. G. Green, A. Holt, V. Levin, C. Yu and especially L. Royden for helpful discussions, and to Schlumberger for a scholarship. He is also grateful to V. Levin and S. Roecker for making all seismo-grams from the Y2 network freely available through the IRIS Data Management Centre. We also thank three anonymous reviewers for thorough, constructive reviews. Data were processed using ObsPy. All figures were prepared using Matplotlib, alongside the Cartopy library for mapping.Peer reviewedPostprin