Simultaneous velocity and interface tomography of normal-incidence and wide-aperture seismic traveltime data

A tomographic inversion technique that inverts traveltimes to obtain a model of the subsurface in terms of velocities and interfaces is presented. It uses a combination of refraction, wide-angle reflection and normal-incidence data, it simultaneously inverts for velocities and interface depths, and it is able to quantify the errors and trade-offs in the final model. The technique uses an iterative linearized approach to the non-linear traveltime inversion problem. The subsurface is represented as a set of layers separated by interfaces, across which the velocity may be discontinuous. Within each layer the velocity varies in two dimensions and has a continuous first derivative. Rays are traced in this medium using a technique based on ray perturbation theory, and two-point ray tracing is avoided by interpolating the traveltimes to the receivers from a roughly equidistant fan of rays. The calculated traveltimes are inverted by simultaneously minimizing the misfit between the data and calculated traveltimes, and the roughness of the model. This 'smoothing regularization' stabilizes the solution of the inverse problem. In practice, the first iterations are performed with a high level of smoothing. As the inversion proceeds, the level of smoothing is gradually reduced until the traveltime residual is at the estimated level of noise in the data. At this point, a minimum-feature solution is obtained, which should contain only those features discernible over the noise.
The technique is tested on a synthetic data set, demonstrating its accuracy and stability and also illustrating the desirability of including a large number of different ray types in an inversion.     

Signature of remnant slabs in the North Pacific from P-wave tomography

A 3-D ray-tracing technique was used in a global tomographic inversion in order to obtain tomographic images of the North Pacific. The data reported by the Geophysical Survey of Russia (1955–1997) were used together with the catalogues of the International Seismological Center (1964–1991) and the US Geological Survey National Earthquake Information Center (1991–1998), and the recompiled catalogue was reprocessed. The final data set, used for following the inversion, contained 523 430 summary ray paths. The whole of the Earth's mantle was parametrized by cells of 2° × 2° and 19 layers. The large and sparse system of observation equations was solved using an iterative LSQR algorithm.
A subhorizontal high-velocity anomaly is revealed just above the 660 km discontinuity beneath the Aleutian subduction zone. This high-velocity feature is observed at latitudes of up to ~70°N and is interpreted as a remnant of the subducted Kula plate, which disappeared through ridge subduction at about 48 Ma. A further positive velocity perturbation feature can be identified beneath the Chukotka peninsula and Okhotsk Sea, extending from ~300 to ~660 km depth and then either extending further down to ~800 km (Chukotka) or deflecting along the 660 km discontinuity (Okhotsk Sea). This high-velocity anomaly is interpreted as a remnant slab of the Okhotsk plate accreted to Siberia at ~55 Ma.     

A traveltime reciprocity discrepancy in the Podvin & Lecomte time3d finite difference algorithm

We have found that the extensively used finite difference scheme time3d produces time fields which are 'asymmetric' in the sense that traveltimes computed to the right of the source are faster than traveltimes computed to the left. All finite difference schemes will, as they are approximations to the wave equation, to some extent fail to obey reciprocity perfectly. We show, however, that the errors in time3d may be significant—and unnecessarily large. An asymmetry in the point source initialization has been identified, and after correction time3d produces time fields with an improved reciprocity.     

P- and S-velocity images of the lithosphere–asthenosphere system in the Central Andes from local-source tomographic inversion

About 50 000 P and S arrival times and 25 000 values of t * recorded at seismic arrays operated in the Central Andes between 20°S and 25°S in the time period from 1994 to 1997 have been used for locating more than 1500 deep and crustal earthquakes and creating 3-D P , S velocity and Qp models. The study volume in the reference model is subdivided into three domains: slab, continental crust and mantle wedge. A starting velocity distribution in each domain is set from a priori information: in the crust it is based on the controlled sources seismic studies; in slab and mantle wedge it is defined using relations between P and S velocities, temperature and composition given by mineral physics. Each iteration of tomographic inversion consists of the following steps: (1) absolute location of sources in 3-D velocity model using P and S arrival times; (2) double-difference relocation of the sources and (3) simultaneous determination of P and S velocity anomalies, P and S station corrections and source parameters by inverting one matrix. Velocity parameters are computed in a mesh with the density of nodes proportional to the ray density with double-sided nodes at the domain boundaries. The next iteration is repeated with the updated velocity model and source parameters obtained at the previous step. Different tests aimed at checking the reliability of the obtained velocity models are presented. In addition, we present the results of inversion for Vp and Vp/Vs parameters, which appear to be practically equivalent to Vp and Vs inversion. A separate inversion for Qp has been performed using the ray paths and source locations in the final velocity model. The resulting Vp , Vs and Qp distributions show complicated, essentially 3-D structure in the lithosphere and asthenosphere. P and S velocities appear to be well correlated, suggesting the important role of variations of composition, temperature, water content and degree of partial melting.     

Sensitivities of seismic traveltimes and amplitudes in reflection tomography

Seismic traveltimes and amplitudes in reflection-seismic data show different dependences on the geometry of reflection interfaces, and on the variation of interval velocities. These dependences are revealed by eigenanalysis of the Hessian matrix, defined in terms of the Fréchet matrix and its adjoint associated with different norms chosen in the model space. The eigenvectors and eigenvalues of the Hessian clearly show that for reflection tomographic inversion, traveltime and amplitude data contain complementary information. Both for reflector-geometry and for interval-velocity variations, the traveltimes are sensitive to the model components with small wavenumbers, whereas the amplitudes are more sensitive to the components with high wavenumbers. The model resolution matrices, after the rejection of eigenvectors corresponding to small eigenvalues, give us some insight into how the addition of amplitude information could potentially contribute to the recovery of physical parameters.
In order to cooperatively invert seismic traveltimes and amplitudes simultaneously, we propose an empirical definition of the data covariance matrix which balances the relative sensitivities of different types of data. We investigate the cooperative use of both data types for, separately, interface-geometry and 2-D interval-velocity variations. In both cases we find that cooperative inversions can provide better solutions than those using traveltimes alone. The potential benefit of including amplitude-data constraints in seismic-reflection traveltime tomography is therefore that it may be possible to resolve the known ambiguity between the reflector-depth uncertainty and the interval-velocity uncertainty better.     

Three-dimensional geometrical ray theory and modelling of transmitted seismic energy of data from the Nevada Test Site

This paper presents a geometrically based algorithm for computing synthetic seismograms for energy transmitted through a 3-D velocity distribution. 3-D ray tracing is performed to compute the traveltimes and geometrical spreading (amplitude). The formulations of both kinematic and dynamic ray-tracing systems are presented. The two-point ray-tracing problem is solved by systematically updating the initial conditions and adjusting the ray direction until the ray intersects the specified endpoint. The amount of adjustment required depends on the derivatives of the position with respect to the given starting angles between consecutive rays. The algorithm uses derivatives to define the steepest-descent direction and to update the initial directions. The convergence rate depends on the complexity of the model.
Test seismograms compare favourably with those from a 2-D asymptotic ray theory algorithm and a 3-D Gaussian-beam algorithm. The algorithm is flexible in modelling arbitrary source and recorder geometries for various smoothly varying 3-D velocity distributions. The algorithm is further tested by simulating surface-to-tunnel vibroseis field data. Shear waves as well as compressional waves may be approximately included. Application of the algorithm to a data set from the Rainier Mesa of the Nevada Test Site produced a good fit to the transmitted (first arrival) traveltimes and amplitudes, with approximately 15 per cent variation in the local 3-D velocity.