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The nonlinear problem of inversion of seismic waveforms can be set up using least-squares methods. The inverse problem is then reduced to the problem of minimizing a (nonquadratic) function in a space of many (lo4 to 106) variables. Using gradient methods leads to iterative algorithms, each iteration implying a forward propagation generated by the actual sources, a backward propagation generated by the data residuals (acting as if they were sources), and a correlation at each point of the space of the two fields thus obtained, which gives the updated model. The quality of the results of any inverse method depends heavily on the realism of the forward modeling. Finite-difference schemes are a good choice relative to realism because, although they are time-consuming, they give excellent results. Numerical tests performed with multioffset synthetic data from a two-dimensional model prove the feasibility of the approach. If only surface-recorded reflections are used, the high spatial frequency content of the model (but not the low spatial frequencies) is recovered in few (= 5) iterations. By using transmitted data also (e.g., between two boreholes), all the spatial frequencies are recovered. Since the problem is nonlinear. if the initial guess is far enough from the true solution, the iterative algorithm may conveige inti3 a secondary solution. A nonlinear inversion with 8 shots, each shot recorded at 400 receiver locations. with 700 samples in each seismogram, corresponding to a 2-D model described by 40 000 grid points, takes approximately 1 hour in a CRAY 1S supercomputer. INTRODUCTJON Linearized inversion of seismic waveforms has received considerable attention in the iiterature. For instance, Clayton and Stolt (1981) and Tarantola (1984a) propose methods for solving the linearized multidimensional inverse problem with multioffset seismic reflection data. Woodhouse and Dziewonski (1984) and Tanimoto (1984) also use linearized inversion of waveforms to obtain global Earth models, If a starting model is known to be close enough to the actual medium, linearized inversion will probably perform well. Unfortunately, since there is no practical test to check the accuracy of the linearization, nonlinear inverse techniques are more promising. There are two basic options: a full exploration of the parameter space (systematic or Monte Carlo), or a local descent method. The first approach has the advantage of avoiding local minima, but it is too time-consuming for modern computers. The second approach gives the correct solution when the starting model is inside the valley of the global minimum, irrespective of the choice of starting point. Thus the starting model plays a much less crucial role than in linearized inversion.

A two-dimensional active seismic experiment was performed on Mount Vesuvius: Explosive charges were set off at three sites, and the seismic signal along a dense line of 82 seismometers was recorded. A high-velocity basement, formed by Mesozoic carbonates, was identified 2 to 3 kilometers beneath the volcano. A slower (P-wave velocity Vp 3.4 to 3.8 kilometers per second) and shallower high-velocity zone underlies the central part of the volcano. Large-amplitude late arrivals with a dominant horizontal wave motion and low-frequency content were identified as a P to S phase converted at a depth of about 10 kilometers at the top of a low-velocity zone (Vp < 3 kilometers per second), which might represent a melting zone.

We have developed a finite difference method that is especially adapted to the study of dynamic shear cracks. We studied a number of simple earthquake source models in two and three dimensions with special emphasis on the modeling of the stress field. We compared our numerical results for semi-infinite and self-similar shear crar'ks with the few exact solutions that are avadable in the literature. We then studied spontaneous rupture propagation with the help of a maximum stress criterion. From dimensional arguments and a few simple examples, we showed that the maximum stress criterion depended on the physical dimensions of the fault. For a given maximum stress intensity, the finer the numerical mesh, the higher the maximum stress that had to be adopted. A study of in-plane cracks showed that at high rupture velocities, the numerical results did not resolve the stress concentration due to the rupture front from the stress peak associated with the shear wave propagating in front of the crack. We suggest that this is the reason why transonic rupture velocR,es are found in the numerical solutions of in-plane faulting when the rupture resistance Is rather low. Finally, we studied the spontaneous propagation of an initially circular rupture. Two distinct modes of nucleation of the rupture were studied. In the first, a plane circular shear crack was formed instantaneously in a uniformly prestressed medium. After a while, once stress concentrations had developed around the crack edge, the rupture started to grow, In the second type of nucleation, a preexisting circular crack became unstable at time t = 0 and started to grow, The latter model appeared to us as a more realistm simulation of earthquake triggering. In this case, the initial stress was nonuniform and was the static field of the preexisting fault.

Summary. A preliminary study of the aftershocks of three earthquakes that occurred near to Corinth (Greece) in 1981 is combined with observations of the morphology and faulting to understand the evolution of the Eastern Gulf of Corinth. The well located aftershocks form a zone 60km long and 20km wide. They do not lie on the main fault planes and are mostly located between the north-dipping faulting on which the first two earthquakes occurred and the south-dipping faulting associated with the third event. A cluster of aftershocks also lies in the footwall of the eastern end of the south-dipping fault of the third event.Morphologically, it is observed that in the evolution of the Eastern Gulf of Corinth, antithetic faulting apparently predates the appearance of the main faulting at the surface. This evolution can be explained by motion on a deep seated, shallow angle, aseismic normal fault. A model based on such a fault also accounts for the aftershock distribution of the 1981 earthquakes.

A high-resolution seismic tomography of Mt.Vesuvius was started in May 1994, with the aim of reconstructing the detailed shallow crustal structure underneath the volcano and define its feeding system. The first phase of the experiment was to perform a 2D profile, using three underground explosions as active sources. Data from controlled sources and microearthquakes were jointly used to determine the shallow structure of the volcano. A high-velocity body (Vp=3.5–4 km/s) was identified at about 2 km beneath the Somma-Caldera. It is likely to represent a sub-volcanic structure, formed by a dense network of solidified dikes. A prominent converted P-to-S phase at about 10 km of depth indicates the occurrence of a sharp transition to a very low-velocity zone. This may represent the top of an extended magmatic reservoir.

Procedures for accurate ray tracing in complex three-dimensional media with interfaces are proposed. The ray tracing equations and the associated paraxial linear equations are solved either by a numerical solver or by an analytical perturbation approach. Interfaces are described with an explicit representation or an implicit representation using B-spline interpolation. For the implicit representation, we exploit two important properties of B-splines, the convex hull and subdivision properties, in order to determine the intersection of the ray with the interface.