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Local earthquake tomography (LET) is a popular method for inverting arrival time picks of local-regional earthquakes for P - and S -wave velocities and hypocentre parameters in seismically active regions. This popularity is due to some robust and well-documented open-source codes that are sometimes used as black boxes. The availability of a very complete time-pick database on the Western Alps gives us a chance to thoroughly investigate the influence of the numerous processes and parameters involved when applying LET to the Western Alps or similar targets. From a subset of high-quality manual picks (1989–2014), we compute preliminary P and S velocity models that are used to predict arrival times for later events and allow the selected fusion of picks downloaded from different seismological agencies for a consistent 33-yr database (1989–2021). Different model reconstructions are proposed by selecting different subsets of the arrival time data set. Aside data input into the LET, influence of initial stratified or 3-D velocity models and related initial earthquake locations is investigated together with grid discretization, Laplacian smoothing and damping parameters in the standard penalty approach commonly used by LET codes. These numerical parameters account for the expected limited resolution of seismic waves due to their finite-frequency content. Parameter selection is handled by the user, whereas frequency impact is only implicit in the onset picks. The earthquake distribution allows a reconstruction down to 40-km depth over an area of ∼500 × 500 km2. Robust features such as the high-velocity Ivrea body anomaly, and a deep low-velocity anomaly associated with crustal thickening underneath the mountain belt survive whatever the tomography strategy and parameters. Finally, a comparison with previous LET reconstructions suggests that finite-frequency content be explicitly incorporated through wave equation tomography to improve spatial resolution. This would fully exploit observables collected from seismograms, albeit with a significant increase in computer costs. [ABSTRACT FROM AUTHOR]

Accurate numerical computation of wave traveltimes in heterogeneous media is of major interest for a large range of applications in seismics, such as phase identification, data windowing, traveltime tomography and seismic imaging. A high level of precision is needed for traveltimes and their derivatives in applications which require quantities such as amplitude or take-off angle. Even more challenging is the anisotropic case, where the general Eikonal equation is a quartic in the derivatives of traveltimes. Despite their efficiency on Cartesian meshes, finite-difference solvers are inappropriate when dealing with unstructured meshes and irregular topographies. Moreover, reaching high orders of accuracy generally requires wide stencils and high additional computational load. To go beyond these limitations, we propose a discontinuous-finite-element-based strategy which has the following advantages: (1) the Hamiltonian formalism is general enough for handling the full anisotropic Eikonal equations; (2) the scheme is suitable for any desired high-order formulation or mixing of orders (p-adaptivity); (3) the solver is explicit whatever Hamiltonian is used (no need to find the roots of the quartic); (4) the use of unstructured meshes provides the flexibility for handling complex boundary geometries such as topographies (h-adaptivity) and radiation boundary conditions for mimicking an infinite medium. The point-source factorization principles are extended to this discontinuous Galerkin formulation. Extensive tests in smooth analytical media demonstrate the high accuracy of the method. Simulations in strongly heterogeneous media illustrate the solver robustness to realistic Earth-sciences-oriented applications. [ABSTRACT FROM AUTHOR]

Velocity macromodel building is a crucial step in the seismic imaging workflow as it provides the necessary background model for migration or full waveform inversion. In this study, we present a new formulation of stereotomography that can handle more efficiently long-offset acquisition, complex geological structures and large-scale data sets. Stereotomography is a slope tomographic method based upon a semi-automatic picking of local coherent events. Each local coherent event, characterized by its two-way traveltime and two slopes in common-shot and common-receiver gathers, is tied to a scatterer or a reflector segment in the subsurface. Ray tracing provides a natural forward engine to compute traveltime and slopes but can suffer from non-uniform ray sampling in presence of complex media and long-offset acquisitions. Moreover, most implementations of stereotomography explicitly build a sensitivity matrix, leading to the resolution of large systems of linear equations, which can be cumbersome when large-scale data sets are considered. Overcoming these issues comes with a new matrix-free formulation of stereotomography: a factored eikonal solver based on the fast sweeping method to compute first-arrival traveltimes and an adjoint-state formulation to compute the gradient of the misfit function. By solving eikonal equation from sources and receivers, we make the computational cost proportional to the number of sources and receivers while it is independent of picked events density in each shot and receiver gather. The model space involves the subsurface velocities and the scatterer coordinates, while the dips of the reflector segments are implicitly represented by the spatial support of the adjoint sources and are updated through the joint localization of nearby scatterers. We present an application on the complex Marmousi model for a towed-streamer acquisition and a realistic distribution of local events. We show that the estimated model, built without any prior knowledge of the velocities, provides a reliable initial model for frequency-domain FWI of long-offset data for a starting frequency of 4 Hz, although some artefacts at the reservoir level result from a deficit of illumination. This formulation of slope tomography provides a computationally efficient alternative to waveform inversionmethod such as reflectionwaveforminversion or differential-semblance optimization to build an initial model for pre-stack depth migration and conventional FWI. [ABSTRACT FROM AUTHOR]

A new numerical technique for solving 2-D elastodynamic equations based on a finite-volume frequency-domain approach is proposed. This method has been developed as a tool to perform 2-D elastic frequency-domain full-waveform inversion. In this context, the system of linear equations that results from the discretization of the elastodynamic equations is solved with a direct solver, allowing efficient multiple-source simulations at the partial expense of the memory requirement. The discretization of the finite-volume approach is through triangles. Only fluxes with the required quantities are shared between the cells, relaxing the meshing conditions, as compared to finite-element methods. The free surface is described along the edges of the triangles, which can have different slopes. By applying a parsimonious strategy, the stress components are eliminated from the discrete equations and only the velocities are left as unknowns in the triangles. Together with the local support of the P0 finite-volume stencil, the parsimonious approach allows the minimizing of core memory requirements for the simulation. Efficient perfectly matched layer absorbing conditions have been designed for damping the waves around the grid. The numerical dispersion of this FV formulation is similar to that of staggered-grid finite-difference (FD) formulations when considering structured triangular meshes. The validation has been performed with analytical solutions of several canonical problems and with numerical solutions computed with a well-established FD time-domain method in heterogeneous media. In the presence of a free surface, the finite-volume method requires 10 triangles per wavelength for a flat topography, and fifteen triangles per wavelength for more complex shapes, well below the criteria required by the staircase approximation of FD methods. Comparisons between the frequency-domain finite-volume and the rotated FD methods also show that the former is faster and less memory demanding for a given accuracy level, an attractive feature for frequency-domain seismic inversion. We have thus developed an efficient method for 2-D P– SV-wave modelling on structured triangular meshes as a tool for frequency-domain full-waveform inversion. Further work is required to improve the accuracy of the method on unstructured meshes. [ABSTRACT FROM AUTHOR]

A multi-2-D non linear traveltime tomography of the shallow (3-4 km deep) structure of Mt Vesuvius volcano was performed. Data have been collected during two recent active seismic experiments using a total of 17 on-land shots and about 140 three-component digital seismographs. A newly developed technique for imaging the volcano velocity structure has been applied, based on an adaptive model space investigation where the number of grid nodes is progressively increased (multi-scale approach). The optimal model parametrization is chosen according to the minimum of the Akaike Information Criteria (AIC) parameter. This corresponds to finding the best compromise between the data misfit and simplicity of the model. The model parameter estimate is performed through the computation of an a posteriori probability density function (pdf), defined following the Bayesian approach. The maximum likelihood model is searched by an optimization technique which combines the genetic and simplex algorithms. The evaluation of the a posteriori pdf is based on traveltime computations using ray tracing techniques. Constraints on the model parameters are inserted in the form of prior pdf and error maps are inferred from cross-sections of the posterior probability around the found best fit solution. The retrieved images of Mt Vesuvius volcano show variable P-velocities in the range 1700-5800 ms[sup -1]. A fairly detailed image of the top of the Mesozoic carbonate rocks forming the basement of the volcanic area is obtained. A 9 km long, 1 km deep depression was detected at the N side of the volcano. The presence of a shallow high velocity body is evidenced underneath the Mt Somma caldera and it can be interpreted as a sub- or palaeo-volcanic structure. [ABSTRACT FROM AUTHOR]

We have used a dense wide-angle data set to test a two-step procedure for the separate reversion of first-arrival and reflection traveltimes. Data were collected in a complex thrust belt environment (southern Italy) along a 14-km line, with closely spaced sources (60 m) and receivers (90 m). We have applied a fully non-linear tomographic technique, specially designed to image complex structures, to over 6400 first-arrival traveltimes in order to determine a detailed velocity model. A bi-cubic spline velocity model parametrization is used. The inversion strategy follows a multiscale approach, and employs a non-linear velocity optimization scheme. The tomographic velocity model is adopted as the background reference medium for a subsequent interface inversion aimed at imaging a target upper-crust reflecton The interface inversion method is also based on a multiscale approach and uses a non-linear technique for model parameters (interface position nodes) optimization. We have applied the interface inversion method to over 1600 reflection traveltimes of a target event picked both in the near- and in the wide-angle offset range. The retrieved interface is well resolved in the central part of the model, where ray coverage mainly includes clear post-critical reflections and the background velocity model is accurate in depth thanks to large offset deep turning rays. The velocity and interface models thus determined are consistent with Vertical Seismic Profiling data and correlate well with the geometry of known geological structures. This study shows that the used inversion approach is efficient for target-orientated investigations in complex geological environments. [ABSTRACT FROM AUTHOR]

Proposes a hybrid method for modelling T-wave propagation from an underwater source to an on-land seismic station. Incorporation of a ray tracing method with a finite difference approach; Characteristics of the long-range hydroacoustic wavefield; Analysis of the Sound Fixing And Ranging propagation.

Comments on the query on the accuracy of the algorithm for the approximate estimation of the resolution matrix of tomographic systems. Suggestion of a Newtonian scheme; Question of the usefulness of the one-step backprojection; Similarity between A[sup T]A and the estimated resolution matrix.