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Acoustic tomography in a shallow ultrasonic waveguide is demonstrated at the laboratory scale between two source-receiver arrays. At a 1/1,000 scale, the waveguide represents a 1.1-km-long, 52-m-deep ocean acoustic channel in the kilohertz frequency range. Two coplanar arrays record the transfer matrix in the time domain of the waveguide between each pair of source-receiver transducers. A time-domain, double-beamforming algorithm is simultaneously performed on the source and receiver arrays that projects the multi-reflected acoustic echoes into an equivalent set of eigenrays, which are characterized by their travel times and their launch and arrival angles. Travel-time differences are measured for each eigenray every 0.1 s when a thermal plume is generated at a given location in the waveguide. Travel-time tomography inversion is then performed using two forward models based either on ray theory or on the diffraction-based sensitivity kernel. The spatially resolved range and depth inversion data confirm the feasibility of acoustic tomography in shallow water. Comparisons are made between inversion results at 1 and 3 MHz with the inversion procedure using ray theory or the finite-frequency approach. The influence of surface fluctuations at the air-water interface is shown and discussed in the framework of shallow-water ocean tomography., (© 2011 Acoustical Society of America)

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]

Velocity macromodel building is an essential step of the seismic imaging workflow. Indeed, obtaining acceptable results through migration or full waveform inversion is highly dependent on the kinematic accuracy of the background/initial velocity model. Two decades ago, stereotomography was proposed as an alternative to reflection traveltime tomography, the first relying on semi-automatic picking of locally coherent events associated with small reflection or diffraction segments tied to scatterers in depth by a pair of rays, while the latter on interpretive picking of laterally continuous reflections. The flexibility of stereotomography paved the way for many developments that have shown the efficiency of the method whilst emphasizing on the complementary information carried out by traveltimes and slopes of locally coherent events. A recent formulation recast stereotomography under a matrix-free formulation based on eikonal solvers and the adjoint-state method. In the latter, like in the previous works, the scatterer positions and the velocity field are updated jointly to tackle the ill-famed velocity–position coupling in reflection tomography. Following on from this adjoint-state formulation, we propose a new parsimonious formulation of slope tomography that offers the chance to restrain the problem to minimizing the residuals of a single data class being a slope, in search of a sole parameter class being the subsurface velocity field. This parsimonious formulation results from a variable projection, which is implemented by enforcing a consistency between the scatterer coordinates and the velocity macromodel through migration of kinematic attributes. We explain why the resulting reduced-parametrization inversion is more suitable for tomographic problems than the most common joint inversion strategy. We benchmark our method against the complex Marmousi model along with a validation through time domain full waveform inversion and then present the results of a field data case study. [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]

Full waveform inversion of ground-penetrating radar data is an emerging technique for the quantitative, high-resolution imaging of the near subsurface. Here, we present a 2-D frequency-domain full waveform inversion for the simultaneous reconstruction of the dielectric permittivity and of the electrical conductivity. The inverse problem is solved with a quasi-Newton optimization scheme, where the influence of the Hessian is approximated by the L-BFGS-B algorithm. This formulation can be considered to be fully multiparameter since it enables to update permittivity and conductivity values within the same descent step, provided we define scales of measurement through a reference permittivity, a reference conductivity, and an additional scaling factor. Numerical experiments on a benchmark from the literature demonstrate that the inversion is very sensitive to the parameter scaling, despite the consideration of the approximated Hessian that should correct for parameter dimensionalities. A proper scaling should respect the natural sensitivity of the misfit function and give priority to the parameter that has the most impact on the data (the permittivity, in our case). We also investigate the behaviour of the inversion with respect to frequency sampling, considering the selected frequencies either simultaneously or sequentially. As the relative imprint of permittivity and conductivity in the data varies with frequency, the simultaneous reconstruction of both parameters takes a significant benefit from broad frequency bandwidth data, so that simultaneous or cumulative strategies should be favoured. We illustrate our scaling approach with a realistic synthetic example for the imaging of a complex subsurface from on-ground multioffset data. Considering data acquired only from the ground surface increases the ill-posedness of the inverse problem and leads to a strong indetermination of the less-constrained conductivity parameters. A Tikhonov regularization can prevent the creation of high-wavenumber artifacts in the conductivity model that compensate for erroneous low-wavenumber structures, thus enabling to select model solutions. We propose a workflow for multiparameter imaging involving both parameter scaling and regularization. Optimal combinations of scaling factors and regularization weights can be identified by seeking regularization levels that exhibit a clear minimum of final data misfit with respect to parameter scaling. We confirm this workflow by inverting noise-contaminated synthetic data. In a surface-to-surface acquisition configuration, we have been able to reconstruct an accurate permittivity structure and a smooth version of the conductivity distribution, based entirely on the analysis of the data misfit with respect to parameter scaling, for different regularization levels. [ABSTRACT FROM AUTHOR]

A new three-dimensional delay traveltime tomography is performed to image the intermediate structure of the western Gulf of Corinth. A large data set, collected in 1991 during a two-month passive tomographic experiment, has been reanalysed for the reconstruction of detailedVpandVsimages. An improved tomography method, based on an accurate traveltime computation, is applied to invert simultaneously delayedPandSfirst-arrival traveltimes for both velocity and hypocentre parameters. We perform different synthetic tests to analyse the sensitivity of tomography results to the model parametrization and to the starting 1-D model selection. The analysis of the retrievedVpandVsmodels as well as deducedVp/ VsandVp· Vsimages allows us to interpret and delineate the distribution of lithological variation, porosity/crack content and fluid saturation in the upper 9–11 km of the crust beneath the gulf. The tomographic models image a rather complex crustal structure, which is characterized by a vertical change in both velocity features and seismicity distribution. We identify a shallower zone of the crust (0–5 km depth), in which velocity distributions seem to be controlled by the still active N–S extensional regime and a deeper zone (7–11 km depth), which matches the seismogenic zone. The correlation between this latter and a specific unit of the Hellenic mountain structure (the Pyllite–Quartzite series) allows us to suggest a possible explanation for seismicity concentration in a narrow band at 7–9 km depth. Finally, the occurrence of clusters showing low-angle normal fault mechanisms in areas characterized by highVp/ Vsvalues indicates a possible role of fluids in triggering brittle creep along the identified low-angle normal faults. [ABSTRACT FROM AUTHOR]

An application of full-waveform tomography to dense onshore wide-aperture seismic data recorded in a complex geological setting (thrust belt) is presented.The waveform modelling and tomography are implemented in the frequency domain. The modelling part is solved with a finite-difference method applied to the visco-acoustic wave equation. The inversion is based on a local gradient method. Only theP-wave velocity is involved in the inversion. The inversion is applied iteratively to discrete frequency components by proceeding from low to high frequencies. This defines a multiscale imaging in the sense that high wavenumbers are progressively incorporated in images. The linearized waveform tomography requires an accurate starting velocity model that has been developed by first-arrival traveltime tomography.After specific pre-processing of the data, 16 frequency components ranging between 5.4 and 20 Hz were inverted. Ten iterations were computed per frequency component leading to 160 tomographic models. The waveform tomography has successfully imaged southwest-dipping structures previously identified from other geophysical data as being associated with high-resistivity bodies. The relevance of the tomographic images is locally demonstrated by comparison of a velocity–depth function extracted from the waveform tomography models with a coincident vertical seismic profiling (VSP) log available on the profile. Moreover, comparison between observed and synthetic seismograms computed in the (starting) traveltime and waveform tomography models demonstrates unambiguously that the waveform tomography successfully predicts for wide-angle reflections from southwest-dipping geological structures.This study demonstrates that the combination of first-arrival traveltime and frequency-domain full-waveform tomographies applied to dense wide-aperture seismic data is a promising approach to quantitative imaging of complex geological structures. Indeed, wide-aperture acquisition geometries offer the opportunity to develop an accurate background velocity model for the subsequent waveform tomography. This is critical, because the building of the macromodel remains an open question when only near-vertical reflection data are considered. [ABSTRACT FROM AUTHOR]

An integrated multiscale seismic imaging flow is applied to dense onshore wide-aperture seismic data recorded in a complex geological setting (thrust belt).An initial P-wave velocity macromodel is first developed by first-arrival traveltime tomography. This model is used as an initial guess for subsequent full-waveform tomography, which leads to greatly improved spatial resolution of the P-wave velocity model. However, the application of full-waveform tomography to the high-frequency part of the source bandwidth is difficult, due to the non-linearity of this kind of method. Moreover, it is computationally expensive at high frequencies since a finite-difference method is used to model the wave propagation. Hence, full-waveform tomography was complemented by asymptotic prestack depth migration to process the full-source bandwidth and develop a sharp image of the short wavelengths. The final traveltime tomography model and two smoothed versions of the final full-waveform tomography model were used as a macromodel for the prestack depth migration.In this study, wide-aperture multifold seismic data are used. After specific preprocessing of the data, 16 frequency components ranging from 5.4 Hz to 20 Hz were inverted in cascade by the full-waveform tomography algorithm. The full-waveform tomography successfully imaged SW-dipping structures previously identified as high-resistivity bodies. The relevance of the full-waveform tomography models is demonstrated locally by comparison with a coincident vertical seismic profiling (VSP) log available on the profile. The prestack depth-migrated images, inferred from the traveltime, and the smoothed full-waveform tomography macromodels are shown to be, on the whole, consistent with the final full-waveform tomography model. A more detailed analysis, based on common-image gather computations, and local comparison with the VSP log revealed that the most accurate migrated sections are those obtained from the full-waveform tomography macromodels. A resolution analysis suggests that the asymptotic prestack depth migration successfully migrated the wide-aperture components of the data, allowing medium wavelengths in addition to the short wavelengths of the structure to be imaged.The processing flow that we applied to dense wide-aperture seismic data is shown to provide a promising approach, complementary to more classical seismic reflection data processing, to quantitative imaging of complex geological structures. [ABSTRACT FROM AUTHOR]

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.