First-arrival Travel-Time Tomography using Second Generation Wavelets

International audienceWavelet decomposition of the slowness model has been proposed as a multiscale strategy for seismic first-arrival time tomography. We propose the introduction of so-called second generation wavelets which could be used for any mesh structure and does not need a number of samples as the power of two in each direction. Moreover, one can handle easily boundary effects. A linearized procedure for inverting delayed travel-times considering either slowness coefficients or wavelet coefficients. The ray tracing is solved at each iteration through an eikonal solver while the linear system to be solved at each iteration goes through an iterative solver as LSQR algorithm. We develop wavelet decomposition over constant patches (Haar wavelet) or over linear patches (Battle-Lemarie wavelet) of coefficients at different scales. This decomposition is introduced in the linear system to be solved and wavelet coefficients are considered as unknowns to be inverted. Synthetic examples show that the inversion behaves in a better way as wavelet decomposition seems to act as a preconditioner of the linear system. Local discretisation is possible but requires additional implementation as artefacs once built inside the model description never disappear because of the linearized approach. A binary mask operator is designed for each scale grid and could be applied locally leading to quite different spatial resolution depending on the analysis we could perform of the expected resolution at a given position of the medium. We show that indeed it is possible to design this binary operator and we apply it to synthetic examples as a crosswell experiment inside the Marmousi model. An application to a surface-surface experiment has been performed and the waveled decomposition shows that indeed we may recover detailed features nearby the free surface while preventing imprints of ray coverage at greater depths giving us smooth features at that depths. In spite of the increase demand of computer resources, the wavelet decomposition seems to be a rather promising alternative for controlling the resolution variation of seismic first-arrival tomography

Merging Active and Passive Data Sets in Travel-Time Tomography: The Case Study of Campi Flegrei Caldera (Southern Italy)

We propose a strategy for merging both active and passive data sets in linearized tomographic inversion. We illustrate this in the reconstruction of 3D images of a complex volcanic structure, the Campi Flegrei caldera, located in the vicinity of the city of Naples, southern Italy. The caldera is occasionally the site of significant unrests characterized by large ground uplifts and seismicity. The P and S velocity models of the caldera structure are obtained by a tomographic inversion based on travel times recorded during two distinct experiments. The first data set is composed of 606 earthquakes recorded in 1984 and the second set is composed of recordings for 1528 shots produced during the SERAPIS experiment in 2001. The tomographic inversion is performed using an improved method based on an accurate finite-difference traveltime computation and a simultaneous inversion of both velocity models and earthquake locations. In order to determine the adequate inversion parameters and relative data weighting factors, we perform massive synthetic simulations allowing one to merge the two types of data optimally. The proper merging provides high resolution velocity models, which allow one to reliably retrieve velocity anomalies over a large part of the tomography area. The obtained images confirm the presence of a high P velocity ring in the southern part of the bay of Pozzuoli and extends its trace inland as compared to previous results. This annular anomaly represents the buried trace of the rim of the Campi Flegrei caldera. Its shape at 1.5 km depth is in good agreement with the location of hydrothermalized lava inferred by gravimetric data modelling. The Vp/Vs model confirms the presence of two characteristic features. At about 1 km depth a very high Vp/Vs anomaly is observed below the town of Pozzuoli and is interpreted as due to the presence of rocks that contain fluids in the liquid phase. A low Vp/Vs body extending at about 3–4 km depth below a large part of the caldera is interpreted as the top of formations that are enriched in gas under supercritical conditions

A rock physics and seismic tomography study to characterize the structure of the Campi Flegrei caldera

The Campi Flegrei (CF) caldera experiences dramatic ground deformations unsurpassed anywhere in the world. The source responsible for this phenomenon is still debated. With the aim of exploring the structure of the caldera as well as the role of hydrothermal fluids on velocity changes, a multidisciplinary approach dealing with 3-D delay-time tomography and rock physics characterization has been followed. Selected seismic data were modeled by using a tomographic method based on an accurate finite-difference travel-time computation which simultaneously inverts P-wave and S-wave first-arrival times for both velocity model parameters and hypocenter locations. The retrieved P-wave and S-wave velocity images as well as the deduced Vp/Vs images were interpreted by using experimental measurements of rock physical properties on CF samples, to take into account steam/water phase transition mechanisms affecting P-wave and S-wave velocities. Also, modelling of petrophysical properties for site-relevant rocks constrains the role of overpressured fluids on velocity. A flat and low Vp/Vs anomaly lies at 4 km depth under the city of Pozzuoli. Earthquakes are located at the top of this anomaly. This anomaly implies the presence of fractured over-pressured gas-bearing formations and excludes the presence of melted rocks. At shallow depth, a high Vp/Vs anomaly located at 1 km suggests the presence of rocks containing fluids in the liquid phase. Finally, maps of the Vp*Vs product show a high Vp*Vs horse-shoe shaped anomaly located at 2 km depth. It is consistent with gravity data and well data and might constitute the on-land remainder of the caldera rim, detected below sea level by tomography using active source seismic data. For a more exhaustive description of the utilized methodologies, of synthetic tests for spatial resolution and uncertainty assessment and, the interpretation of results, the reader may refer to the paper Vanorio et al. (2005)

Free and smooth boundaries in 2-D finite-difference schemes for transient elastic waves

A method is proposed for accurately describing arbitrary-shaped free boundaries in single-grid finite-difference schemes for elastodynamics, in a time-domain velocity-stress framework. The basic idea is as follows: fictitious values of the solution are built in vacuum, and injected into the numerical integration scheme near boundaries. The most original feature of this method is the way in which these fictitious values are calculated. They are based on boundary conditions and compatibility conditions satisfied by the successive spatial derivatives of the solution, up to a given order that depends on the spatial accuracy of the integration scheme adopted. Since the work is mostly done during the preprocessing step, the extra computational cost is negligible. Stress-free conditions can be designed at any arbitrary order without any numerical instability, as numerically checked. Using 10 grid nodes per minimal S-wavelength with a propagation distance of 50 wavelengths yields highly accurate results. With 5 grid nodes per minimal S-wavelength, the solution is less accurate but still acceptable. A subcell resolution of the boundary inside the Cartesian meshing is obtained, and the spurious diffractions induced by staircase descriptions of boundaries are avoided. Contrary to what occurs with the vacuum method, the quality of the numerical solution obtained with this method is almost independent of the angle between the free boundary and the Cartesian meshing.Comment: accepted and to be published in Geophys. J. In

Converted phase identification and retrieval of Vp/Vs ratios from move-out reflection analysis: application to the Campi Flegrei caldera

Here, we propose a method for the determination of Vp/Vs ratios in a horizontally layered propagation media using maximization of a coherency function along theoretical travel-times of PS reflected phases. The theoretical travel-times are computed using the information about the propagation media that is extracted by velocity analysis or by topographic analysis performed on the first arrivals. The method is also a valid tool for the identification of the PS phases associated with a fixed seismic reflector, and it is particularly suitable for data that is stored in common mid-point and common conversion point bin- ning; for this kind of data the hypothesis of horizontally and layered media can usually be verified. We applied the method to both simulated and real datasets. The use of the real data that was acquired in the Campi Flegrei caldera (southern Italy) allowed us to estimate a relatively high Vp/Vs ratio (3.5 ± 0.6) for a very shallow layer (maximum depth, 600 m). This hypothesis has been tested by theoretical rock physical modeling of the Vp/Vs ratios as a function of porosity, suggesting that the shallow layer appears to be formed of unconsolidated, water-saturated, volcanic and marine sediments that filled Pozzuoli Bay during the post-caldera activity

Seismic waves synthesis by gaussian beams summation: A comparison with finite differences

ABSTRACT We apply Gaussian beam summation to the calculation of seismic reflections from complex interfaces, introducing several modifications of the original method. First, we use local geographical coordinates for the representation of paraxial rays in the vicinity of the recording surface, In this way we avoid the timeconsuming evaluation of the ray-centered coordinates of the observation points. Second, we propose a method for selecting the beams that ensures numerical stability of the synthetic seismograms, Third, we introduce a simple source wave packet that simplifies and stabilizes the calculations of inverse Fourier transforms. We compare reflection seismograms computed using the Gaussian beam-summation method with those calculated by finite differences. Two simple models are used. The first is a continuous curved interface separ

Challenges in shallow target reconstruction by 3D elastic full-waveform inversion - Which initial model?

Elastic full-waveform inversion (FWI) is a powerful tool for high-resolution subsurface multiparameter characterization. However, 3D FWI applied to land data for near-surface applications is particularly challenging because the seismograms are dominated by highly energetic, dispersive, and complex-scattered surface waves (SWs). In these conditions, a successful deterministic FWI scheme requires an accurate initial model. Our study, primarily focused on field data analysis for 3D applications, aims at enhancing the resolution in the imaging of complex shallow targets, by integrating devoted SW analysis techniques with a 3D spectral-element-based elastic FWI. From dispersion curves, extracted from seismic data recorded over a sharp-interface shallow target, we build different initial S-wave (VS) and P-wave (VP) velocity models (laterally homogeneous and laterally variable), using a specific data transform. Starting from these models, we carry out 3D FWI tests on synthetic and field data, using a relatively straightforward inversion scheme. The field data processing before FWI consists of band-pass filtering and muting of noisy traces. During FWI, a weighting function is applied to the far-offset traces. We test 2D and 3D acquisition layouts, with different positions of the sources and variable offsets. The 3D FWI workflow enriches the overall content of the initial models, allowing a reliable reconstruction of the shallow target, especially when using laterally variable initial models. Moreover, a 3D acquisition layout guarantees a better reconstruction of the target's shape and lateral extension. In addition, the integration of model-oriented (preliminary monoparametric FWI) and data-oriented (time windowing) strategies into the main optimization scheme has produced further improvement of the FWI results

On the use of simulated annealing method and cross-validation theory for deconvolution of seismograms Bull

Abstract In order to retrieve the apparent source time function (ASTF) seen at a given station, one must take into account propagation effects, site, and instrumental influences. Removing these effects can be performed by a deconvolution of the mainshock seismogram by a seismogram of a smaller event recorded at the same station. This smaller event must occur nearby the mainshock, and the associated seismogram is considered as an empirical Green's function. We propose a deconvolution based on the simulated annealing method, and we compare it with the often-used spectral division technique. We show on both synthetic and real signals that the simulated annealing deconvolution (SAD) provides stable and positive ASTF, whereas results from spectral division are very sensitive to an ad hoc parameter called water level. Finally, the application of cross-validation analysis between the three components of the seismogram in addition to the SAD allows us to estimate errors on the ASTF