Alessandra Ribodetti

Asymptotic theory for imaging the attenuation factor Q

To describe accurately the propagation of elastic waves for characterizing and monitoring hydrocarbon reservoirs, as well as to obtain improved earth models, it is important to take into account seismic attenuation. We describe a method to estimate anelastic medium properties by a complete SH-waveform inversion. We use an optimization approach based on the iterative minimization of the mismatch between the seismic data and the computed response. To obtain a fast analytical imaging procedure, we include an asymptotic theory for attenuation in a linearized inverse scattering formulation. The forward modeling is solved by the Born approximation for a smooth and attenuative background medium. An asymptotic ray-tracing method is used to calculate traveltime, amplitude, and attenuation between source, receiver, and scattering points. The resulting method is computationally efficient and allows for a variety of data-acquisition geometries, including those with redundant or incomplete source-receiver coverage. Synthetic examples with realistic surface-to-surface geometry show an acceptable convergence in a few iterations when anomaly perturbations are less than 10% of the reference values and when associated diffracting structures are smaller than one-tenth of the predominant seismic wavelength. Through there remains the fundamental trade-off between density and shear modulus, the iterative asymptotic inversion is able to recover the elastic parameters (density and shear modulus) and the attenuation factor.

Subducted Oceanic Relief Locks the Shallow Megathrust in Central Ecuador

Whether subducted oceanic reliefs such as seamounts promote seismic rupture or aseismic slip remains controversial. Here, we use swath bathymetry, pre-stack-depth-migrated multichannel seismic reflection lines and wide-angle seismic data collected across the Central Ecuador subduction segment to reveal a broad ~55-km x 50-km, ~ 1.5-2.0-km-high, low height-to-width ratio, multi-peaked, sediment-bare, shallow subducted oceanic relief. Owing to La Plata island and the coastline being located, respectively, ~35 km and ~50-60 km from the trench, GPS measurements allow us to demonstrate that the subducted oceanic relief spatially correlates to a shallow, ~80-km x 55-km locked interplate asperity within a dominantly creeping subduction segment. The oceanic relief geometrical anomaly together with its highly jagged topography, the absence of a subduction channel, and a stiff erosive oceanic margin are found to be long-term geological characteristics associated with the shallow locking of the megathrust. Although the size and level of locking observed at the subducted relief scale could produce a Mw > 7+ event, no large earthquake are known to have happened for several centuries. On the contrary, frequent slow slip events (SSE) have been recorded since 2010 within the locked patch, and regular seismic swarms have occurred in this area during the last 40 years. These transient processes, together with the rough subducted oceanic topography, suggest that interplate friction might actually be heterogeneous within the locked patch. Additionally, we find that the subducted relief undergoes internal shearing, and produces a permanent flexural bulge of the margin, which uplifted La Plata Island.

Modelling Seismic Wave Propagation for Geophysical Imaging

The Earth is an heterogeneous complex media from the mineral composition scale (10−6m) to the global scale ( 106m). The reconstruction of its structure is a quite challenging problem because sampling methodologies are mainly indirect as potential methods (Gunther et al., 2006; Rucker et al., 2006), diffusive methods (Cognon, 1971; Druskin & Knizhnerman, 1988; Goldman & Stover, 1983; Hohmann, 1988; Kuo & Cho, 1980; Oristaglio & Hohmann, 1984) or propagation methods (Alterman & Karal, 1968; Bolt & Smith, 1976; Dablain, 1986; Kelly et al., 1976; Levander, 1988; Marfurt, 1984; Virieux, 1986). Seismic waves belong to the last category. We shall concentrate in this chapter on the forward problem which will be at the heart of any inverse problem for imaging the Earth. The forward problem is dedicated to the estimation of seismic wavefields when one knows the medium properties while the inverse problem is devoted to the estimation of medium properties from recorded seismic wavefields.

Joint ray + Born least-squares migration and simulated annealing optimization for target-oriented quantitative seismic imaging

A seismic processing workflow based on iterative ray + Born migration/inversion and target-oriented postprocessing of the migrated image is developed for fine-scale quantitative characterization of reflectors. The first step of the workflow involves linear iterations of the ray + Born migration/inversion. The output of the first step is a true-amplitude migrated image parameterized by velocity perturbations. In a second step, postprocessing of the migrated image is performed through a random search with a very-fast simulated annealing (VFSA) algorithm. The forward problem of the global optimization is a simple convolutional model that linearly relates a vertical profile of the band-limited migrated image after depth-to-time conversion to a 1D velocity model composed of a stack of homogeneous layers of arbitrary velocity and thickness. The aim of the postprocessing is to eliminate the limited bandwidth effects of the source from the migrated image for resolution improvement and enhanced geological interpre...

Hierarchical approach of seismic full waveform inversion

Full waveform inversion (FWI) of seismic traces recorded at the free surface allows the reconstruction of the physical parameters structure on the underlying medium. For such a reconstruction, an optimization problem is defined, where synthetic traces, obtained through numerical techniques as finite-difference or finite-element methods in a given model of the subsurface, should match the observed traces. The number of data samples is routinely around 1 billion for 2D problems and 1 trillion for 3D problems while the number of parameters ranges from 1 million to 10 million degrees of freedom. Moreover, if one defines the mismatch as the standard least-squares norm between values sampled in time/frequency and space, the misfit function has a significant number of secondary minima related to the ill-posedness and the nonlinearity of the inversion problem linked to the so-called cycle skipping. Taking into account the size of the problem, we consider a local linearized method where gradient is computed using the adjoint formulation of the seismic wave propagation problem. Starting for an initial model, we consider a quasi-Newtonian method, which allows us to formulate the reconstruction of various parameters such as P and S waves velocities or density or attenuation factors. A hierarchical strategy based on the incremental increase of the data complexity starting from low-frequency content to high-frequency content, from initial wavelets to later phases in the data space from narrow azimuths to wide azimuths and from simple observables to more complex ones. Different synthetic examples on realistic structures illustrate the efficiency of this strategy based on the data manipulation. This strategy related to the data space has to be inserted into a more global framework where we could improve significantly the probability to converge to the global minimum. When considering the model space, we may rely on the construction of the initial model or add constraints such as smoothness of the searched model and/or prior informations collected by other means. An alternative strategy concerns the building of the objective function and various possibilities must be considered, which may increase the linearity of the inversion procedure.

Imaging of VTI media by elastic frequency‐domain full‐waveform inversion of global offset data

It is well acknowledged that accounting for anisotropy in seismic imaging improves focusing and depth positioning of reflectors. Indeed, at present day, seismic imaging of anisotropic media still remains one of the most challenging problem in exploration geophysics because of the possible coupling between the different anisotropic parameters. In this study, we develop a frequency-domain full-waveform inversion (FWI) method for imaging 2D visco-elastic VTI media from wideaperture data. Frequency-domain seismic modeling is performed in VTI media with a hp-adaptive finite-element discontinuous Galerkin (DG) method implemented on unstructured triangular meshes that allows for accurate seismic modeling in complex media with reflectors of arbitrary shape. The inversion relies on a quasi-Newton algorithm which allows for proper scaling of misfit-function gradients associated with different parameter classes. The model parameters are either the P and S wave speeds on the symmetry axis and the Thomsen’s parameters δ and e , or the stiffness coefficients c11, c33, c13 and c44.

Mixed‐grid finite‐difference frequency‐domain viscoacoustic modeling in 2D TTI anisotropic media

We present a 2D finite-difference frequency-domain method for modeling viscoacoustic wave propagation in TTI media. The numerical method relies on a parsimonious staggered-grid method implemented in the frequency domain. Differential operators are discretized along different rotated coordinate systems (the classic Cartesian one and a 45o rotated one) with second-order accurate staggered-grid stencils. The resulting discrete operators are combined linearly to mitigate numerical anisotropy. An anti-lumped mass strategy is applied to mitigate numerical dispersion. A dispersion analysis for infinite homogeneous media suggests a discretization rule of 5 grid points per wavelength. Numerical tests confirm the accuracy of the stencil.

Direct and indirect inversions

A bridge is highlighted between the direct inversion and the indirect inversion. They are based on fundamental different approaches: one is looking after a projection from the data space to the model space while the other one is reducing a misfit between observed data and synthetic data obtained from a given model. However, it is possible to obtain similar structures for model perturbation, and we shall focus on P-wave velocity reconstruction. This bridge is built up through the Born approximation linearizing the forward problem with respect to model perturbation and through asymptotic approximations of the Green functions of the wave propagation equation. We first describe the direct inversion and its ingredients and then we focus on a specific misfit function design leading to a indirect inversion. Finally, we shall compare this indirect inversion with more standard least-squares inversion as the FWI, enabling the focus on small weak velocity perturbations on one side and the speed-up of the velocity perturbation reconstruction on the other side. This bridge has been proposed by the group led by Raul Madariaga in the early nineties, emphasizing his leading role in efficient imaging workflows for seismic velocity reconstruction, a drastic requirement at that time.

An overview of the SEISCOPE project on frequency-domain Full Waveform Inversion Multiparameter inversion and efficient 3D full-waveform inversion

We present an overview of the SEISCOPE project on frequency-domain full waveform inversion (FWI). The two main objectives are the reconstruction of multiple classes of parameters and the 3D acoustic and elastic FWI. The optimization relies on a preconditioned L-BFGS algorithm which provided scaled gradients of the misfit function for each classes of parameter. For onshore applications where body waves and surface waves are jointly inverted, P- and S-wave velocities (VP and VS) must be reconstructed simultaneously using a hierarchical inversion algorithm with two nested levels of data preconditioning with respect to frequency and arrival time. Simultaneous inversion of multiple frequencies rather than successive inversions of single frequencies significantly increases the S/N ratio of the models. For offshore applications where VS can have a minor footprint in the data, a hierarchical approach which first reconstructsVP in the acoustic approximation from the hydrophone component followed by the joint reconstruction of VP and VS from the geophone components can be the approach of choice. Among all the possible minimization criteria, we found that the L1 norm provides the most robust and easy-to-tune criterion as expected for this norm. In particular, it allowed us to successfully reconstruct VP and VS on a realistic synthetic offshore case study, when white noise with outliers has been added to the data. The feasibility of 3D FWI is highly dependent on the efficiency of the seismic modelling. Frequency-domain modelling based on direct solver allows one to tackle small-scale problems involving few millions of unknowns at low frequencies. If the seismic modelling engine embeds expensive source-dependent tasks, source encoding can be used to mitigate the computational burden of multiple-source modelling. However, we have shown the sensitivity of the source encoding to noise in the framework of efficient frequency-domain FWI where a limited number of frequencies is inverted sequentially. Simultaneous inversion of multiple frequencies is required to achieve an acceptable S/N ratio with a reasonable number of FWI iterations. Therefore, time-domain modelling for the estimation of harmonic components of the solution can be the approach of choice for 3D frequency-domain FWI because it allows one to extract an arbitrary number of frequencies at a minimum extra cost.

2D fine-scale imaging of the subduction channel in Gulf of Guayaquil by integrated iterative PSDM and simulated annealing optimization

To analyze the physical properties of seismic reflectors as possible indicators of the presence of fluids, we apply a processing sequence based on preserved amplitude prestack depth migration/inversion (PSDM) coupled with a post-processing of the depth migrated image. Aim of the post-processing is to remove the effects of the limited source bandwidth, that is, to build a structural velocity model and an impulsional migrated section from the limited-bandwidth migrated image and to estimate the uncertainties of velocities and layer thicknesses.We present here an application of this depth-domain processing sequence to a 2D multichannel seismic reflection dataset for the study of the decollement reflector in the Gulf of Guayaquil (Ecuadorian margin). Preliminary results show that the decollement mainly corresponds to a layer of 80–100 meters in thickness with a mean and maximum negative velocity contrasts of −50 m/s and −150m/s respectively on top of it. Along the decollement, these negative velocity contrasts result from the contrast in the physical properties between the subducted sediments and the overriding plate materials above the decollement. Very likely, this velocity decrease is also associated with changes in fluid pressure.