Nicola Bienati

Two-grid stochastic full waveform inversion of 2D marine seismic data

We apply stochastic Full Waveform Inversion (FWI) to 2D marine seismic data to estimate the macro-model velocity field which can be a suitable input for subsequent local (gradient based) FWI. Genetic Algorithms are used as the global optimization method. Our two-grid representation of the subsurface, made of a coarse grid for the inversion and of a fine grid for the modeling, allows us to reduce the number of unknowns to an acceptable number for the given computer resources and to perform a stable and reliable finite difference modeling. Thus, notwithstanding the known high computational costs that characterize global inversion methods, we are able to reconstruct a smooth, low wavenumber, acoustic velocity model of the subsurface. The reliability of the estimated velocity macro-model is checked through the inspection of prestack depth migrated gathers and through the superposition of observed and modeled seismograms. The method we propose is less affected by the risk of being trapped in local minima of the misfit functional than gradient based FWI methods, and can be a viable alternative to estimate proper starting models for gradient based full waveform inversions.

Some practical issues related to migration in the angle domain

Summary The benefits of recasting pre-stack depth migration in the angle domain are such to suggest its application in industrial Kirchhoff PSDM software. Here we examine some practical aspects of the implementation in the angle domain, namely those that mostly impact performances and effectiveness: memory requirements, poor illumination and errors in velocity estimation.

Irregular interpolation of seismic data through low-rank tensor approximation

Seismic data usually show irregular spatial sampling because of cable feathering (for marine acquisitions) or physical obstacles in acquisition area (for land surveys). Seismic traces can be also irregularly distributed because of missing or noisy recordings and sensor faults. In recent literature, matrix and tensor rank optimization have been applied to achieve seismic data interpolation and to attenuate unstructured additive noise. In fact, low-rank components can capture the local features of the recorded data, such as envelope and slopes of the events. In this work, we derive a novel interpolation technique based on the low-rank approximation of matrices and tensors, which can interpolate irregularly sampled seismic data onto an arbitrary output geometry. Results on real data prove the feasibility of the proposed approach.

Comparison of pursuit algorithms for seismic data interpolation imposing sparseness

Recently, technical results from the theory of Compressive Sensing have been applied to the Fourier class of algorithms for solving the ever-increasing seismic data interpolation problem while handling potentially irregularly sampled geometries. The method we here propose makes use of the so-called Conjugate Gradient Pursuit with the Stagewise Selection Strategy, a novel general purpose algorithm for sparse representation, which brings advantages in terms of computational costs when compared to the well-known Matching Pursuit, while not affecting accuracy. The effectiveness and efficiency of the derived interpolation method is proved and compared to the performances of the Matching Pursuit-based interpolation method when applied on a real dataset showing, in turns, intrinsic sampling irregularity and heavy manual trace decimation.

Appraisal problem in the 3D least squares Fourier seismic data reconstruction

Least squares Fourier reconstruction is basically a solution to a discrete linear inverse problem that attempts to recover the Fourier spectrum of the seismic wavefield from irregularly sampled data along the spatial coordinates. The estimated Fourier coefficients are then used to reconstruct the data in a regular grid via a standard inverse Fourier transform (inverse discrete Fourier transform or inverse fast Fourier transform). Unfortunately, this kind of inverse problem is usually under-determined and illconditioned. For this reason, the least squares Fourier reconstruction with minimum norm adopts a damped least squares inversion to retrieve a unique and stable solution. In this work, we show how the damping can introduce artefacts on the reconstructed 3D data. To quantitatively describe this issue, we introduce the concept of “extended” model resolution matrix, and we formulate the reconstruction problem as an appraisal problem. Through the simultaneous analysis of the extended model resolution matrix and of the noise term, we discuss the limits of the Fourier reconstruction with minimum norm reconstruction and assess the validity of the reconstructed data and the possible bias introduced by the inversion process. Also, we can guide the parameterization of the forward problem to minimize the occurrence of unwanted artefacts. A simple synthetic example and real data from a 3D marine common shot gather are used to discuss our approach and to show the results of Fourier reconstruction with minimum norm reconstruction.

Internal multiple attenuation by Kirchhoff extrapolation

Surface-related multiple elimination is the leading methodology for surface multiple removal. This data-driven approach can be extended to interbed multiple prediction at the expense of a huge increase of the computational burden. This cost makes model-driven methods still attractive, especially for the three dimensional case. In this paper we present a methodology that extends Kirchhoff wavefield extrapolation to interbed multiple prediction. In Kirchhoff wavefield extrapolation for surface multiple prediction a single round trip to an interpreted reflector is added to the recorded data. Here we show that interbed multiples generated between two interpreted reflectors can be predicted by applying the Kirchhoff wavefield extrapolation operator twice. In the first extrapolation step Kirchhoff wavefield extrapolation propagates the data backward in time to simulate a round trip to the shallower reflector. In the second extrapolation step Kirchhoff wavefield extrapolation propagates the data forward in time to simulate a round trip to the deeper reflector. In the Kirchhoff extrapolation kernel we use asymptotic Green’s functions. The prediction of multiples via Kirchhoff wavefield extrapolation is possibly sped up by computing the required traveltimes via a shifted hyperbola approximation. The effectiveness of the method is demonstrated by results on both synthetic and field data sets.

Sensitivity Analysis of Joint Diving Wave+Reflection Tomography in Anisotropic Media

It is more and more evident that the transmitted component of the wavefield recorded by reflection acquisitions does contain precious information about velocity. Indeed, the results obtained from firstarrival traveltime tomography, and in general those obtained by the various works recently presented on Full Waveform Inversion are motivating an increasing interest for transmitted waves, i.e. refractions and diving waves.