Daniela Donno

Curvelet-based multiple prediction

The suppression of multiples is a crucial task when processing seismic reflection data. Using the curvelet transform for surface-related multiple prediction is investigated. From a geophysical point of view, a curvelet can be seen as the representation of a local plane wave and is particularly well suited for seismic data decomposition. For the prediction of multiples in the curvelet domain, first it is proposed to decompose the input data into curvelet coefficients. These coefficients are then convolved together to predict the coefficients associated with multiples, and the final result is obtained by applying the inverse curvelet transform. The curvelet transform offers two advantages. The directional characteristic of curvelets allows for exploitation of Snells law at the sea surface. Moreover, the possible aliasing in the predicted multiple is better managed by using the curvelet multiscale property to weight the prediction according to the low-frequency part of the data. 2D synthetic and field data examples show that some artifacts and aliasing effects are indeed reduced in the multiple prediction with the use of curvelets, thus allowing for an improved multiple subtraction result.

Velocity Estimation with the Normalized Integration Method

In the context of velocity estimation, classical full waveform inversion suffers from many local minima. We propose an alternative method referred as the Normalized Integration Method, where the objective function measures the misfit between the integral of the square of the signal. By integrating a positive function, we only compare functions increasing with time. It appears that the objective function has a more convex shape. We first indicate how to efficiently compute the gradient of the misfit function. We then compare the new approach to the classical full waveform inversion through an application on a simple 2D synthetic data set. This example shows that the new approach can be useful for the determination of the long wavelengths of the velocity model.

A study of the geophysical response of distributed fibre optic acoustic sensors through laboratory‐scale experiments

ABSTRACT In the past few years, distributed acoustic sensing has gained great interest in geophysics. This acquisition technology offers immense improvement in terms of efficiency when compared with current geophysical acquisition methods. However, the fundamentals of the measurement are still not fully understood because direct comparisons of fibre data with conventional geophysical sensors are difficult during field tests. We present downscaled laboratory experiments that enabled us to characterise the relationship between the signals recorded by conventional seismic point receivers and by distributed fibre optic sensors. Interrogation of the distributed optical fibre sensor was performed with a Michelson interferometer because this system is suited to compact test configurations, and it requires only a very simple data processing workflow for extracting the signal outputs. We show acoustic data that were recorded simultaneously by both the fibre optical interferometer and conventional three‐component accelerometers, thus enabling the comparison of sensor performance. We present results focused on the directionality of fibre measurements, on the amplitude variation with angle of incidence, and on the transfer function that allows accelerometer signals to be transformed into optical fibre signals. We conclude that the optical fibre response matches with the array of the displacement differences of the inline accelerometers deployed along the fibre length. Moreover, we also analysed the influence of various types of coupling and fibre cable coating on the signal responses, emphasising the importance of these parameters for field seismic acquisitions when using the distributed fibre optic technology.

Finite-difference strategy for elastic wave modelling on curved staggered grids

Waveform modelling is essential for seismic imaging and inversion. Because including more physical characteristics can potentially yield more accurate Earth models, we analyse strategies for elastic seismic wave propagation modelling including topography. We focus on using finite differences on modified staggered grids. Computational grids can be curved to fit the topography using distribution functions. With the chain rule, the elasto-dynamic formulation is adapted to be solved directly on curved staggered grids. The chain-rule approach is computationally less expensive than the tensorial approach for finite differences below the 6th order, but more expensive than the classical approach for flat topography (i.e. rectangular staggered grids). Free-surface conditions are evaluated and implemented according to the stress image method. Non-reflective boundary conditions are simulated via a Convolutional Perfect Matching Layer. This implementation does not generate spurious diffractions when the free-surface topography is not horizontal, as long as the topography is smoothly curved. Optimal results are obtained when the angle between grid lines at the free surface is orthogonal. The chain-rule implementation shows high accuracy when compared to the analytical solution in the case of the Lamb’s problem, Garvin’s problem and elastic interface.

Alternative Objective Function for Inversion of Surface Waves in 2D Media

The inversion of surface wave properties contributes to the creation of a near-surface model. In seismic exploration, the proper knowledge of the near surface can improve model building in depth. Most surface wave inversion approaches are based on 1D layered models. We propose here to estimate 2D model parameters by using a full waveform inversion approach with an alternative objective function formulated in the frequency-wavenumber domain. In the novel objective function, oscillations are reduced thanks to the exploitation of the dispersive behavior of surface waves that map into localized propagation modes in the frequency-wavenumber domain. Moreover, spatial windowing is used to allow local comparison of modelled and observed data. For the objective function minimization, a gradient-based approach will be used. We implement the adjoint-state method for an efficient gradient computation. We use simple velocity models to show the reliability of our ormulation to localize anomalies, by comparing the gradients computed with the classical full waveform inversion and the novel approach.

A necessary and sufficient condition for the blind extraction of the sparsest source in convolutive mixtures

This paper addresses sparse component analysis, a powerful framework for blind source separation and extraction that is built upon the assumption that the sources of interest are sparse in a known domain. We propose and discuss a necessary and sufficient condition under which the ℓ0 pseudo-norm can be used as a contrast function in the blind source extraction problem in both instantaneous and convolutive mixing models, when the number of observations is at least equal to the number of sources. The obtained conditions allow us to relax the sparsity constraint of the sources to its maximum limit, with possibly overlapping sources. In particular, the W-disjoint orthogonality assumption of the sources can be discarded. Moreover, no assumption is done on the mixing system except invertibility. A differential evolution algorithm based on a smooth approximation of the ℓ0 pseudo-norm is used to illustrate the benefits brought by our contribution.

SEISMIC SIGNAL PROCESSING: SOME RECENT ADVANCES

The goal of this work is to provide a brief overview of some recent advances in the field of seismic signal processing. In particular, we shall focus on tasks such as multiple attenuation and coherent noise elimination, paying special attention to the application of signal separation methods that are able to take into account prior information such as sparsity, which is ubiquitous in reflection seismic. In addition, we briefly review the application of signal transforms, such as wavelets and curvelets, to process seismic data. This article introduces the special session “Seismic Signal Processing”, which covers other applications and methods not discussed here.

2D Surface Wave Inversion in the F-K Domain

Full waveform inversion offers a robust and automated way to estimate high resolution velocity models at the expense of a good initial model. This technique is classically applied on wide angle data, but more rarely on surface waves because of their dispersive nature. However, surface wave information is significantly useful for near surface imaging. We propose to use a modified approach, here named windowed amplitude waveform inversion, as an alternative to the classical full waveform inversion. We first window the input data, then apply a 2D Fourier transform and minimize the misfit between the absolute values. The windowed amplitude waveform inversion is less restrictive with respect to the initial model as shown in a synthetic example. Inversion results confirm that the proposed approach may converge when using initial models for which the classical formulation does not converge to the exact velocity model.

Finite difference resistivity modeling on unstructured grids with large conductivity contrasts

The 3-D geo-electrical forward problem solved with a finite difference approach faces several difficulties. Besides the singularity at the source location, major issues are caused by the definition of the computational domain to match a particular topography, and by high conductivity contrasts. To address these issues, we combine here two methods. First, we implement a specific finite difference method that takes into account specified interfaces in elliptic problems. Here, the contrasts are defined along grid lines. Second, we extend the method to unstructured meshes by integrating it to the generalized finite difference technique. In practice, once the conductivity model is defined, the approach does not need to explicitly specify where the large contrasts are located. Several numerical tests are carried out for various Poisson problems and show a high degree of accuracy.

LS‐DIP: An adaptive dip‐based subtraction of predicted multiples

The adaptive subtraction of the predicted multiples from the input data plays an important role on the overall multiple removal result. The existing least-squares adaptive subtraction in the space-time domain, though quite robust, does have some limitations. In this paper, we propose a novel subtraction approach which combines the advantages of the least-squares and pattern dip-based subtraction methods. The reliability and good results of the proposed subtraction method is tested through application to a real marine dataset.