Some reflections on reflectors and wave amplitudes

International audienceThe paper describes the refl ector from a seismic viewpoint, and investigates the imprint of such a description on the wave reflection process. More specifically, the spatial region in the vicinity of the interface which actually aff ects the refl ected wavefield is determined using the Fresnel volume and the Interface Fresnel zone (IFZ) concepts. This region is represented by a volume of integration of properties above and below the interface whose maximum lateral extent corresponds to the lateral extent of the IFZ, and whose maximum vertical extent corresponds to a thickness we evaluate accurately and which can be greater than the seismic wavelengths. Considering this description of a reflector, we then calculate the amplitude of the P-wave emanating from a point source and recorded at a receiver after its specular reflection on a smooth homogeneous interface between two elastic media. As the problem under consideration can be viewed as a problem of diff raction by the IFZ which is the physically relevant part of the interface which actually aff ects the refl ected wavefi eld in this simple case, we then apply the Angular Spectrum Approach (ASA) combined with the IFZ concept to get the 3D analytical solution. The variation in the refl ected P-wave amplitude evaluated with the ASA, as a function of the incidence angle, is fi nally compared with the plane-wave refl ection coeffi cient, and with the exact solution obtained with the 3D code OASES. Below but close to the critical angle, the prediction of our approximation better fi ts the exact solution than the plane-wave refl ection coefficient, which emphasizes the importance of accounting for the IFZ in amplitude calculations even for a very simple elastic model

Influence of the Interface Fresnel zone on the reflected P-wave amplitude modelling

International audienceThe aim of the paper is to emphasize the importance of accounting for the Fresnel volume and for the Interface Fresnel zone (IFZ) for calculating the amplitude of the P wave emanating from a point source and recorded at a receiver after its specular reflection on a smooth homogeneous interface between elastic media. For this purpose, by considering the problem of interest as a problem of diffraction by the IFZ, that is, the physically relevant part of the interface which actually affects the reflected wavefield, we have developed a method which combines the Angular Spectrum Approach (ASA) with the IFZ concept to get the 3-D analytical solution. The variation in the reflected P-wave amplitude evaluated with the ASA, as a function of the incidence angle, is compared with the plane wave (PW) reflection coefficient and with the exact solution provided by the 3-D code OASES, for one solid/solid configuration and two dominant frequencies of the source. For subcritical incidence angles the geometrical spreading compensation is mostly quite sufficient to reduce the point-source amplitudes to the PW amplitudes. On the contrary, for specific regions of incidence angles for which the geometrical spreading compensation is not sufficient anymore, that is, near the critical region and in the post-critical domain, the ASA combined with the IFZ concept yields better results than the PW theory whatever the dominant frequency of the source, which suggests that the additional application of the IFZ concept is necessary to obtain the reflected P-wave amplitude. Nevertheless, as the ASA combined with the IFZ has been used only for evaluating the contribution of the reflected wavefield at the receiver, its predictions fail when the interference between the reflected wave and the head wave becomes predominant

The Interface Fresnel Zone revisited

We determine the part of reflectors which actually affects the reflected wavefield, which is of particular interest for the characterization of the interfaces from physical and seismic viewpoints, and for seismic resolution. We reformulate the concepts of Fresnel volumes (FV) and Interface Fresnel zones (IFZ), by accounting for all possible rays defining the isochrone for the source-receiver pair and the specular reflected wave. In the case of a plane homogeneous interface, the results obtained with our reformulation (in particular, the size of the IFZ) are identical to previous published works. Nevertheless, with the help of the lens formula of geometrical optics, we propose a correction to the classical expression for the depth penetration of the FV across the interface in the transmission medium, which can result in a depth penetration 50% greater than the classical one. Additionally, we determine a region above the interface in the incidence medium, which is also involved in the wave reflection. Finally, we propose a new definition for the minimal volume of integration and homogenization of properties above and beyond the interface, which is necessary to the evaluation of an effective reflectivity of interfaces with lateral change in physical and geometrical properties

Usefulness of the Interface Fresnel zone for simulating the seismic reflected amplitudes

The aim of the paper is to emphasize the importance of accounting for the Fresnel volume (FV) and for the Interface Fresnel zone (IFZ) for simulating the amplitudes of the spherical waves reflected from an interface between elastic media and recorded at the receiver. For this purpose, by considering the problem of interest as a problem of diffraction by the IFZ, we have developed a method wich combines the Angular Spectrum Approach (ASA) with the IFZ concept to get the 3D analytical solution. The comparison between the amplitude-versusangle curve predicted by our approximation with that predicted by the classical plane-wave theory, and also with the exact solution, clearly enlightens three points. First, for specific regions of incidence angles, for which the geometrical-spreading compensation is not sufficient anymore to reduce the point-source amplitudes to the plane-wave amplitudes, the additional application of the FV and of IFZ concept is necessary. Second, as our approximation is concerned only with the reflected wave, its predictions fit well the exact solution, provided there is no interference between the reflected wave and the head wave. Third, they exhibit oscillations in the postcritical region which result from the interference of the IFZ with the sharp edge of the reflection coefficient

Wavefront decomposition and propagation through complex models with analytical ray theory and signal processing

We present a novel method which can perform the fast computation of the times of arrival of seismic waves which propagate between a source and an array of receivers in a stratified medium. This method combines signal processing concepts for the approximation of interfaces and wavefronts, and ray theory for the propagation of wavefronts. This new approach leads to the redefinition and simplification of the model through which waves propagate. The modifications are governed by the spectral characteristics of the source signal. All rays are computed without any omission at a much lower cost in computing time than classical method

THIS COMMUNICATION IS CANCELLED (PAPER IS AVAILABLE). Laboratory benchmarks vs. Synthetic modeling of seismic wave propagation in complex environments (BENCHIE Project)

International audienceAccurate simulations of seismic wave propagation in complex geological structures with great and rapid variations of topography are of primary interest for environmental & industrial applications. Unfortunately, difficulties arise for such complex environments, due essentially to the existence of shadow zones, head waves, diffractions & edge effects. Usually, methods and codes are tested against " validated " ones, but one might wonder which method/code ultimately approaches the " real " solution. An original approach for seismics is to compare synthetic seismic data to controlled laboratory data for a well-described configuration, in order to analyze the respective limitations of each method/code. This is one of the objectives of the BENCHIE project. In this presentation we will present some preliminary results provided by both laboratory experiments conducted in a tank and numerical simulations of wave propagation. The laboratory data have been obtained by zero-offset acquisitions at different ultrasonic frequencies on the Marseille model which is made up of anticlines, fault and truncated pyramid. The numerical results have been obtained by two methods: the Spectral-Element Method and the Tip-Wave Superposition Method

Wavefield extraction using multi-channel chirplet decomposition

International audienceIn acoustical and seismic fields, wavefield extraction has alwaysbeen a crucial issue to solve inverse problem. Depending on the experimentalconfiguration, conventional methods of wavefield decomposition might nolonger likely to hold. In this paper, an original approach is proposed based ona multichannel decomposition of the signal into a weighted sum of elementaryfunctions known as chirplets. Each chirplet is described by physical parametersand the collection of chirplets makes up a large adaptable dictionary,so that a chirplet corresponds unambiguously to one wave componen

An axisymmetric time-domain spectral-element method for full-wave simulations: Application to ocean acoustics

The numerical simulation of acoustic waves in complex 3D media is a key topic in many branches of science, from exploration geophysics to non-destructive testing and medical imaging. With the drastic increase in computing capabilities this field has dramatically grown in the last twenty years. However many 3D computations, especially at high frequency and/or long range, are still far beyond current reach and force researchers to resort to approximations, for example by working in 2D (plane strain) or by using a paraxial approximation. This article presents and validates a numerical technique based on an axisymmetric formulation of a spectral finite-element method in the time domain for heterogeneous fluid-solid media. Taking advantage of axisymmetry enables the study of relevant 3D configurations at a very moderate computational cost. The axisymmetric spectral-element formulation is first introduced, and validation tests are then performed. A typical application of interest in ocean acoustics showing upslope propagation above a dipping viscoelastic ocean bottom is then presented. The method correctly models backscattered waves and explains the transmission losses discrepancies pointed out in Jensen et al. (2007). Finally, a realistic application to a double seamount problem is considered.Comment: Added a reference, and fixed a typo (cylindrical versus spherical

Broadband transmission losses and time dispersion maps from time-domain numerical simulations in ocean acoustics

In this letter, a procedure for the calculation of transmission loss maps from numerical simulations in the time domain is presented. It can be generalized to arbitrary time sequences and to elastic media and provides an insight into how energy spreads into a complex configuration. In addition, time dispersion maps can be generated. These maps provide additional information on how energy is distributed over time. Transmission loss and time dispersion maps are generated at a negligible additional computational cost. To illustrate the type of transmission loss maps that can be produced by the time-domain method, the problem of the classical two-dimensional upslope wedge with a fluid bottom is addressed. The results obtained are compared to those obtained previously based on a parabolic equation. Then, for the same configuration, maps for an elastic bottom and maps for non-monochromatic signals are computed