Paul Cristini

Some illustrative examples of the use of a spectral-element method in ocean acoustics

Some numerical results in the time domain obtained with the spectral-element method are presented in order to illustrate the high potential of this technique for modeling the propagation of acoustic waves in the ocean in complex configurations. A validation for a simple configuration with a known solution is shown, followed by some simulations of the propagation of acoustic waves over different types of ocean bottoms (fluid, elastic, and porous) to emphasize the wide variety of media that can be considered within the framework of this method. Finally, a movie illustrating upslope propagation over a viscoelastic wedge is presented and discussed.

What is a seismic reflector like

The spatial region that is in the vicinity of an interface and actually affects the interface response, and hence the reflected wavefield, is of particular interest for the characterization of reflectors from a seismic viewpoint. This region is represented by a volume of integration of medium properties above and below the interface whose maximum lateral extent corresponds to the lateral extent of the interface Fresnel zone, and whose maximum vertical extent is equal to a thickness we evaluate approximately for subcritical incidence angles for a plane interface as well as for curved interfaces of anticline and syncline type. The maximum vertical extent might be larger than the seismic wavelengths for subcritical incidence angles close to the critical angle and for a strong impedance contrast at the interface. Although the part of the reflector volume lying below the interface and affecting traveltime measurements actually is smaller than described in previous studies, the whole part of the reflector volume that affects the amplitude of the reflected wavefield is larger than estimates in previous studies, which considered only the spatial region below the interface. For a syncline respectively, an anticline, it is larger respectively, smaller than described for a plane interface. In addition to providing more physical insights into the wave reflection process, this study might have significant implications for seismic interpretation using amplitude-variation-with-angle methodologies.

Numerical modeling with high performance computing of seismic waves for complex marine environments: Benchmarking with laboratory experiments

Numerical simulations are widely used for forward and inverse problems in seismic exploration to investigate different wave propagation phenomena. However, the numerical results are hard to be compared to real seismic measurements as the subsurface is never exactly known. Using laboratory measurements for small-scale physical models can provide a valuable link between purely numerical and real seismic datasets. We present a case study for comparing ultrasonic data for a complex model with spectral-element and finite-difference synthetic results. The small-scale model was immersed in a water tank. Reflection data was recorded with piezoelectric transducers using a conventional pulse-echo technique. We paid special attention to the implementation of the real source signal—and radiation pattern—in the numerical domain. It involved a laboratory calibration measurement, followed by an inversion process. The model geometry was implemented using a non-structured mesh for the spectral-element simulations. The com...

Some examples of the application of high-performance computing for time-domain full-wave simulations in underwater acoustics using a spectral-element method

Being able to perform accurate time-domain full-wave simulations in underwater acoustics is important within the context of complex environments. Among the numerical methods that can be used to perform such types of simulations, the spectral-element method is a method of choice because it can take advantage of the possibilities offered by high-performance computing. This capability is very important because accurate numerical simulations require a high computational power. In this presentation we will show some examples of the use a spectral-element method for underwater acoustics applications. 2D simulations as well as 3D simulations will be considered for various configurations, illustrating the interest of performing such simulations. Shallow water propagation, deep water propagation as well as diffraction by objects in complex environments will be analyzed.

An immersed interface method for the solution of the standard parabolic equation in range-dependent ocean environments

A numerical approach for the treatment of irregular ocean bottoms within the framework of the standard parabolic equation is proposed. The present technique is based on the immersed interface method originally developed by LeVeque and Li [(1994). SIAM J. Numer. Anal. 31(4), 1019-1044]. The method conserves energy to high order accuracy and naturally handles generic range-dependent bathymetries, without requiring any additional specific numerical procedure. An illustration of its capabilities is provided by solving the well-known wedge problem.

Microseismic wavefield separation using multi‐channel chirplet decomposition

Small earthquakes and acoustic emissions making up microseismic events are characterized by interfering complex wavefields. Many authors have discussed the problem of achieving satisfactorily wavefield separation process mainly by considering propagation only as elastic and specular. Because microseismic wavefield is based on specular and not specular propagation with dispersion and scattering phenomena, conventional wavefield separation methods are no longer efficient. In this paper, a new type of wavefield separation approach is proposed allowing each event to vary independently in amplitude, phase, time-shift and waveform while it propagates across the microseismic array. This method is based on a multi-channel generalized wavelet transform characterized by the fact that the microseismic wavefield is decomposed into a weighted sum of atoms known as chirplets. A dictionary consisted of collections of parameterized chirplets allows a powerful adaptability to quantify the morphological attributes of the recorded microseismic events. The decomposition is performed through an algorithm that combines a conventional Matching Pursuit algorithm with a combinatorial algorithm providing the atomic decomposition in an optimal way.