Wave Field Dynamics Research Articles

Construction and Validation of a Dense Gas Shock Tube

Results from initial tests of a shock tube designed to verify the nonclassical dynamics of Bethe-Zel'dovich-Thompson (BZT) fluids are presented. These tests employed nitrogen at pressures and temperatures required for shock-tube initial conditions that will produce nonclassical phenomena in a BZT fluid. A single-diaphragm, stainless steel shock tube is enclosed in a resistance-heated tube furnace. Each of the 16 segments of the furnace is controlled by a proportional integral differential loop to sustain a uniform temperature along the tube. Water-cooled static and dynamic pressure transducers and thermocouples are used to monitor the static initial conditions and the dynamic wave field. The nitrogen test cases are compared to the ideal gas Riemann problem. The pressure differential of the incident expansion wave matches the theoretical magnitude to within 2%, whereas the average wave speed agrees within 7%

A later-arrival based inversion scheme to recover diffractors and reflectors

Seismic tomography techniques based on first break time inversion are a convenient way to recover velocity fields. However, these techniques only use a small fraction of the available seismogram data. Migration uses entire reflection seismograms but stops short of an actual inversion, using a summing/averaging method. The result is a smeared image of diffractor points, which makes it difficult to image weaker events.In this paper we develop a seismic inversion technique to recover diffractors and reflectors from full-waveform seismograms by direct inversion, rather than a migration-based approach. We choose a simple, idealised modelling scheme to highlight the basic advantages and limitations inherent in this class of inversion techniques, and derive several important and generic guidelines applicable to the design and development of full-waveform-based inversion algorithms.We propose a modelling scheme for diffractions, reflections and refractions in an arbitrary velocity field. By using a sourcewavelet based estimation method, we linearise the forward model and are able to obtain a diffractor/reflector field recovery scheme that is based on standard iterative matrix inversion.Our investigation reveals that the algorithm provides vastly superior resolution of the structure compared to time-of-flight tomography and requires only a surprisingly small number of sources and receivers for successful operation. However, it is highly prone to noise capture, where noise is any system unknown. This translates into inaccuracies in the macro-velocity field estimate and the seismic wave amplitudes. Our experiments show that the background velocity field must be known with an accuracy of better than 1%, suggesting that this class of linearised inversion scheme is unsuitable for field data sets. Nevertheless, the scheme highlights the pitfalls of any full-waveform inversion approach, where without careful calibration, wavefield dynamics can easily be mis-inverted to produce spurious structure.

Resonance layers in the interactions of rapidly oscillating wave fields

Effects pertaining to weak resonance interactions of rapidly oscillating wave fields are investigated. In the general case, there exist narrow transient layers where the wave field dynamics can be described in terms of the nonlinear Schrodinger equation.

Suppression of the Rabi oscillations in a cavity partially filled with a dielectric having a time-dependent refractive index

In this paper the dynamics of wave fields in a cavity, part of which is filled with a dielectric, are investigated. The wave equation is solved approximately using the method of multiple time scales. Phase modulations of the cavity modes in an adiabatic case are given up to the first order. A simple effective field Hamiltonian operator is derived and then used to analyze the interaction of radiation with a two-level atom passing through the cavity. Corrections to the Rabi oscillations due to the time-dependent frequency of the cavity photons are investigated. It is shown that adiabatic time dependence of the refractive index of the dielectric can lead to suppression of the Rabi oscillations of atomic inversion.

ELASTIC PARAMETER ESTIMATION BY COHERENCY OPTIMIZATION1

We present a method for estimating P- and S-velocities within defined layers (macromodel), using only kinematic properties (i.e. traveltimes) of the wavefield. The method does not require identification of mixed-mode events on prestack or post-stack data. After obtaining a Vp-depth model by coherency inversion, S-velocities are determined by coherency optimization along computed traveltime curves for mixed-mode events on prestack data. Since the method does not involve any dynamic wavefield computations, a simple ray-tracing algorithm is used to solve the forward problem. The simplicity of the scheme, together with the ability to apply it locally, makes it highly suitable for interactive use. Results of this method may be used to detect Poisson's ratio anomalies within or between layers and may serve as an initial model for more complicated elastic inversion algorithms.

A method for the numerical solution of problems of the dynamics of wave fields with singularities

A numerical method is presented for solving a non-linear equation of the Schrodinger type, based on a hydrodynamic analogy for Schrodinger's equation and the introduction of Lagrangian mass coordinates.