Copyright (c) 2009 All rights reserved. http://works.bepress.com/kasper_van_wijk Recent documents in Kasper van Wijk en-us Tue, 22 Sep 2009 23:41:21 PDT 3600 http://works.bepress.com/kasper_van_wijk/7 http://works.bepress.com/kasper_van_wijk/7 Mon, 21 Sep 2009 11:46:03 PDT Radiative transfer (RT) theory is often invoked to describe energy propagation in strongly scattering media. Fitting RT to measured wave field intensities is rather different at late times, when the transport is diffusive, than at intermediate times (around one extinction mean free time), when ballistic and diffusive behavior coexist. While there are many examples of late-time RT fits, we describe ultrasonic multiple scattering measurements with RT over the entire range of times--from ballistic to diffusive. In addition to allowing us to retrieve the scattering and absorption mean free paths independently, our results also support theoretical predictions in 1D that suggest an intermediate regime of diffusive (nonlocalized) behavior. Kasper van Wijk http://works.bepress.com/kasper_van_wijk/6 http://works.bepress.com/kasper_van_wijk/6 Wed, 14 Jan 2009 13:18:49 PST Anisotropic attenuation can provide sensitive attributes for fracture detection and lithology discrimination. This paper analyzes measurements of the P-wave attenuation coefficient in a transversely isotropic sample made of phenolic material. Using the spectral-ratio method, we estimate the group (effective) attenuation coefficient of P-waves transmitted through the sample for a wide range of propagation angles (from 0° to 90°) with the symmetry axis. Correction for the difference between the group and phase angles and for the angular velocity variation help us to obtain the normalized phase attenuation coefficient A governed by the Thomsen-style attenuation-anisotropy parameters εQ and δQ. Whereas the symmetry axis of the angle-dependent coefficient practically coincides with that of the velocity function, the magnitude of the attenuation anisotropy far exceeds that of the velocity anisotropy. The quality factor Q increases more than tenfold from the symmetry axis (slow direction) to the isotropy plane (fast direction). Inversion of the coefficient using the Christoffel equation yields large negative values of the parameters εQ and δQ. . The robustness of our results critically depends on several factors, such as the availability of an accurate anisotropic velocity model and adequacy of the homogeneous concept of wave propagation, as well as the choice of the frequency band. The methodology discussed here can be extended to field measurements of anisotropic attenuation needed for AVO (amplitude-variation-with-offset) analysis, amplitude-preserving migration, and seismic fracture detection. Kasper van Wijk http://works.bepress.com/kasper_van_wijk/5 http://works.bepress.com/kasper_van_wijk/5 Wed, 14 Jan 2009 13:18:46 PST The extraction of the Green's function by cross correlation of waves recorded at two receivers nowadays finds much application. We show that for an arbitrary small scatterer, the cross terms of scattered waves give an unphysical wave with an arrival time that is independent of the source position. This constitutes an apparent inconsistency because theory predicts that such spurious arrivals do not arise, after integration over a complete source aperture. This puzzling inconsistency can be resolved for an arbitrary scatterer by integrating the contribution of all sources in the stationary phase approximation to show that the stationary phase contributions to the source integral cancel the spurious arrival by virtue of the generalized optical theorem. This work constitutes an alternative derivation of this theorem. When the source aperture is incomplete, the spurious arrival is not canceled and could be misinterpreted to be part of the Green's function. We give an example of how spurious arrivals provide information about the medium complementary to that given by the direct and scattered waves; the spurious waves can thus potentially be used to better constrain the medium. Kasper van Wijk http://works.bepress.com/kasper_van_wijk/4 http://works.bepress.com/kasper_van_wijk/4 Wed, 14 Jan 2009 13:18:43 PST We present a pair of coupled partial differential equations to describe the evolution of the average total intensity and intensity flux of a wave field inside a randomly layered medium. These equations represent a modification of the Kubelka-Munk equations, or radiative transfer. Our modification accounts for wave interference (e.g., localization), which is neglected in radiative transfer. We numerically solve the modified Kubelka-Munk equations and compare the results to radiative transfer as well as to simulations of the wave equation with randomly located thin layers. Kasper van Wijk