Another Proof of the Preceding Theory

Another Proof of the Preceding Theory was produced as part of a residency run by Artists in Archeology in conjunction with the Stonehenge Riverside project. The film explores the relationship between science, work and ritual, imagining archaeology as a future cult. As two robed disciples stray off from the dig, they are drawn to the drone of the stones and proceed to play the henge like a gigantic Theremin. Just as a Theremin is played with the hand interfering in an electric circuit and producing sound without contact, so the stones respond to the choreographed bodily proximity. Finally, one of the two continues alone to the avenue at Avebury, where the magnetic pull of the stones reaches its climax. Shot on VHS, the film features a score by Zuzushi Monkey, with percussion and theremin sounds mirroring the action. The performers are mostly artists and archeologists from the art and archaeology teams. The archeologists were encouraged to perform their normal work in the robes, in an attempt to explore the meeting points of science and ritual and interrogate our relationship to an ultimately unknowable prehistoric past where activities we do not understand are relegated to the realm of religion. Stonehenge has unique acoustic properties, it’s large sarsen stones are finely worked on the inside, left rough on the outside, intensifying sound waves within the inner horseshoe, but since their real use, having been built over centuries, remains ambiguous, the film proposes that our attempts to decode them may themselves become encoded in their cumulative meaning for future researchers.

A multiwave range test for obstacle reconstructions with unknown physical properties

We develop a new multiwave version of the range test for shape reconstruction in inverse scattering theory. The range test [R. Potthast, et al., A ‘range test’ for determining scatterers with unknown physical properties, Inverse Problems 19(3) (2003) 533–547] has originally been proposed to obtain knowledge about an unknown scatterer when the far field pattern for only one plane wave is given. Here, we extend the method to the case of multiple waves and show that the full shape of the unknown scatterer can be reconstructed. We further will clarify the relation between the range test methods, the potential method [A. Kirsch, R. Kress, On an integral equation of the first kind in inverse acoustic scattering, in: Inverse Problems (Oberwolfach, 1986), Internationale Schriftenreihe zur Numerischen Mathematik, vol. 77, Birkhäuser, Basel, 1986, pp. 93–102] and the singular sources method [R. Potthast, Point sources and multipoles in inverse scattering theory, Habilitation Thesis, Göttingen, 1999]. In particular, we propose a new version of the Kirsch–Kress method using the range test and a new approach to the singular sources method based on the range test and potential method. Numerical examples of reconstructions for all four methods are provided.

The acoustic signature of fluid flow in complex porous media

Effective medium approximations for the frequency-dependent and complex-valued effective stiffness tensors of cracked/ porous rocks with multiple solid constituents are developed on the basis of the T-matrix approach (based on integral equation methods for quasi-static composites), the elastic - viscoelastic correspondence principle, and a unified treatment of the local and global flow mechanisms, which is consistent with the principle of fluid mass conservation. The main advantage of using the T-matrix approach, rather than the first-order approach of Eshelby or the second-order approach of Hudson, is that it produces physically plausible results even when the volume concentrations of inclusions or cavities are no longer small. The new formulae, which operates with an arbitrary homogeneous (anisotropic) reference medium and contains terms of all order in the volume concentrations of solid particles and communicating cavities, take explicitly account of inclusion shape and spatial distribution independently. We show analytically that an expansion of the T-matrix formulae to first order in the volume concentration of cavities (in agreement with the dilute estimate of Eshelby) has the correct dependence on the properties of the saturating fluid, in the sense that it is consistent with the Brown-Korringa relation, when the frequency is sufficiently low. We present numerical results for the (anisotropic) effective viscoelastic properties of a cracked permeable medium with finite storage porosity, indicating that the complete T-matrix formulae (including the higher-order terms) are generally consistent with the Brown-Korringa relation, at least if we assume the spatial distribution of cavities to be the same for all cavity pairs. We have found an efficient way to treat statistical correlations in the shapes and orientations of the communicating cavities, and also obtained a reasonable match between theoretical predictions (based on a dual porosity model for quartz-clay mixtures, involving relatively flat clay-related pores and more rounded quartz-related pores) and laboratory results for the ultrasonic velocity and attenuation spectra of a suite of typical reservoir rocks. (C) 2003 Elsevier B.V. All rights reserved.

Acoustic and petrophysical relationships in low-shale sandstone reservoir rocks

This paper describes the measurements of the acoustic and petrophysical properties of two suites of low-shale sandstone samples from North Sea hydrocarbon reservoirs, under simulated reservoir conditions. The acoustic velocities and quality factors of the samples, saturated with different pore fluids (brine, dead oil and kerosene), were measured at a frequency of about 0.8 MHz and over a range of pressures from 5 MPa to 40 MPa. The compressional-wave velocity is strongly correlated with the shear-wave velocity in this suite of rocks. The ratio V-P/V-S varies significantly with change of both pore-fluid type and differential pressure, confirming the usefulness of this parameter for seismic monitoring of producing reservoirs. The results of quality factor measurements were compared with predictions from Biot-flow and squirt-flow loss mechanisms. The results suggested that the dominating loss in these samples is due to squirt-flow of fluid between the pores of various geometries. The contribution of the Biot-flow loss mechanism to the total loss is negligible. The compressional-wave quality factor was shown to be inversely correlated with rock permeability, suggesting the possibility of using attenuation as a permeability indicator tool in low-shale, high-porosity sandstone reservoirs.

Ocean acoustic models for low frequency propagation in 2D and 3D environments

In this paper we are mainly concerned with the development of efficient computer models capable of accurately predicting the propagation of low-to-middle frequency sound in the sea, in axially symmetric (2D) and in fully 3D environments. The major physical features of the problem, i.e. a variable bottom topography, elastic properties of the subbottom structure, volume attenuation and other range inhomogeneities are efficiently treated. The computer models presented are based on normal mode solutions of the Helmholtz equation on the one hand, and on various types of numerical schemes for parabolic approximations of the Helmholtz equation on the other. A new coupled mode code is introduced to model sound propagation in range-dependent ocean environments with variable bottom topography, where the effects of an elastic bottom, of volume attenuation, surface and bottom roughness are taken into account. New computer models based on finite difference and finite element techniques for the numerical solution of parabolic approximations are also presented. They include an efficient modeling of the bottom influence via impedance boundary conditions, they cover wide angle propagation, elastic bottom effects, variable bottom topography and reverberation effects. All the models are validated on several benchmark problems and versus experimental data. Results thus obtained were compared with analogous results from standard codes in the literature.