We study the diffusion of monochromatic classical waves in a disordered acoustic medium by scattering theory. In order to avoid artifacts associated with mathematical point scatterers, we model the randomness by small but finite insertions. We derive expressions for the configuration-averaged energy flux, energy density, and intensity for one-, two-, and three-dimensional (3D) systems with an embedded monochromatic source using the ladder approximation to the Bethe-Salpeter equation. We study the transition from ballistic to diffusive wave propagation and obtain results for the frequency dependence of the medium properties such as mean free path and diffusion coefficient as a function of the scattering parameters. We discover characteristic differences of the diffusion in 2D as compared to the conventional 3D case, such as an explicit dependence of the energy flux on the mean free path and quite different expressions for the effective transport velocity.
Distributed Acoustic Sensing (DAS) deployed in multiple wells was used in Brunei for simultaneous recording of seismic signals emitted by a source grid on the surface. Such a configuration works similar to a 3D Vertical Seismic Profiling (VSP) survey with conventional geophones and provides interval velocities, time-depth relationship as well as images below the wells based on the reflected seismic rays. DAS VSP data has provided the opportunity of impacting asset performance by: (1) improving the image of the legacy 3D surface seismic by remigration using the updated shallow velocity model, thus minimizing both the structural as well as the depth uncertainty, and by (2) providing compelling DAS-only 2D and 3D images beneath the wells with higher resolution than the surface seismic. These can be employed for the reservoir static and dynamic model update and identification of sub-surface seismic faults and/or other events. Additionally, this technology presents the possibility of fluid monitoring in this type of reservoir where production is supported by water injection.
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