Existing techniques in correlation spectroscopy, such as coda wave interferometry and diffusing acoustic wave spectroscopy, determine the average motion of scatterers or change in the propagation velocity from the temporal change of multiply scattered sound. However, neither of them gives an indication of the spatial extent of the change in the medium. This study is an extension of the technique coda wave interferometry, where multiply scattered waves are used to determine the change in the wave field due to a localized perturbation in the propagation velocity. Here, the propagation of multiply scattered sound is described using the diffusion approximation, which allows the cross-correlation function of the unperturbed and perturbed wave fields to be related to the localized change in the propagation velocity. The technique is tested numerically for two-dimensional ͑2D͒ acoustic waves using synthetic seismograms calculated using finite-differences before and after a small perturbation in the propagation velocity has been introduced. Despite the relatively small size and magnitude of the change, multiple scattering greatly amplifies small perturbations, making changes in the phase or travel time of the wave field visible in the later-arriving waveforms. Potential applications of this technique include nondestructive evaluation of inhomogeneous materials and time-lapse monitoring of volcanoes and highly heterogeneous reservoirs.

S U M M A R YWe present a technique based on the single-scattering approximation that relates time-lapse localized changes in the propagation velocity to changes in the traveltime of singly scattered waves. We describe wave propagation in a random medium with homogeneous statistical properties as a single-scattering process where the fluctuations of the velocity with respect to the background velocity are assumed to be weak. This corresponds to one of two end-member regimes of wave propagation in a random medium, the first being single scattering, and the second multiple scattering. We present a formulation that relates the change in the traveltime of the scattered waves to a localized change in the propagation velocity by means of the Born approximation for the scattered wavefield. We validate the methodology with synthetic seismograms calculated with finite differences for 2-D acoustic waves. Potential applications of this technique include non-destructive evaluation of heterogeneous materials and time-lapse monitoring of heterogeneous reservoirs.

Previous formulations of coda wave interferometry make it possible to assess the average change of the medium, but they do not allow for the spatial localization of this change (Snieder et al., 2002; Snieder, 2002). We present an approach for localizing temporal changes in the medium using strongly scattered waves, and test it with numerical models for 2D scalar waves. Using an integral representation for the diffuse wavefield, we derive an expression for the mean traveltime perturbation due to a small perturbation in the slowness. We validate the theory using synthetic seismograms calculated with a finite-difference algorithm. In general, for localized slowness perturbations, the theory predicts the mean traveltime change of the diffuse wavefield in a multiplescattering medium. The technique presented here can be used in many applications such as medical imaging, non-destructive testing, and reservoir monitoring, to infer temporal changes of the multiple-scattering medium.

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Pumping sand through coiled tubing (CT) with real-time capabilities is not a common practice because of potential risks associated with cable integrity. A successful sand plug settling procedure supported by a real-time fiber-optic integrated system under critical well conditions was of high importance during a recompletion intervention, allowing optimization of time and costs. Multiple methods are used to isolate a well during recompletion activities; nevertheless, a cost-effective method to divert involves setting sand plugs with CT and a real-time fiber-optic integrated system, which is essential to achieving precise settlement of the sand, not just for depth but also for volume of sand pumped. Without this complete system, the operator would need to make extra runs for correlations with electric line (e-line) or CT units, which increases both cost and operational time. A real-time fiber-optic integrated system allows adjustment to the sand plug stages in real time to help ensure top of sand (TS) necessary to isolate the producer formation and keep out the wireline entry guide without additional runs and increased costs. A casing collar locator (CCL) tool permitted the correlation depth to be measured in each tag, ensuring knowledge of where the sand was placed and helping prevent incorrect depths resulting from uncontrollable factors, such as elongation. More than 6,500 lbm of sand was pumped through CT using a real-time fiber-optic integrated system without losing communication with the downhole tools and without affecting cable integrity, which could lead to bird nesting the cable because of high friction and excessive slack inside the pipe. This real-time fiber-optic integrated system begins a new generation of sand plug operations by helping prevent additional runs or having other units correlate, particularly if a recompletion activity is programmed and space accommodation is a challenge because of the workover unit.