Oleg V. Poliannikov

Retrieving reflections by source-receiver wavefield interferometry

Source-receiver wavefield interferometry has been proposed recently as an extension of classical correlation-based interferometry. Under idealized assumptions, it allows the Greens function between a source and a receiver to be reconstructed from boundary data that are collected using two closed contours of sources and receivers, respectively. An intuitive geometric description of this method, based on ray theory, can be used to design a method for reconstructing virtual-gather events that typically are lost when conventional interferometry is employed. In classical interferometry, events in the Greens function between two receiver locations are reconstructed by automatically finding a ray that emanates from a stationary source, passes through the virtual source, reflects off the structure, and finally is recorded by the second receiver. The common path to both receivers is then canceled by a suitable crosscorrelation. If illumination of the structure is not ideal, such a ray may not exist and the reflection is not reconstructed. Source-receiver wave interferometry can be given a similar geometric description. The reflection off the structure can be constructed using not one but multiple rays produced simultaneously by two stationary sources. This new redatuming technique proves successful in geometries in which classical interferometry fails. Extensive numerical simulations support these theoretical conclusions.

Interferometric imaging condition for wave-equation migration

The fidelity of depth seismic imaging depends on the accuracy of the velocity models used for wavefield reconstruction. Models can be decomposed in two components, corresponding to large-scale and small-scale variations. In practice, the large-scale velocity model component can be estimated with high accuracy using repeated migration/tomography cycles, but the small-scale component cannot. When the earth has significant small-scale velocity components, wavefield reconstruction does not completely describe the recorded data, and migrated images are perturbed by artifacts. There are two possible ways to address this problem: (1) improve wavefield reconstruction by estimating more accurate velocity models and image using conventional techniques (e.g., wavefield crosscorrelation) or (2) reconstruct wavefields with conventional methods using the known background velocity model but improve the imaging condition to alleviate the artifacts caused by the imprecise reconstruction. Wedescribe the unknown component o...

Interferometric microseism localization using neighboring fracture

We show how interferometric methods can be used to improve the location of microseismic events when those events come from several different fractures and are observed from a single well. This is the standard setup for a multi‐stage hydraulic fracturing experiment. Traditionally, in such experiments each event is located separately. Here, we adapt the interferometric approach to the problem of locating events relative to one another and show that this reduces the uncertainty in location estimates. To completely recover the Greens function between two events with interferometry requires a 2D array of receivers. When only a single observation well is available, we do not attempt to recover the full Greens function, but instead perform a partial redatuming of the data allowing us to reduce the uncertainty in two of the three components of the event location.

How can we use one fracture to locate another

Hydraulic fracturing is an important tool that helps extract fluids from the subsurface. It is critical in applications ranging from enhanced oil recovery to geothermal energy production. As the goal of fracturing is to increase flow rates within the reservoir volume, and because the reservoir is typically heterogeneous, several fractures are often created. Because of confining stresses, most fractures that have been created and remain open are nearly vertical (Zoback et al., 2003). Creating a set of almost parallel fractures is quite common in situations with smoothly varying stress (Figure 1).

Imaging the underside of subducted slabs by interferometry

Seismic interferometry provides tools for redatuming physical data to a receiver or event location. Placing a virtual source close to a structure of interest yields many benefits for imaging. For example, it allows to mitigate the effect of velocity uncertainty in the overburden. Here, we consider the problem of estimating the Green’s function between two earthquakes located inside a subducted slab using earthquake data recorded at the surface. Our primary focus is to obtain an accurate timeimage of a subducted interface. Known techniques, such as classical or source-receiver interferometry, are not directly applicable due to inadequate acquisition geometry. We propose a two-step kinematically correct redatuming procedure that first redatums the data from earthquakes below the subducted interface to the surface via classical interferometry, and then utilizes source-receiver wavefieled interferometry to redatum virtual surface seismic data to the location of a particular earthquake event.

Interferometric correlogram‐space analysis

Seismic interferometry is a method of obtaining a virtual shot gather from a collection of physical shot gathers. The set of traces corresponding to two common receiver gathers from many physical shots is used to synthesize a virtual shot located at one of the receivers and a virtual receiver at the other. An estimate of a Greens function between these two receivers is obtained by first cross-correlating corresponding pairs of traces from each of the shots and then stacking the resulting cross-correlograms. In this paper, we study the structure of cross-correlograms obtained from a VSP acquisition geometry using surface sources and down-hole receivers. The model is purely acoustic and contains flat or dipping layers and/or point inclusions that act as diffractors. Results of a semblance-based moveout scan of the cross-correlograms are used to identify the potential geometry of the reflectors. This new information allows improvements in the quality of the trace at the virtual receiver by either rejecting those moveouts or enhancing them before the stack is performed.

Detecting medium changes from coda by interferometry

In many applications, sequestering CO2 underground for example, determining whether or not the medium has changed is of primary importance, with secondary goals of locating and quantifying that change. We consider an acoustic model of the Earth as a sum of a smooth background velocity, isolated velocity jumps and random small scale fluctuations. Although the first two parts of the model can be determined precisely, the random fluctuations are never known exactly and are thus modeled as a realization of a random process with assumed statistical properties. We exploit the so‐called coda of multiply scattered energy recorded in such models to monitor for change and to localize and quantify that change, by examining the shape and frequency content of correlations of the coda produced by different parts in the medium. These ideas build upon past work in time‐reversal detection methods that have often been limited to theoretical regimes in which the scales of scattering and reflection are strictly separated. This results in an application of time‐reversal detection methods to non‐theoretical regimes in which the separation of scales is not strictly satisfied, opening up the possiblity, discussed here, of using such techniques to monitor CO2 sequestration sites for leakage.

A New Approach to Global Optimiation by an Adapted Diffusion

In this paper, we study a problem of global optimization of an energy functional by a stochastic dynamics with a general diffusion coefficient. The main result is that adapting the diffusion coefficient to the shape of the functional enables the dynamics to escape wide local minima, and attracts it to narrower global minima that are missed by conventional diffusions. We discuss how to properly choose the diffusion coefficient and show numerically the superior performance of the resulting optimization algorithm.

Interferometric Imaging Condition For Wave-equation Migration

The fidelity of depth seismic imaging depends on the accuracy of the velocity models used for wave7 field reconstruction. Models can be decomposed in two components corresponding to large scale 8 and small scale variations. In practice, the large scale velocity model component can be estimated 9 with high accuracy using repeated migration/tomography cycles, but the small scale component 10 cannot. Therefore, wavefield reconstruction does not completely describe the recorded data and 11 migrated images are perturbed by artifacts. 12 There are two possible ways to address this problem: improve wavefield reconstruction by 13 estimating more accurate velocity models and image using conventional techniques (e.g. wavefield 14 cross-correlation), or reconstruct wavefields with conventional methods using the known smooth 15 velocity model, and improve the imaging condition to alleviate the artifacts caused by the imprecise 16 reconstruction, as suggested in this paper. 17 In this paper, the unknown component of the velocity model is described as a random function 18 with local spatial correlations. Imaging data perturbed by such random variations is characterized 19 by statistical instability, i.e. various wavefield components image at wrong locations that depend on 20

Identification of a discrete planar symmetric shape from a single noisy view

In this paper, we propose a method for identifying a discrete planar symmetric shape from an arbitrary viewpoint. Our algorithm is based on a newly proposed notion of a views skeleton. We show that this concept yields projective invariants which facilitate the identification procedure. It is, furthermore, shown that the proposed method may be extended to the case of noisy data to yield an optimal estimate of a shape in question. Substantiating examples are provided.