Locating point diffractors in layered media by spatial dynamics

We present a new approach to the problem of detecting point diffractors from active source surface seismic data. We formulate an optimization problem in the configuration space of possible collections of scatterers and construct a birth-and-death spatial dynamic, which converges to the optimal solution. By design, this dynamic does not have resolution limits typical of migration based techniques, which allows for subwavelength sensing.Massachusetts Institute of Technology. Earth Resources Laborator

Kinematic redatuming by two source interferometry

Interferometry is a method of redatuming physical sources to receiver locations. Under idealized assumptions stacking the cross correlogram of the two common receiver gathers yields a bandlimited Green's function between the receivers. Geometrically this process amounts to isolating a physical source, which generates a path containing both receivers, and canceling the common part. In this paper, we show that in order to recover the travel time between two receivers, one could creatively use rays from more than one physical source. With this approach redatuming is possible even in situations where the conventional interferometry fails.Massachusetts Institute of Technology. Earth Resources Laborator

Effect of velocity uncertainty on migrated reflectors

We study the problem of uncertainty quantification for migrated images. A traditional migrated image contains deterministic reconstructions of subsurface structures. However, the input parameters used in migration, such as reflection data and a velocity model, are inherently uncertain. This uncertainty is carried through to the migrated images. We use Bayesian analysis to quantify the uncertainty of migrated structures by constructing a joint statistical distribution of the structures in question. From this distribution we can deduce the uncertainty in absolute positions of the structures, or a relative position of one structure with respect to another. In some cases the relative position has a much smaller uncertainty than the absolute position

Detecting medium changes from coda by interferometry

In many applications, sequestering CO[subscript 2] 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 possibility, discussed here, of using such techniques to monitor CO[subscript 2] sequestration sites for leakage.Massachusetts Institute of Technology. Earth Resources Laborator

What moved where?: The impact of velocity uncertainty on microseismic location and moment-tensor inversion

With the rise of unconventional resources, microseismic monitoring is becoming increasingly important because of its cost-effectiveness. This has led to significant research activity on how best to locate events and characterize their moment tensors. Locations tell us where fracturing is occurring, allow the tracking of fluid movement, and fracture propagation. Moment tensors help to determine the type of failure occurring, which is beneficial in planning and interpreting the results of hydraulic-fracturing jobs and in monitoring production. The rising number of methods to determine parameters raises important questions about how uncertainties in the input parameters are translated into uncertainties in the final locations and moment tensors. We present a framework for assessing these uncertainties and use it to demonstrate how velocity uncertainty — as well as uncertainties in arrival times and amplitudes — translates into uncertainties on the recovered quantities of location and moment-tensor parameters

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 Green's 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 Green's 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

Relative event localization in uncertain velocity model

We study a problem of localization of an unknown event location relative to previously located events using a single monitoring array in a monitoring well. It has been shown that using the available information about the previously located events for locating new events is advantageous to localizing each event independently. We compare the performance of two previously proposed localization methods, double-difference and interferometry, in varying signal noise and velocity uncertainty, and propose a framework for selecting the optimal method for a given experiment

Improved Green’s functions from seismic interferometry

Under certain theoretical assumptions, the theory of seismic interferometry allows the construction of artificial (or virtual) sources and receivers at the locations of receivers in a physical experiment. This is done by redatuming the physical sources to be at the locations of the physical receivers. Each redatumed trace is formed by stacking the cross-correlations of appropriate recorded traces from each physical shot. For the resulting stacked traces to be a valid approximation certain requirements, like an adequate number of surface sources with a small enough spacing in the acquisition geometry, must be met. If these requirements are not met, the resulting virtual shot gather will contain artifacts. In this paper, we analyze both the sets of correlated traces (correlograms) and their stack. We observe that it is possible to reduce certain artifacts in the stacked traces by novel filtering operations. These filtering operations may have broad utility in all of seismic interferometric applications.Massachusetts Institute of Technology. Earth Resources Laborator

Joint location of microseismic events in the presence of velocity uncertainty

The locations of seismic events are used to infer reservoir properties and to guide future production activity, as well as to determine and understand the stress field. Thus, locating seismic events with uncertainty quantification remains an important problem. Using Bayesian analysis, a joint probability density function of all event locations was constructed from prior information about picking errors in kinematic data and explicitly quantified velocity model uncertainty. Simultaneous location of all seismic events captured the absolute event locations and the relative locations of some events with respect to others, along with their associated uncertainties. We found that the influence of an uncertain velocity model on location uncertainty under many realistic scenarios can be significantly reduced by jointly locating events. Many quantities of interest that are estimated from multiple event locations, such as fault sizes and fracture spacing or orientation, can be better estimated in practice using the proposed approach

Interferometric correlogram-space analysis

Seismic interferometry is a method of obtaining a virtual shot gather from a collection of actual shot gathers. The set of traces corresponding to multiple actual shots recorded at two receivers is used to synthesize a virtual shot located at one of the receivers and a virtual receiver at the other. An estimate of a Green’s function between these two receivers is obtained by first cross-correlating pairs of traces from each of the common 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 a surface source reflected by flat or dipping layers and/or diffracted by point inclusions. The model is purely acoustic. The shape of events in the cross-correlogram space can be used to infer the location and geometry of a subsurface structure. A pilot wavelet created by a curvilinear stacking process is used as a detector of predicted events in the cross-correlogram. Results of a semblance-based velocity scan of the cross-correlograms using curvilinear stacks can be used to improve the quality of the virtual gather.Massachusetts Institute of Technology. Earth Resources Laborator