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

A unified Bayesian framework for relative microseismic location

We study the problem of determining an unknown microseismic event location relative to previously located events using a single monitoring array in a monitoring well. We show that using the available information about the previously located events for locating new events is advantageous compared to locating each event independently. By analysing confidence regions, we compare the performance of two previously proposed location methods, double-difference and interferometry, for varying signal-to-noise ratio and uncertainty in the velocity model. We show that one method may have an advantage over another depending on the experiment geometry, assumptions about uncertainty in velocity and recorded signal, etc. We propose a unified approach to relative event location that includes double-difference and interferometry as special cases, and is applicable to velocity models and well geometries of arbitrary complexity, producing location estimators that are superior to those of double-difference and interferometry

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

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

Joint microseismic event location with uncertain velocity

We study the problem of the joint location of seismic events using an array of receivers. We show that locating multiple seismic events simultaneously is advantageous compared to the more traditional approaches of locating each event independently. Joint location, by design, includes estimating an uncertainty distribution on the absolute position of the events. From this can be deduced the distribution on the relative position of one event with respect to others. Many quantities of interest, such as fault sizes, fracture spacing or orientation, can be directly estimated from the joint distribution of seismic events. Event relocation methods usually update only the target event, while keeping the reference events fixed. Our joint approach can be used to update the locations of all events simultaneously. The joint approach can also be used in a Bayesian sense as prior information in locating a new event.Massachusetts Institute of Technology. Earth Resources Laboratory (Founding Members Consortium); National Science Foundation (U.S.) (Grant SES-0962484

A unified framework for relative source localization using correlograms

We study the problem of determining an unknown event location relative to previously located events using a single monitoring array in a monitoring well. We show that using the available information about the previously located events for locating new events is advantageous to localizing each event independently. By analyzing confidence regions, we compare the performance of two previously proposed localization methods, double-difference and interferometry, in varying signal noise and velocity uncertainty. We show that the double-difference method combats the signal noise much better due to the averaging over a larger number of travel time measurements. The interferometric method is superior where the main source of error is the velocity uncertainty between the event locations and the monitoring array. We propose a hybrid method that automatically balances these two approaches and produces a location estimator that is superior to either.ConocoPhillips (Firm