Michael Prange

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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 analyzing confidence(More)
NMR relaxation and diffusion data analysis commonly uses a wide range of methods from simple exponential fitting to Laplace inversions. The pros and cons of these methods are often the subject of intense debate. We show that the ill-conditioned nature of such analysis gives rise to a range of solutions for every method resulting in uncertainty in the(More)
Hydraulic fracturing is the process of injecting high-pressure fluids into a reservoir to induce fractures and thus improve reservoir productivity. Microseismic event localization is used to locate created fractures. Traditionally, events are localized individually. Available information about events already localized is not used to help estimate other(More)
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(More)
Relaxation and diffusion data are often analyzed using a Laplace inversion algorithm that incorporates regularization. Regularization is used because Laplace inversion with finite and noisy data is an ill-conditioned problem for which many solutions exist for a given data set. This paper reports a different approach. Instead of finding a "best" solution by(More)
We have considered the problem of using microseismic data to characterize the flow of injected fluid during hydraulic fracturing. We have developed a simple probabilistic physical model that directly ties the fluid pressure in the subsurface during the injection to observations of induced microseismicity. This tractable model includes key physical(More)
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(More)