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Why Gamma Distribution Of Seismic Inter-Event Times: A Theoretical Explanation, Laxman Bokati, Aaron A. Velasco, Vladik Kreinovich Dec 2019

Why Gamma Distribution Of Seismic Inter-Event Times: A Theoretical Explanation, Laxman Bokati, Aaron A. Velasco, Vladik Kreinovich

Departmental Technical Reports (CS)

It is known that the distribution of seismic inter-event times is well described by the Gamma distribution. Recently, this fact has been used to successfully predict major seismic events. In this paper, we explain that the Gamma distribution of seismic inter-event times can be naturally derived from the first principles.


How To Monitor Possible Side Effects Of Enhanced Oil Recovery Process, Jose Manuel Dominguez Esquivel, Solymar Ayala Cortez, Aaron A. Velasco, Vladik Kreinovich Feb 2018

How To Monitor Possible Side Effects Of Enhanced Oil Recovery Process, Jose Manuel Dominguez Esquivel, Solymar Ayala Cortez, Aaron A. Velasco, Vladik Kreinovich

Departmental Technical Reports (CS)

To extract all the oil from a well, petroleum engineers pump hot reactive chemicals into the well. This enhanced oil recovery process needs to be thoroughly monitored, since the aggressively hot liquid can seep out and, if unchecked, eventually pollute the sources of drinking water. At present, to monitor this process, engineers measure the seismic waves generated when the liquid fractures the minerals. However, the resulting seismic waves are weak in comparison with the background noise. Thus, the accuracy with which we can locate the spreading liquid based on these weak signals is low, and we get only a very …


Need For A Large-N Array (And Wavelets And Differences) To Determine The Assumption-Free 3-D Earth Model, Solymar Ayala Cortez, Aaron A. Velasco, Vladik Kreinovich Sep 2017

Need For A Large-N Array (And Wavelets And Differences) To Determine The Assumption-Free 3-D Earth Model, Solymar Ayala Cortez, Aaron A. Velasco, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main objectives of geophysical seismic analysis is to determine the Earth's structure. Usually, to determine this structure, geophysicists supplement the measurement results with additional geophysical assumptions. An important question is: when is it possible to reconstruct the Earth's structure uniquely based on the measurement results only, without the need to use any additional assumptions? In this paper, we show that for this, one needs to use large-N arrays -- 2-D arrays of seismic sensors. To actually perform this reconstruction, we need to use differences between measurements by neighboring sensor and we need to apply wavelet analysis to …


How Geophysicists' Intuition Helps Seismic Data Processing, Afshin Gholamy, Vladik Kreinovich Mar 2015

How Geophysicists' Intuition Helps Seismic Data Processing, Afshin Gholamy, Vladik Kreinovich

Departmental Technical Reports (CS)

In geophysics, signals come with noise. It is desirable to minimize the effect of this noise. If we knew the probabilities of different values of signal and noise, we could use statistical filtering techniques. In geophysics, however, we rarely know the exact values of these probabilities; instead, we have to rely on the expertise and intuition of experts. We show how fuzzy techniques can transform this expertise into precise de-noising methods, we explain that the resulting methods indeed satisfy several natural requirements, and that these methods are in good accordance with heuristic techniques successfully used by geophysicists.