This thesis is on the mathematics of seismic data acquisition and processing, with a particularfocus on distributed acoustic sensing. Distributed acoustic sensing (DAS) is a relatively newmeans of seismic acquisition. It utilizes strain on a fibre-optic cable to deduce informationabout nearby events. DAS systems possess the potential for a wide variety of applicationsbeyond seismic acquisition including security and monitoring. In order to pursue theseapplications, developing techniques for detecting and identifying events in DAS-acquireddata is essential.
In this thesis, we explore various methods for locating and classifying events in data acquired using a distributed acoustic sensor. We begin with an investigation of reflection and transmission coeffients as they define where events and anomalies occur in data. We find exact solutions for these coeffcients and use them to provide insight into the success of numerical methods in modelling seismic data. Then, we consider seismic processing techniques such as wavelets and time-frequency analysis. We also develop a wavelet transform: the inverted wavelet transform.
An explanation of distributed acoustic sensing and how it works is provided. Afterwards, we produce models of DAS-acquired data and use these models to offer insight into the amplitude response of a DAS system. It also enables the employment of a homotopy to compare different formations of fibre.
Applications to distributed acoustic sensors fill the final chapters of the work. The first example involves the use of DAS for acquiring vertical seismic profiles at the Containment and Monitoring Institute's Field Research Station in Newell County, AB. We then employ Gaussian mixture models and independent component analysis to detect a vehicle signal in data acquired using a DAS system. To address classification of events, we utilize a convolutional neural network to identify events in microseismic data as well as in data monitoring someone walking and digging next to a distributed acoustic sensor. This investigation leads to a discussion of feature-based image registration with regards to distributed acoustic sensii ing acquired data. Finally, we establish the Hyperbola Method to determine the distance between an event and the DAS system from the data.
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