Recent developments in quantum annealing have shown promising results in logistics, life sciences, machine learning and more. However, in the field of geophysical sciences the applications have been limited. A quantum annealing application was developed for residual statics estimation. Residual statics estimation is a highly non-linear problem in geophysical subsurface imaging. The problem is run on a quantum annealer as well as on a hybrid solver. Quantum annealers solve binary quadratic models, which are a specific type of NP-Hard problem. The hybrid solver uses quantum annealers together with classical computers to solve optimisation problems. Two binary quadratic models were developed for the purpose of residual statics estimation, one based on the one-hot encoding and the other on standard binary encoding. These two models were theoretically analysed and subsequently implemented and tested. Tests with synthetic data were done using the quantum annealer. The solutions found with quantum annealing were often only a few bit-flips away from the global optimum. Therefore, the results were further improved by post-processing of the data with the steepest descent method. It was found that the one-hot encoding with steepest descent performed superior to the other methods. As a final test the hybrid solver was used to solve a business-sized and realistically difficult problem. The hybrid solver outperformed a current industry standard cross-correlation solver.

The analysis of microseismic measurements acquired during borehole acquisition surveys is essential for a thorough understanding of the source mechanisms in hydraulic fracturing operations. Due to the injection of high-pressure fluids, induced fractures can produce seismic events of low magnitude that can be recorded and subsequently analyzed to infer the stress field at the location of the event. The seismic moment tensor has been widely used to describe general seismic sources as it can provide information about the type of motion and the distribution of forces. Estimating such quantities from the recorded data can significantly improve the real-time microseismic monitoring operations and help to make assumptions about the structure of the reservoir. However, several challenges have to be faced when working with microseismic borehole measurements. They are characterized by a low signal-to-noise ratio and a limited angle coverage, which may ultimately affect the predictions about the location and the fracturing behavior inside the reservoir. In this thesis the inversion of microseismic measurements for retrieving the moment tensor has been tackled by using a deep feedforward neural network. The seismograms used to train the network were generated through the discrete-wavenumber method. The neural network was used to predict the six independent moment-tensor components and the fault angles from seismic sources at different positions than those used during the training. The predictive capabilities of the network were tested for realistic borehole acquisition geometries and wave propagation models. The moment-tensor components were retrieved with good accuracy when using noisy seismograms and, non-double-couple source mechanisms. As the generation of synthetic data can be expensive in terms of memory consumption, the training and prediction have been also implemented in the frequency domain using only a limited portion of the Fourier transform of the seismograms. The inversion results indicated that using narrow bands can still yield satisfactory results when predicting the moment-tensor components.

A key practice in the development of unconventional hydrocarbon resources is to monitor hydraulic fracturing operations and analyze in detail the induced microseismicity, for understanding the extent of the volume affected by the fractures. Even though microseismic data are one of the few geophysical measurements that can be used for this purpose they are not always used at their full potential: the common analyses are limited to the interpretation of the locations of the induced seismic events in terms of fractured volume, while the propagation and the dynamic evolution of the microseismic events that are directly related to the source process are not studied. The source moment tensor can be used to describe the deformation mechanism occurring at the seismic source and the corresponding geomechanical parameters, which are relevant aspects for the monitoring of hydraulic fracturing operations. Its value can be estimated through an inversion process using the P-wave and S-wave waveforms from the observations at the seismic receivers. However, the limited aperture of the receiver arrays in borehole acquisition is inadequate to solve the inverse problem. The goal of this thesis project is study the feasibility of estimating the source moment tensor with borehole microseismic data making use of machine learning algorithms. The task is done by implementing a forward model to compute waveforms generated by known values of the source moment tensor in a borehole acquisition geometry (forward problem). Forward modeling was carried out using a modied version of the discrete wavenumber method. Afterwards, this data is used to train a neural network to estimate the moment tensor at the source given the microseismic data (inverse problem). The neural network was designed, adapting an existing architecture used in previous studies to solve similar inverse problems. The implementation was done entirely in the Python programming language, using the Tensorflow library for the machine learning parts. The network was trained with the dataset generated in the forward model until reaching an optimal mean squared error minimum. Finally, the capability of the network to invert microseismic measurements and retrieve acceptable values of the source moment-tensor components was tested using synthetic data, resulting in an average prediction accuracy of 0.997. Our results indicate that for this case, a neural network is able to satisfactory invert for the full moment-tensor components. Additionally, the neural network was also trained to handle the presence of Gaussian noise, achieving an average prediction accuracy of 0.990 for tested synthetic data with 10% Gaussian noise.