Retrieving accurate microseismic source locations induced by hydraulic-fracturing operations is an important step to gain insights into the hydraulically stimulated reservoir volume. Recently, deep neural networks have been proposed that directly recover source locations from the seismic waveforms. The optimal performance of the proposed deep neural networks usually requires large training sets. The need for a large training set can be circumvented if a previously trained deep neural network can be used to start the training process with its weights instead of randomly initialized weights. These weights can then be fine-tuned using a smaller training set, which is also known as transfer learning. In this work, we implement a transfer learning workflow to update the weights of a deep neural network that was initially trained on a large synthetic dataset to localize microseismic events. We present two methods of processing, namely one post-monitoring mode and one continuous mode where the processing takes place during the monitoring period. We apply the methods to field data from a hydraulic fracturing site in Texas, USA. In the first scenario, a subset of the field data from the entire monitoring period is used to update the weights of the deep neural network, which is then applied to the remaining data resulting in mean and median distances of 227 and 182 m, respectively, compared to the results of a good localization method. In the second scenario, the deep neural network is updated daily with previously detected and located events and applied to the events detected the following day. Since the observed data used for training generally do not cover a wide range of source locations, we enrich the training set with synthetic data. The addition of synthetics for transfer learning ensures that the updated deep neural network provides accurate source locations for events with locations far from locations used during transfer learning. Transfer learning combining synthetic and real data performs significantly better (more consistent) locations than transfer learning without synthetics.

Continuous seismic monitoring systems aid us to act on preventing strong earthquakes, such as induced by oil and gas extraction, deep geothermal systems and carbon sequestration. These systems provide the data to detect and locate such events and to determine their source magnitude and mechanism. Estimating the location of the source is one of the first parameters to be determined. Most source localization methods in the field of induced seismicity combine migration-based operators with grid-search algorithms. These are computationally intensive and therefore not instantaneous. To improve the time to locate events via grid-search based methods, we investigate the use of Convolutional Neural Networks (ConvNets) to reduce the search space. This is achieved by feeding the ConvNets with the waveforms and outputting a possible area/volume for the source location. Once the ConvNet is trained, it can produce the output almost in real-time. Therefore, it can be used by grid-search type approaches to focus the grid search over the smaller volume provided by the ConvNet. In this study we train ConvNets with synthetic data and apply them to field data. To our knowledge this is the first attempt of training ConvNets on synthetic data for the task of earthquake localization of field data.

Waveform inversion for ultrasound computed tomography (USCT) is a promising imaging technique for breast cancer screening. However, the improved spatial resolution and the ability to constrain multiple parameters simultaneously demand substantial computational resources for the recurring simulations of the wave equation. Hence, it is crucial to use fast and accurate methods for numerical wave propagation, on the one hand, and to keep the number of required simulations as small as possible, on the other hand. We present an efficient strategy for acoustic waveform inversion that combines (i) a spectral-element continuous Galerkin method for solving the wave equation, (ii) conforming hexahedral mesh generation to discretize the scanning device, (iii) a randomized descent method based on mini-batches to reduce the computational cost for misfit and gradient computations, and (iv) a trust-region method using a quasi-Newton approximation of the Hessian to iteratively solve the inverse problem. This approach combines ideas and state-of-the-art methods from global-scale seismology, large-scale nonlinear optimization, and machine learning. Numerical examples for a synthetic phantom demonstrate the efficiency of the discretization, the effectiveness of the mini-batch approximation and the robustness of the trust-region method to reconstruct the acoustic properties of breast tissue with partial information.

Waveform inversion is a promising method for ultrasound computed tomography able to produce high-resolution images of human breast tissue. However, the computational complexity of waveform inversion remains a considerable challenge, and the costs per iteration are proportional to the number of emitting transducers. We propose a twofold strategy to accelerate the time-to-solution by identifying the optimal number and location of emitters using sequential optimal experimental design (SOED). SOED is a powerful tool to iteratively add the most informative transducer or remove redundant measurements, respectively. This approach simultaneously provides optimized transducer configurations and a cost-benefit curve that quantifies the information gain versus the computational cost. First, we propose a method to identify the emitters that provide reconstructions with minimal expected uncertainties. Using a Bayesian approach, model uncertainties and resolution can be quantified with the trace of the posterior covariance. By linearizing the wave equation, we can compute the posterior covariance using the inverse of the Gauss-Newton approximation of the Hessian. Furthermore, this posterior is independent of the breast model and the experimental data, thus enabling pre-acquisition experimental optimization. Then, for the post-acquisition inversion, we present an approach to select a subsample of sources that accurately approximates the full gradient direction in each iteration. We control the convergence of the angular differences between consecutive gradient directions by randomly adding new emitters into the subsample. We present synthetic studies in 2D and 3D that consider a ring-shaped and a semi-ellipsoidal scanning device, respectively. Numerical results suggest that the provided methods have the potential to identify redundancies from the corresponding cost-benefit curves. Furthermore, the gradient direction rapidly converges to the direction of the full gradient, which appears to be independent of the model and the emitter locations.