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Register a new userDeep Recurrent Architectures for Seismic Tomography
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This paper introduces novel deep recurrent neural network architectures for Velocity Model Building (VMB), which is beyond what Araya-Polo et al 2018 pioneered with the Machine Learning-based seismic tomography built with convolutional non-recurrent neural network. Our investigation includes the utilization of basic recurrent neural network (RNN) cells, as well as Long Short Term Memory (LSTM) and Gated Recurrent Unit (GRU) cells. Performance evaluation reveals that salt bodies are consistently predicted more accurately by GRU and LSTM-based architectures, as compared to non-recurrent architectures. The results take us a step closer to the final goal of a reliable fully Machine Learning-based tomography from pre-stack data, which when achieved will reduce the VMB turnaround from weeks to days.
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Incorporating prior knowledge on model unknowns of interest is essential when dealing with ill-posed inverse problems due to the nonuniqueness of the solution and data noise. Unfortunately, it is not trivial to fully describe our priors in a convenient and analytical way. Parameterizing the unknowns with a convolutional neural network (CNN), and assuming an uninformative Gaussian prior on its weights, leads to a variational prior on the output space that favors natural images and excludes noisy artifacts, as long as overfitting is prevented. This is the so-called deep-prior approach. In seismic imaging, however, evaluating the forward operator is computationally expensive, and training a randomly initialized CNN becomes infeasible. We propose, instead, a weak version of deep priors, which consists of relaxing the requirement that reflectivity models must lie in the network range, and letting the unknowns deviate from the network output according to a Gaussian distribution. Finally, we jointly solve for the reflectivity model and CNN weights. The chief advantage of this approach is that the updates for the CNN weights do not involve the modeling operator, and become relatively cheap. Our synthetic numerical experiments demonstrate that the weak deep prior is more robust with respect to noise than conventional least-squares imaging approaches, with roughly twice the computational cost of reverse-time migration, which is the affordable computational budget in large-scale imaging problems.
The effects of several nonlinear regularization techniques are discussed in the framework of 3D seismic tomography. Traditional, linear, $ell_2$ penalties are compared to so-called sparsity promoting $ell_1$ and $ell_0$ penalties, and a total variation penalty. Which of these algorithms is judged optimal depends on the specific requirements of the scientific experiment. If the correct reproduction of model amplitudes is important, classical damping towards a smooth model using an $ell_2$ norm works almost as well as minimizing the total variation but is much more efficient. If gradients (edges of anomalies) should be resolved with a minimum of distortion, we prefer $ell_1$ damping of Daubechies-4 wavelet coefficients. It has the additional advantage of yielding a noiseless reconstruction, contrary to simple $ell_2$ minimization (`Tikhonov regularization) which should be avoided. In some of our examples, the $ell_0$ method produced notable artifacts. In addition we show how nonlinear $ell_1$ methods for finding sparse models can be competitive in speed with the widely used $ell_2$ methods, certainly under noisy conditions, so that there is no need to shun $ell_1$ penalizations.
Small magnitude earthquakes are the most abundant but the most difficult to locate robustly and well due to their low amplitudes and high frequencies usually obscured by heterogeneous noise sources. They highlight crucial information about the stress state and the spatio-temporal behavior of fault systems during the earthquake cycle, therefore, its full characterization is then crucial for improving earthquake hazard assessment. Modern DL algorithms along with the increasing computational power are exploiting the continuously growing seismological databases, allowing scientists to improve the completeness for earthquake catalogs, systematically detecting smaller magnitude earthquakes and reducing the errors introduced mainly by human intervention. In this work, we introduce OKSP, a novel automatic earthquake detection pipeline for seismic monitoring in Costa Rica. Using Kabre supercomputer from the Costa Rica High Technology Center, we applied OKSP to the day before and the first 5 days following the Puerto Armuelles, M6.5, earthquake that occurred on 26 June, 2019, along the Costa Rica-Panama border and found 1100 more earthquakes previously unidentified by the Volcanological and Seismological Observatory of Costa Rica. From these events, a total of 23 earthquakes with magnitudes below 1.0 occurred a day to hours prior to the mainshock, shedding light about the rupture initiation and earthquake interaction leading to the occurrence of this productive seismic sequence. Our observations show that for the study period, the model was 100% exhaustive and 82% precise, resulting in an F1 score of 0.90. This effort represents the very first attempt for automatically detecting earthquakes in Costa Rica using deep learning methods and demonstrates that, in the near future, earthquake monitoring routines will be carried out entirely by AI algorithms.
A qualitative comparison of total variation like penalties (total variation, Huber variant of total variation, total generalized variation, ...) is made in the context of global seismic tomography. Both penalized and constrained formulations of seismic recovery problems are treated. A number of simple iterative recovery algorithms applicable to these problems are described. The convergence speed of these algorithms is compared numerically in this setting. For the constrained formulation a new algorithm is proposed and its convergence is proven.
To optimally monitor earthquake-generating processes, seismologists have sought to lower detection sensitivities ever since instrumental seismic networks were started about a century ago. Recently, it has become possible to search continuous waveform archives for replicas of previously recorded events (template matching), which has led to at least an order of magnitude increase in the number of detected earthquakes and greatly sharpened our view of geological structures. Earthquake catalogs produced in this fashion, however, are heavily biased in that they are completely blind to events for which no templates are available, such as in previously quiet regions or for very large magnitude events. Here we show that with deep learning we can overcome such biases without sacrificing detection sensitivity. We trained a convolutional neural network (ConvNet) on the vast hand-labeled data archives of the Southern California Seismic Network to detect seismic body wave phases. We show that the ConvNet is extremely sensitive and robust in detecting phases, even when masked by high background noise, and when the ConvNet is applied to new data that is not represented in the training set (in particular, very large magnitude events). This generalized phase detection (GPD) framework will significantly improve earthquake monitoring and catalogs, which form the underlying basis for a wide range of basic and applied seismological research.
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