Abstract. We present an efficient probabilistic workflow for the estimation of source parameters of induced seismic events in three-dimensional heterogeneous media. Our workflow exploits a linearized variant of the Hamiltonian Monte Carlo (HMC) algorithm. Compared to traditional Markov chain Monte Carlo (MCMC) algorithms, HMC is highly efficient in sampling high-dimensional model spaces. Through a linearization of the forward problem around the prior mean (i.e., the “best” initial model), this efficiency can be further improved. We show, however, that this linearization leads to a performance in which the output of an HMC chain strongly depends on the quality of the prior, in particular because not all (induced) earthquake model parameters have a linear relationship with the recordings observed at the surface. To mitigate the importance of an accurate prior, we integrate the linearized HMC scheme into a workflow that (i) allows for a weak prior through linearization around various (initial) centroid locations, (ii) is able to converge to the mode containing the model with the (global) minimum misfit by means of an iterative HMC approach, and (iii) uses variance reduction as a criterion to include the output of individual Markov chains in the estimation of the posterior probability. Using a three-dimensional heterogeneous subsurface model of the Groningen gas field, we simulate an induced earthquake to test our workflow. We then demonstrate the virtue of our workflow by estimating the event's centroid (three parameters), moment tensor (six parameters), and the earthquake's origin time. Using the synthetic case, we find that our proposed workflow is able to recover the posterior probability of these source parameters rather well, even when the prior model information is inaccurate, imprecise, or both inaccurate and imprecise.

Using common-image-point gathers (CIPs) instead of conventional image gathers for migration velocity analysis is an efficient approach for analyzing migrated images at locations that are related to geological structures. This approach reduces computational costs and may improve migration velocity analysis by acounting for diving energy. However, manually picking CIP locations is tedious and time-consuming, especially for 3D images; therefore, an automated method for picking CIPs is desirable. To take advantage of the potential computational cost savings, CIPs should be constructed at relatively sparse locations throughout an image. Furthermore, to facilitate improved analysis, CIPs should be constructed along geological features. We provide a new method for automatically picking CIP locations from seismic images. This method uses local image properties including planarity, structure-oriented semblance, and the amplitude envelope to compute a priority-map (PMAP) of seismic images, where higher PMAP values indicate better CIP locations. After the priority map is computed, CIP locations are picked sparsely throughout the image using a greedy heuristic.

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Abstract. We present an efficient probabilistic workflow for the estimation of source parameters of induced seismic events in three-dimensional heterogeneous media. Our workflow exploits a linearized variant of the Hamiltonian Monte Carlo (HMC) algorithm. Compared to traditional Markov-Chain Monte Carlo (MCMC) algorithms, HMC is highly efficient in sampling high-dimensional model spaces. Through a linearization of the forward problem around the prior mean (i.e., the "best" initial model), this efficiency can be further improved. We show, however, that this linearization leads to a performance in which the output of an HMC chain strongly depends on the quality of the prior; in particular, because not all (induced) earthquake model parameters have a linear relationship with the recordings observed at the surface. To mitigate the importance of an accurate prior, we integrate the linearized HMC scheme into a workflow that (i) allows for a weak prior through linearization around various (initial) centroid locations, (ii) is able to converge to the mode containing the model with the (global) minimum misfit by means of an iterative HMC approach, and (iii) uses variance reduction as a criterion to include the output of individual Markov chains in the estimation of the posterior probability. Using a three-dimensional heterogeneous subsurface model of the Groningen gas field, we simulate an induced earthquake to test our workflow. We then demonstrate the virtue of our workflow by estimating the event's centroid (three parameters), moment tensor (six parameters), and the earthquake's origin time. We find that our workflow is able to recover the posterior probability of these source parameters rather well, even when the prior model information is inaccurate, imprecise, or both inaccurate and imprecise.