Prediction of measured earthquake waveforms from synthetic data: a two-step deep learning approach

Single-station waveforms of teleseismic earthquakes are highly complex, because they are a superposition of numerous phases corresponding to different wave types and propagation paths. Moreover, data recorded at single stations is contaminated by noise, which often has similar or larger amplitudes than the arrivals of teleseismic earthquakes, especially in densely-populated areas. For high precision research facilities, for example in the field of particle physics or gravity wave detection, a precise knowledge of the seismic wavefield generated by teleseismic earthquakes can be critical for the calibration of experiments. However, the density of seismological stations is often sparse, particularly in regions with low seismic hazard such as Northern Germany.

To overcome this limitation, we introduce a deep learning scheme for the prediction of very-low-frequency earthquake waveforms from synthetic data at arbitrary locations within the metropolitan area of Hamburg, Germany. For this aim, we propose to train a convolutional neural network (CNN) to predict the measured earthquake waveforms from their synthetic counterparts. While synthetic earthquake waveforms can be conveniently generated for arbitrary coordinates and moment tensors with Instaseis and the IRIS synthetics engine (Syngine), the amount of available measured waveforms is constrained by the availability of seismological stations and their installation date. In this work, we use measured data from a station in Bad Segeberg, north of Hamburg, which has been measuring continuously since 1996. During first experiments, we trained a CNN on data from earthquakes larger than M6.0 and obtained reasonable initial results. However, the number of such earthquakes is limited and the measured waveforms used as labels partly contained noise of considerable amplitude, which caused the neural network to predict unwanted noise.

In order to increase the amount of earthquakes in the training data and mitigate their contamination with noise, we propose a two-step approach. In the first step, we generate a large number of noise-free synthetic waveforms and contaminate them with artificially generated noise that has the same characteristics as the noise measured at the station in Bad Segeberg. With this dataset, we train a first CNN to denoise the synthetic earthquake waveforms. In the second step, we apply the trained neural network to the actual earthquake waveforms measured in Bad Segeberg to denoise them. We then train a second CNN to translate synthetic earthquake waveforms to the denoised measured ones. Results for earthquakes not part of the training data demonstrate that the second CNN provides convincing estimates of measured earthquake waveforms, not only for the station in Bad Segeberg, but also for stations in Hamburg. This can be seen as a first step towards a three-dimensional prediction of the earthquake wavefield without the need for densely-distributed stations.