Earthquake Source Depth Determination using Single Station Waveforms and Deep Learning

TL;DR

This study tackles the challenge of constraining earthquake depth in regions with sparse station coverage by mapping single-station three-component seismic waveforms directly to depth using VGGDepth, a deep learning network inspired by VGG16. Two modeling approaches are developed: a single-station model and a regionally generalized model that learn regional waveform features and enable depth estimation at any station within a region; both are validated on the 2016-2017 Central Apennines sequence, achieving sub-kilometer depth accuracy and robust performance across stimuli. Multi-station averaging further reduces depth errors to the 0.6–0.8 km range while maintaining high event recovery, and transfer learning demonstrates rapid adaptation to newly deployed or pseudo-new stations. The results indicate strong potential for refining historical earthquake depths and supporting depth estimation in sparse networks, with implications for seismic hazard assessment and cross-planetary seismology.

Abstract

In areas with limited station coverage, earthquake depth constraints are much less accurate than their latitude and longitude. Traditional travel-time-based location methods struggle to constrain depths due to imperfect station distribution and the strong trade-off between source depth and origin time. Identifying depth phases at regional distances is usually hindered by strong wave scattering, which is particularly challenging for low-magnitude events. Deep learning algorithms, capable of extracting various features from seismic waveforms, including phase arrivals, phase amplitudes, as well as phase frequency, offer promising constraints to earthquake depths. In this work, we propose a novel depth feature extraction network (named VGGDepth), which directly maps seismic waveforms to earthquake depth using three-component waveforms. The network structure is adapted from VGG16 in computer vision. It is designed to take single-station three-component waveforms as inputs and produce depths as outputs, achieving a direct mapping from waveforms to depths. Two scenarios are considered in our model development: (1) training and testing solely on the same seismic station, and (2) generalizing by training and testing on different seismic stations within a particular region. We demonstrate the efficacy of our methodology using seismic data from the 2016-2017 Central Apennines, Italy earthquake sequence. Results demonstrate that earthquake depths can be estimated from single stations with uncertainties of hundreds of meters. These uncertainties are further reduced by averaging results from multiple stations. Our method shows strong potential for earthquake depth determination, particularly for events recorded by single or sparsely distributed stations, such as historically instrumented earthquakes.

Figures (19)

• Figure 1: (a) Diagram showing the architecture of VGGDepth. The architecture consists of two integrated neural network modules: a feature extraction module and a deep feature translation module. The input to the network is a three-component waveform, which first passes through the feature extraction module --- a convolutional neural network-based structure. The resulting features are then fed into the deep feature translator, which is composed of a fully connected network. Finally, the network outputs the probability density function of the earthquake depth. (b) Comparison of single-station and regionally generalized earthquake depth prediction workflows. Left: Single-station model trained and tested on data from one station. Right: Regionally generalized model trained on data from multiple stations (Sta.1 to Sta.N) and tested across the network. Both models use the same architecture but differ in training strategy.
• Figure 2: The study region with the distribution of earthquakes (gray dots) and stations including permanent network IV (triangles) and temporary network YR (diamonds). The black dashed box represents the study area. Three stations (NRCA, FDMO, CESI) were selected for evaluating single-station model performance. The station ED23 was selected to test the regionally generalized model for a pseudo-newly deployed station, as well as to evaluate the performance of transfer-learning.
• Figure 3: Frequency distributions of earthquake depths (left panel) and epicentral distances (right panel). The depth statistics include all events, while the epicentral distance statistics are shown using station NRCA as an example.
• Figure 4: Depth error of the validation set as a function of training epochs. The blue, red, and green colored lines denote three individual single-station models trained on three different stations in the study area (i.e., NRCA, CESI, and FDMO), while the light blue line represents the regionally generalized model for all stations in the region.
• Figure 5: Depth prediction performance on the testing sets of the three seismic stations (stations NRCA, CESI, and FDMO). The top panels (a-c) show the depth error statistics, and the middle panels (d-f) display the depth comparisons between the predictions and their labels for individual events (blue dots). The mean depth errors and the percentages of the solvable events are indicated in the text within the figures. The bottom panels (g-i) present the normalized recovery matrices, where each cell (X, Y) represents the proportion of events with true depth Y that are predicted at depth X, normalized by the total number of events at that true depth. The diagonal elements indicate accurate depth recovery, with values exceeding 0.6 for most depth bins.