Mathematical innovations enable advances in seismic activity detection

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Amidst the unique landscape of geothermal development within the Tohoku region, subtle seismic activities beneath the Earth’s surface present an interesting challenge for researchers. While earthquake warnings may intermittently alert us to seismic events, there exist quite a few smaller quakes which have long intrigued resource engineers striving to detect and understand them.

Mathematical innovations from Tohoku University researchers are advancing detection of more types — and fainter forms — of seismic waves, paving the best way for more practical earthquake monitoring and risk assessment.

The outcomes of their study were published in IEEE Transactions on Geoscience and Distant Sensing on January 15, 2024.

Collection of seismic data relies on the number and positioning of sensors called seismometers. Especially where only limited deployment of seismic sensors is feasible, similar to in difficult environments just like the planet Mars or when conducting long-term monitoring of captured and stored carbon, optimizing data extraction from every sensor becomes crucial. One promising method for doing so is polarization evaluation, which involves studying 3-D particle motion and has garnered attention for its ability to leverage three-component data, offering more information than one-component data. This approach enables the detection and identification of varied polarized seismic waveforms, including S-waves, P-waves and others.

Polarization evaluation using a spectral matrix (SPM) particularly is a method used to research the best way particles move in three dimensions over time and at different frequencies, in other words, within the time-frequency domain. Nevertheless, in scenarios where the specified signal is weak in comparison with background noise — generally known as low signal-to-noise ratio (SNR) events, that are typical in underground reservoirs — SPM evaluation faces limitations. On account of mathematical constraints, it will possibly only characterize linear particle motion (meaning the fast-moving, easy-to-detect P-waves), making the evaluation of other waveforms (similar to the secondary arriving S-waves) difficult.

“We overcame the technical challenges of conventional SPM evaluation and expanded it for broader polarization realization by introducing time-delay components,” said Yusuke Mukuhira, an assistant professor on the Institute of Fluid Science of Tohoku University and lead writer of the study.

In comparison with existing techniques, his team’s incorporation of time-delay components enhanced the accuracy of SPM evaluation, enabling the characterization of varied polarized waves, including S-waves, and the detection of low-SNR events with smaller amplitudes.

A key innovation within the study is the introduction of a brand new weighting function based on the phase information of the primary eigenvector — a special vector that, when multiplied by the matrix, leads to a scaled version of the unique vector. The aim of the weighting function is to assign different levels of importance to different parts of signals in response to their significance, thereby reducing false alarms. Synthetic waveform tests showed that this addition significantly improved the evaluation of seismic wave polarization, an important consider distinguishing signal from noise.

“Technically, we have now developed a signal processing technique that improves particle motion evaluation within the time and frequency domain,” Mukuhira said.

The research team validated their methodology using real-world data recorded on the Groningen gas field within the Netherlands. The outcomes showcased superior seismic motion detection performance, bringing to light two low-SNR events that had previously gone unnoticed by conventional methods.

These findings hold the potential for applications across various fields, including seismology and geophysics, particularly in monitoring underground conditions with limited remark points. The implications extend to earthquake monitoring, planetary exploration and resource development.

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