Gauss curvature-based unique signatures of individual large earthquakes and its implications for customized data-driven prediction

Abstract

Statistical descriptions of earthquakes offer important probabilistic information, and newly emerging technologies of high-precision observations and machine learning collectively advance our knowledge regarding complex earthquake behaviors. Still, there remains a formidable knowledge gap for predicting individual large earthquakes’ locations and magnitudes. Here, this study shows that the individual large earthquakes may have unique signatures that can be represented by new high-dimensional features—Gauss curvature-based coordinates. Particularly, the observed earthquake catalog data are transformed into a number of pseudo physics quantities (i.e., energy, power, vorticity, and Laplacian) which turn into smooth surface-like information via spatio-temporal convolution, giving rise to the new high-dimensional coordinates. Validations with 40-year earthquakes in the West U.S. region show that the new coordinates appear to hold uniqueness for individual large earthquakes ($$M_w \ge 7.0$$ M w ≥ 7.0 ), and the pseudo physics quantities help identify a customized data-driven prediction model. A Bayesian evolutionary algorithm in conjunction with flexible bases can identify a data-driven model, demonstrating its promising reproduction of individual large earthquake’s location and magnitude. Results imply that an individual large earthquake can be distinguished and remembered while its best-so-far model can be customized by machine learning. This study paves a new way to data-driven automated evolution of individual earthquake prediction.

Sharpen data-driven prediction rules of individual large earthquakes with aid of Fourier and Gauss

“…The reference volume is defined as a discretized volume of the Earth lithosphere with increment of (longitude, latitude, depth), . For the convolution process, the geodetic coordinates, are transformed into the earth-centered rectilinear coordinate 17 . Each observed EQ’s moment magnitude are assumed to reside at , following the “point source” concept.…”

“…The second data transformation is to convert the spatio-temporal IIs into the pseudo physics quantities. Amongst many physics quantities, the best-so-far set of pseudo physics quantities are identified as {released energy, power, vorticity, Laplacian} 17 . To be purely data-driven, no pre-defined statistical or empirical laws are used.…”

“…Any mathematical form can be used as LF, and a simple yet general exponential form LF works well 17 , i.e., for the pseudo released energy = where . The pseudo “vorticity” is generated by where corresponds to the pseudo “power” and the pseudo “Laplacian” is calculated as where means the spatial gradient with respect to the geodetic coordinate system ( ).…”

“…As shown in Ref. 17 , amongst many pseudo physics quantities and their combinations, ML selected out the four quantities—the released energy, power, the first vorticity term, and the first Laplacian term, ( ), at least for the western U.S. region. Again, this selection is purely data-driven since ML simply seeks to find the best combination that can outperform other cases without any prejudice.…”

“…This study seeks to add a new dimension to this daunting question. The author’s prior study 17 shows that, after multi-layered data transformations, individual large EQs appear to have unique signatures that can be represented by new high-dimensional features. In particular, the observed EQ catalog data are transformed via spatio-temporal convolution, and then further transformed into a number of pseudo physics quantities (i.e., energy, power, vorticity, and Laplacian).…”