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Ground Motion and Entropy

Description: 

How ordered is earthquake ground motion? We examine this question through the framework of entropy, a concept from information theory that measures the uncertainty or disorder in a set of data. For example, a lower seismic entropy implies a higher certainty of specific ground motion levels occurring, whereas higher entropy levels could indicate more complex source, wave propagation, and site effects, leading to increased uncertainty in shaking predictions. Here, we seek to quantify the entropy of both ground motion phase and amplitude. To do so, we discretize 3-component acceleration waveforms in a spherical coordinate system, where each (East, North, Vertical) time sample is mapped to a pixel on a sphere of radius norm(E, N, Z). We partition all acceleration waveforms, from a data set containing ~18,000 earthquakes, 1.3 million waveforms, and ~10 billion total samples, recorded by the Japanese National Research Institute for Earth Science and Disaster Resilience (NIED) K-NET and KiK-net networks from 1997 – 2023, into logarithmically-spaced amplitude bins and equal-area pixels distributed over a sphere. We calculate entropy as S = -sum(P * log P), where P(bin) is the probability of a ground motion sample (E,N,Z) being in a particular amplitude bin or pixel. We find that ground motion amplitudes have lower entropy, or more order, than phases. Physically, this means ground motion amplitudes concentrate at levels far below the peak ground acceleration, whereas phases more evenly sample the focal sphere, though we observe peaks in phase angles near +-90 and 0 degrees polarity, coinciding with expected polarities of P-waves and S-waves, respectively. Our entropy calculations could aid in the generation of realistic ground motions, especially for the challenging problem of simulating physical high-frequencies.

Session: From Earthquake Recordings to Empirical Ground-Motion Modelling - III

Type: Oral

Date: 5/2/2024

Presentation Time: 02:00 PM (local time)

Presenting Author: Tim

Student Presenter: No

Invited Presentation: 

Authors