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Estimation of Subsurface Structure by Combining Physics-Informed Neural Network and Statistical Analysis:
Expected quantification of uncertainties in the seismic source process


1. Key Points

  • The analysis of seismic data to characterize earthquakes, such as the evolution process of earthquake source and epicenter location, uses estimated information about the subsurface structure in which the earthquake occurs. To accurately understand the characteristics of earthquakes based on this relationship, it is essential to quantify the uncertainty in the subsurface structure; however, this quantification of the uncertainty has proven to be a technical challenge.

  • The team developed a new method for estimating subsurface structure by combining a Physics-Informed Neural Network※1 with a statistical analysis method called Bayesian inference※2 to quantify the uncertainty of the estimation results.

  • The developed subsurface structure estimation method is expected to be used for uncertainty quantification in various seismic data analyses derived from the subsurface structure estimation results, including the estimation of seismic source processes.

Supplemental Information

Physics-Informed Neural Network (PINN): A deep learning method that utilizes not only the observed data but also the information from equations describing the physical phenomena governing the data generation process. Its goal is to discover patterns by learning from the observed data.


Bayesian inference: A statistical estimation method based on Bayes’ theorem. The Bayes’ theorem describes the probability of an event when new information is obtained in addition to prior knowledge of the factors that may be associated with the event.

2. Overview

A team led by Researcher Ryoichiro Agata, Senior Researcher Kazuya Shiraishi, and Director Gou Fujie of Subduction Dynamics Research Center, Research Institute for Marine Geodynamics, Japan Agency for Marine-Earth Science and Technology, has developed a new method for estimating subsurface structure. They used a Physics-Informed Neural Network (PINN) to quantify the uncertainty in the results of the estimates.

Understanding the seismic wave velocity structure of the subsurface rocks in earthquake prone areas is crucial for analyzing seismic data and characterizing earthquake properties like the seismic source process and epicenter location. Subsurface structures are estimated using methods such as the seismic refraction method. However, the utility of these methods is invariably accompanied by uncertainty due to limitations on the quality and quantity of elastic wave exploration. The degree of uncertainty in the subsurface structure is directly related to the seismic source process-estimated analysis on the seismic data. To accurately understand the characteristics of earthquakes, quantifying the uncertainty in the results of subsurface structure estimates based on statistical analysis methods such as Bayesian inference, has become increasingly important in various fields. However, such an analysis requires extensive computational processing for statistical analysis, posing technical challenges. Simplifying the structure results in a loss of continuity, a fundamentally important physical property in subsurface structures. PINN, a novel method for analyzing scientific data, offers advantages over conventional methods, such as the ability to represent subsurface structures as continuous distributions. However, a method for quantifying uncertainty in the analysis using PINN has not yet been established.

In this research, the team combined PINN with a Bayesian inference method, which is compatible with deep learning, to develop a novel method for estimating subsurface structure that quantifies uncertainty. In addition, numerical experiments simulating a real-world seismic refraction method confirmed the applicability of this method to real analysis. The team thus quantified the uncertainty in the analyzing of scientific data with PINN with practical accuracy using Bayesian inference in a practical problem. This research is the first of its kind in the world in the field of earth science.

The study evaluated the uncertainty in the estimation results while maintaining the important physical feature of a “continuous” distribution of subsurface structures through PINN. This evaluation opens the door to understanding not only the results of subsurface structure estimation results using the seismic refraction method but also the uncertainty in the analysis of various seismic data derived from these estimations, such as estimating the location of epicenter and the seismic source process.

This research was supported by JSPS KAKENHI Grant Number 21K14024. JAMSTEC's Earth Simulator was used for parallel training of deep neural networks.

The official version of this result was published in IEEE Transactions on Geoscience and Remote Sensing on October 9th, 2023(local time).

Bayesian seismic tomography based on velocity-space Stein variational gradient descent for physics-informed neural network

Ryoichiro Agata, Kazuya Shiraishi, Gou Fujie

Japan Agency for Marine-Earth Science and Technology(JAMSTEC)

For this study

Ryoichiro Agata, Resercher, Research Institute for Marine Geodynamics (IMG), Subduction Dynamics Research Center (SDR), Marine Seismology Research Group, JAMSTEC

For press release

Press Office, Marine Science and Technology Strategy Department, JAMSTEC