10:10 AM - 10:30 AM
[MGI26-05] Forward/inverse problems and data assimilation in earthquake seismology
★Invited Papers
Keywords:seismic wavefield, data assimilation, inverse problem
Earthquakes are fault ruptures in the earth's interior, and the shaking caused by earthquakes (seismic ground motion) is caused by elastic waves propagating through the earth's interior. The rupture in a fault is very complex and is itself a subject of study, but from the point of view of the excitation source of the waves, it is equivalent to a combination of volumetric forces in an elastic body, and the estimation of these volumetric forces - or more precisely, moments composed of such combinations - from the observational record is a powerful tool in the study of the dynamic epicenters of earthquakes. For small earthquakes, the source is represented by a point in space-time, but for large earthquakes, the effect of rupture propagation on a finite-sized fault plane within a finite time cannot be ignored. Such effects provide important information for understanding the earthquake.
The characteristics of elastic bodies are determined by their mass density and two (or more) elastic moduli, and their estimation from the observational record corresponds to a seismological estimation of the Earth's interior structure. To a first approximation, the Earth's interior has a one-dimensional structure that varies only in depth, which explains relatively well long-period seismic waves. However, the Earth's interior structure is fractal in nature, and the effect of three-dimensional heterogeneity on smaller scales becomes more prominent at shorter wavelengths and higher frequencies.
The seismic waves that form the basis for estimating these quantities are obtained as time-series records of the displacement (or velocity, acceleration, etc.) vectors of elastic bodies at the seismic stations. The time sampling is sufficiently fine and covers well the frequency band (~ several tens Hz) that is the main target of seismology, but the spatial distribution of observation stations is sparse compared to the wavelength of seismic waves, and the spatial distribution is heterogeneous and biased toward land in some countries due to the difficulty of setting up observation stations and accessing them. The observation stations are located almost on the surface of the earth or at depths of ~100 m in most cases and ~3000 m at the most. Compared to the scale of the entire solid earth (average radius of 6371 km) and the region where earthquakes occur (depth of ~700 km), the observation stations are practically only on a two-dimensional plane.
Therefore, the problem of seismic wave motion is the problem of estimating the internal structure of the earth, which is characterized by the input of fault rupture at the epicenter and the output of seismic wave observation records obtained through the process of elastic wave propagation in the heterogeneous internal structure of the earth. The difficulty and challenge of earthquake seismology lies in the fact that both the input and the process are both uncertain and only the output exists, and that the output is spatially sparse and biased. Although the observations are sparse, the amount of continuous earthquake observation records accumulated since the construction of the modern observational network has reached the order of PB in Japan alone, and handling the large amount of data generated by numerical simulations is also becoming a major challenge.
Since earthquakes are caused by spatiotemporally localized fault ruptures and a significant portion of the seismic wave propagation process can be described as a linear problem, seismologists have developed the inverse problem (or inversion) based on the description of the wave propagation process by Green's function. In recent years, data assimilation methods and concepts have been introduced and applied to seismology. These include full-wave inversion, which estimates the Earth's interior structure using the entire seismic waveform without converting it into arrival times or other features; direct estimation of the seismic tsunami wavefield to immediately forecast the arrival of seismic waves and tsunamis after an earthquake; and direct imaging of the epicenter without a priori conditions on location and under a three-dimensional heterogeneous structure model. In this talk, I would like to review these issues from the viewpoint of a researcher who specializes in seismology and is at the entry point of the world of data assimilation.
The characteristics of elastic bodies are determined by their mass density and two (or more) elastic moduli, and their estimation from the observational record corresponds to a seismological estimation of the Earth's interior structure. To a first approximation, the Earth's interior has a one-dimensional structure that varies only in depth, which explains relatively well long-period seismic waves. However, the Earth's interior structure is fractal in nature, and the effect of three-dimensional heterogeneity on smaller scales becomes more prominent at shorter wavelengths and higher frequencies.
The seismic waves that form the basis for estimating these quantities are obtained as time-series records of the displacement (or velocity, acceleration, etc.) vectors of elastic bodies at the seismic stations. The time sampling is sufficiently fine and covers well the frequency band (~ several tens Hz) that is the main target of seismology, but the spatial distribution of observation stations is sparse compared to the wavelength of seismic waves, and the spatial distribution is heterogeneous and biased toward land in some countries due to the difficulty of setting up observation stations and accessing them. The observation stations are located almost on the surface of the earth or at depths of ~100 m in most cases and ~3000 m at the most. Compared to the scale of the entire solid earth (average radius of 6371 km) and the region where earthquakes occur (depth of ~700 km), the observation stations are practically only on a two-dimensional plane.
Therefore, the problem of seismic wave motion is the problem of estimating the internal structure of the earth, which is characterized by the input of fault rupture at the epicenter and the output of seismic wave observation records obtained through the process of elastic wave propagation in the heterogeneous internal structure of the earth. The difficulty and challenge of earthquake seismology lies in the fact that both the input and the process are both uncertain and only the output exists, and that the output is spatially sparse and biased. Although the observations are sparse, the amount of continuous earthquake observation records accumulated since the construction of the modern observational network has reached the order of PB in Japan alone, and handling the large amount of data generated by numerical simulations is also becoming a major challenge.
Since earthquakes are caused by spatiotemporally localized fault ruptures and a significant portion of the seismic wave propagation process can be described as a linear problem, seismologists have developed the inverse problem (or inversion) based on the description of the wave propagation process by Green's function. In recent years, data assimilation methods and concepts have been introduced and applied to seismology. These include full-wave inversion, which estimates the Earth's interior structure using the entire seismic waveform without converting it into arrival times or other features; direct estimation of the seismic tsunami wavefield to immediately forecast the arrival of seismic waves and tsunamis after an earthquake; and direct imaging of the epicenter without a priori conditions on location and under a three-dimensional heterogeneous structure model. In this talk, I would like to review these issues from the viewpoint of a researcher who specializes in seismology and is at the entry point of the world of data assimilation.