RESEARCH INTEREST OF PO CHEN
My primary research interest is to develop a unified methodology for seismic source and Earth structure inversions in a fully 3D setting.
Real-time Seismic Source Inverion in 3D Earth Structure Model
- Parameterization of a kinematic seismic source
Currently there are 3 types of source representations commonly employed in seismic source inversion studies: isotropic point source (IPS), centroid moment tensor (CMT) and fault-slip distribution (FSD). We have introduced another type of source representation which we call Finite Moment Tensor (FMT) (Figure 1a). FMT representation resolves the fault-plane-ambiguity from the CMT representation and provides the characteristic dimension, duration as well as a directivity vector of the finite rupture. An example of an FMT representation is shown in (Figure 1b). Recovering FMT parameters in a routine manner will not only advance our understanding on earthquake physics but also provide us additional constraints on the state of regional tectonics, illuminate hidden faults and facilitate earthquake hazard analysis and mitigation.
- Sensitivity derivatives of observations w.r.t. source parameters
The sensitivity derivatives of observations with respect to seismic source parameters (IPS, CMT, FMT, FSD, etc.) are computed from the Receiver Green Tensors (RGTs) by applying the reciprocity principle. A RGT is the space-time wavefields generated by 3 orthognal impulsive point forces acting at the receiver location. Details about RGTs can be found in this paper. Advantages of this method are the following:
- A RGT is a completely general representation of the propagation path effects from any point in the modeling volume to the receiver. Only 3 wave-propagation simulations are needed to construct and store the RGT for each receiver. Once we know the RGTs, any types of source inversions can be easily done.
- Synthetic seismograms for any types of sources (point or finite) can be easily computed by applying the reciprocity principle.
- Capable of incorporating 3D Earth structure model. In our implementation for the Los Angeles region, the RGTs are computed using the 3D Earth structure model SCEC CVM3.0 and the finite-difference method.
- Highly efficient and capable of near-real-time to real-time source parameter inversions.
- Can be used for efficiently constructing sensitivity kernels for full 3D tomography (F3DT) through the scattering-integral (SI) method (see below)
- Applications
- Full FMT inversion for 09/03/2002 Yorba Linda earthquake Download
- Near-real-time waveform inversion for CMT solutons in a 3D Earth structure model Download
- Resolve fault-plane-ambiguity for small earthquakes Download
- Near-real-time waveform inversion for slip-distributions in a 3D Earth structure model (comming soon...)
Full 3D Tomography (F3DT) Using Seismic Waveform
- Generalized Seismological Data Functionals (GSDF)
Seismic wavefield is a very nonlinear function of the Earth model and direct inversion of the seismic waveform itself will be easily locked into local minima without producing useful results if the starting Earth model is not already very close to the true model. To reduce the nonlinearity of seismic waveform tomography, we designed an algorithm to convert time-domain seismic waveform into time- and frequency-dependent phase and amplitude measurements, which we call generalized seismological data functionals or GSDF. The GSDF measurements can more effectively capture waveform differences between observed and model-predicted (synthetic) seismograms and they are much more linear with respect to the Earth model than seismic waveform itself, therefore more suitable for tomographic inversions. The procedures for making GSDF measurements are shown in Figure 2a and Figure 2b demonstrates GSDF measurements can completely parameterize waveform differences if the sampling in frequency is dense enough. This procedure can be applied to any types of waves including body waves, surface waves or just an arbitrary segment of the complete seismogram.
- Scattering-Integral (SI) Method for Constructing Fréchet Kernels
The Fréchet (sensitivity) kernels of the GSDF measurements with respect to the Earth model (density, elastic modula, attenuation factor, anisotropy...) are computed using a full-3D approach, which we call the scattering-integral or SI method. We call our method "full-3D" because in our approach the starting Earth model and the derived model perturbations are all 3D in space and the 3D kernels are constructed by solving the wave-equation numerically. Unlike in ray tomography or even the finite-frequency tomography based on asymptotic ray theory, our full-3D approach is based on solving the wave-equation exactly using numerical methods such as the finite-difference and the spectral-element methods. It eliminates all mathematic approximations, therefore accounts for the full physics of 3D wave propagation.
The details about the theory can be found in this paper. The procedure for full-3D tomography and seismic source inversion using the SI method is following:
- Construct the RGTs for every receiver and store them. The RGTs are computed using the starting Earth model, which can be 3D.
- Invert for seismic source parameters using the RGTs and the reciprocity principle.
- Compute synthetic seismograms using the inverted seismic source parameters, the RGTs and reciprocity.
- Make GSDF measurements to obtain the misfit between the synthetic and observed seismograms.
- Run forward wave propagation simulation for each souce using the inverted seismic source paramters.
- Convolve the gradients of the foward wavefield for each source with the RGTs to construct the kernels (scattering integral).
- Invert GSDF measurements for perturbation to the starting Earth model using the 3D kernels and the LSQR method with model regularization.
- Apply the inverted model perturbation to the starting model and obtain a new starting model.
- Depending on waveform misfit reduction, additional iterations of steps 1-8 may be needed.
- Applications
Numerical Modeling of Wave Propagation
Numerical modeling of wave propagation in complex medium with Adaptive Mesh Refinement (AMR). AMR is a computational technique for improving the efficiency of numerical simulations. The basic idea is to refine, both in space and in time, regions of the computational domain in which high-resolution is needed to resolve developing features, while leaving less interesting areas at lower resolution. I mostly use the Overture package for my wave-propagation code development.
Microlocal Analysis
Exploring microlocal analysis and its application in seismology. Microlocal analysis and Fourier integral operators are potentially useful for seismic imaging because they provide means to manipulate complicated wavefields in the phase space.