Full-Wave Seismic Data Assimilation: Theoretical Background and Recent Advances

The seismological inverse problem has much in common with the data assimilation problem found in meteorology and oceanography. Using the data assimilation methodology, I will formulate the seismological inverse problem for estimating seismic source and Earth structure parameters in the form of weak-constraint generalized inverse, in which the seismic wave equation and the associated initial and boundary conditions are allowed to contain errors. The resulting Euler?CLagrange equations are closely related to the adjoint method and the scattering-integral method, which have been successfully applied in full-3D, full-wave seismic tomography and earthquake source parameter inversions. I will review some recent applications of the full-wave methodology in seismic tomography and seismic source parameter inversions and discuss some challenging issues related to the computational implementation and the effective exploitation of seismic waveform data.