3-D full waveform inversion of seismic data; Part I. Theory

Full waveform inversion of seismic data is a challenging subject partly because of the lack of precise knowledge of the source. Since currently available approaches involve some form of approximations to the source, inversion results are subject to the quality and the choice of the source information used. A new full waveform inversion scheme has been introduced (Lee and Kim, 2003) using normalized wavefield for simple two-dimensional (2-D) scalar problems. The method does not require source information, so potential inversion errors due to source estimation may be eliminated. A gather of seismic traces is first Fourier-transformed into the frequency domain and a normalized wavefield is obtained for each trace in the frequency domain. Normalization is done with respect to the frequency response of a reference trace selected from the gather, so the complex-valued normalized wavefield is source-independent and dimensionless. The inversion algorithm minimizes misfits between measured normalized wavefield and numerically computed normalized wavefield. In this paper the full waveform inversion is extended to three-dimensional (3-D) problems