SVD for Macro-velocity Model Reconstruction by Full-waveform Inversion

The key element of seismic processing workflow in areas with complex geology is a depth velocity model building. A full-waveform inversion technique is considered currently both by academia and industry as a potential solution of the problem. The resolution and sensitivity of the method can be studied reliably by considering the Frechet derivative of the original nonlinear forward map. Examining its singular value decomposition provides the detailed information about the inverse problem, particularly about the low-frequency velocity model reconstruction ability. In the current work we present such study considering a look-ahead VSP experiment in which the velocity model below the borehole bottom is inverted. Using truncated SVD we show that success of the inversion strongly depends on the available low frequencies in the data and on the noise level. For the particular model we find the acceptable noise level and the required frequency content of the data needed for reliable inversion of the smooth velocity model. The presented approach may be adapted to any particular model and acquisition system and may be used as a tool for prediction the solution properties prior to any inversion procedure and for producing the requirements to the data which are necessary for successful inversion.