Improved inversion through use of the null space

Standard least-squares traveltime inversion techniques tend to produce smoothed estimates of the velocity field. More complete results can be obtained by incorporating into the inversion scheme a priori information about the media to be imaged, derived from well logs, core data, and surface geology. A promising technique for achieving this involves projecting this information onto the null space model singular vectors of the inverse problem and including this projection with the non-null space contribution in order to produce a solution. The method, demonstrated with both field and synthetic crosshole traveltime data acquired through layered, anisotropic media, successfully produces improved inversion solutions with lower traveltime residuals, layers that are more homogeneous, sharper interfaces, and better correlated anisotropy parameters than solutions obtained with standard techniques.