Linear geophysical inversion with seismic image-guided kriging

Jack Broderick Muir 

Linear geophysical inversions, such as the mapping of surface gravity anomaly to subsurface
density anomaly, are a cornerstone of geophysical practice. However, the high degree of ill-posedness
of such problems makes interpretation of the resulting subsurface models challenging. I develop a
methodology to combine surface potential field measurements, direct subsurface sampling through
scout boreholes, and seismic reflection imaging, to generate consistent subsurface anomaly models
of significantly greater accuracy and interpretability.
The method relies on non-stationary, anisotropic Gaussian process priors, with the anisotropy
derived from image processing of seismic reflection data. Cast into the language of geostatistics, the
method could be referred to as seismic image-guided kriging. We validate the method on a synthetic
example cropped from the Marmousi2 seismic benchmark, and find that the use of the image-guided
prior resulted in a 39% improvement in correlation with the unknown true density anomaly compared
to use of a stationary prior.