Wave‐equation Hessian by phase encoding

Abstract

I demonstrate a method for computing wave-equation Hessian operators, also known as resolution functions or point-spread functions, under the Born approximation. The proposed method modifies the original explicit Hessian formula, enabling efficient computation of the operator. A particular advantage of this method is that it reduces or eliminates storage of Green’s functions on the hard disk. The modifications, however, also introduce undesired crosstalk artifacts. I introduce two different phase-encoding schemes, namely, plane-wave phase encoding and random phase encoding, to suppress the cross-talk. I applied the Hessian operator obtained by using random phase encoding to the Sigsbee2A synthetic data set, where a better subsalt image with higher resolution is obtained.