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Target‐oriented imaging using extended image volumes: a low‐rank factorization approach

Imaging in geological challenging environments has led to new developments, including the idea of generating reflection responses by means of interferometric redatuming at a given target datum in the subsurface, when the target datum lies beneath a complex overburden. One way to perform this redatuming is via conventional model‐based wave‐equation techniques. But those techniques can be computationally expensive for large‐scale seismic problems since the number of wave‐equation solves is equal to two times the number of sources involved during seismic data acquisition. Also conventional shot‐profile techniques require lots of memory to save full subsurface extended image volumes. Therefore, we can only form subsurface image volumes in either horizontal or vertical directions. To exploit the information hidden in full subsurface extended image volumes, we now present a randomized singular value decomposition‐based approach built upon the matrix probing scheme, which takes advantage of the algebraic structure of the extended imaging system. This low‐rank representation enables us to overcome both the computational cost associated with the number of wave‐equation solutions and memory usage due to explicit storage of full subsurface extended image volumes employed by conventional migration methods. Experimental results on complex geological models demonstrate the efficacy of the proposed methodology and allow practical reflection‐based extended imaging for large‐scale five‐dimensional seismic data.