HOCIGs and VOCIGs via Two-way Reverse Time Migration William Symes, Fuchun Gao Rice University TRIP Oct 29, 2004

Outline Common image gathers (offset domain) Conclusions 1. Theory 2. HOCIGs and VOCIGs--- examples Conclusions

Two-way Reverse Time Migration 1. Forward propagation: finite difference solution to acoustic equation by where : impedance matrix. : seismic wave field vector. : source vector.   The acoustic wave equation is solved in frequency-space domain. Pratt et al.(1998)

Two-way Reverse Time Migration 2. Back-propagation of data 3. Horizontal offset image (frequency domain) Vertical offset image (frequency domain) Common image gathers (time domain): where : recorded wave fields. : back-propagated waves : source location. : image location ( : complex conjugate) The inversion problem is solved by gradient method.

Example 1 No. of source = 51 No. of receiver = 51 Source interval =10m Receiver interval=10m

Frequency domain CIGs

Frequency domain CIGs, tapered

time domain CIGs

Example 2 No. of source =101 No. of receiver = 101 Source interval =1.5m Receiver interval=1.5m

Time domain Frequency domain HOCIGs

Example 3

VOCIGs

HOCIG Filtered HOCIG