hocigs and vocigs via two-way reverse time migration

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)

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.

MωCiωKS 2

fuS s

su

f

,fSus1

Pratt et al.(1998)

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

*1dSur

),,,(),,,(),,,,( zhxxuzhxxuhzxxI srsss

d

sx

Two-way Reverse Time Migration

ddxhzxxIhzxI ss ),,,,(),,(

),,,(),,,(),,,,( hzxxuhzxxuhzxxI srsss

zx,

ru

( : complex conjugate)*

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 domainFrequency domain HOCIGs

Example 3

VOCIGs

Filtered HOCIGHOCIG