Transcript Document

Most Kirchhoff Tricks for Kirchhoff
Reverse
Migration
Migration
canTime
beKirch.
Implemented
for RTM
Generalized
Migration
Trial image pt x
Calc. Green’s Func. By FD solves
w ,r,s
*
G(s|x) [G(x|r)* d(r)] =
m(x)
Generalized Kirchhoff kernel
= dot product data with hyperbola
Convolution
of G(s|x) with G(x|r)
Direct
wave
Backpropagated
T=0
traces
QED: RTM can now enjoy:
Anti-aliasing filter
Obliquity factor
Angle Gathers
UD Separation
Decomplexify
back&forward
felds according 2 taste
Etc. etc.
s
r
x
Phase Shift, Beam, Kirchhoff Migrations
are Special Cases of True RTM
1. RTM: de (x) =
ds
=
S [G(s|x)G(x|g)]* d(s|g)
Frechet Derivative
s,g
S [{ G(s|x)
+ G(s|x) } { G(x|g) + G(x|g) } ]* d(s|g)
s,g
~
S { G(s|x)
G(x|g) }* d(s|g)
True RTM
s,g
First Arrival Filter
& U p+Down filter
Super-wide Angle Phase
Shift Migration
First Arrival Filter
Early Arrival Filter
Single Arrival Kirchhoff
w/o high-freq. appox
Multiple Arrival Kirchhoff
w/o high-freq. appox
(or Super beam migration)
Example (Min Zhou, 2003)
Standard FD Wavefront G(s|x)
Standard RTM
Early Arrival FD Wavefront G(s|x)
vs
Early Arrival RTM
Is Superresolution
bytree..who
RTM Achievable?
This is highest
fruit on the
dares pick it?
Tucson, Arizona Test
Super-resolution Test - Point # 14 at X = 24m
1
Direct - Full Aprature
Direct - Half Aprature
Scatterers - Full Aprature
Scatterers - Half Aprature
0.8
Normalized Amplitude
60 m
0.6
~Kirchhoff Mig.
0.4
0.2
0
Poststack Migration
-0.2
~Scattered RTM
10
12
14
16
18
20 22
X (m)
24
26
28
30
Can Scatterers Beat the Resolution Limit?
Recorded Green’s functions G(s|x) divided into:
- Shot gathers with direct arrivals only
- Shot gathers with scattered arrivals only