Aerial View Eucalyi River, PeruAerial View Eucalyi River, Peru
Seismic View: 2 km Deep Meandering RiverSeismic View: 2 km Deep Meandering River
Overview of Seismic Overview of Seismic ImagingImaging
Jerry Schuster Jerry Schuster
KAUSTKAUST
OutlineOutline• Forward Acoustic Problem Forward Acoustic Problem
• Inverse Acoustic Problem Inverse Acoustic Problem
• Seismic Experiment Seismic Experiment
• Seismic Migration Seismic Migration
ZO Seismic SectionZO Seismic SectionD
epth
Dep
th
Tim
eT
ime
c c 2 2 2 2
c c 1 1 1 1
Monterey Optical Image Monterey Optical Image
Monterey Seismic Image Monterey Seismic Image 0 km0 km
2 km2 km
0 km0 km
0.1 km0.1 km
Acoustic Forward ProblemAcoustic Forward ProblemD
epth
Dep
th
cc22
cc11
Given:Given: dd + k + k dd = = oo22 22 k = k = cc
Find:Find: d(r)
Soln:Soln:
rorr )()(grd)(
dr
PressurePressure SourceSource
Goal: Compute ZO Goal: Compute ZO Seismic SectionSeismic Section
Dep
thD
epth
Tim
eT
ime
c c 2 2 2 2
c c 1 1 1 1
rorr )()(grd
)(
dr
rorr )()(grd
)(
Common Shot GatherCommon Shot GatherD
epth
Dep
thT
ime
Tim
e
Common Midpoint GatherCommon Midpoint GatherD
epth
Dep
th
MidpointMidpoint
Tim
eT
ime
Normal Moveout CorrectionNormal Moveout Correction
MidpointMidpoint
Dep
thD
epth
Tim
eT
ime
Stacked TraceStacked Trace
MidpointMidpoint
Dep
thD
epth
Tim
eT
ime
Stacked Seismic SectionStacked Seismic SectionD
epth
Dep
thT
ime
Tim
e
OutlineOutline• Forward Acoustic Problem Forward Acoustic Problem
• Inverse Acoustic Problem Inverse Acoustic Problem
• Seismic Experiment Seismic Experiment
• Seismic Migration Seismic Migration
What is the Problem?What is the Problem?
V/2V/2
Dep
thD
epth
Tim
eT
ime
Events Can Originate Updip Events Can Originate Updip
Incorrect location. You think Incorrect location. You think events originated directlybelow geophones.events originated directlybelow geophones.
D=
VT
/2D
=V
T/2
What is another Problem?What is another Problem?D
epth
Dep
th
Tim
eT
ime
Events Originate Pt. Diffractors Events Originate Pt. Diffractors
0 m 30 m0 m 30 m
0 km0 km
30 m30 m
cornercorner
ZO DataZO DataZO DataZO DataMigration Migration (Relocates Reflections back to Place of Origin)(Relocates Reflections back to Place of Origin)
0 km 7 km0 km 7 km
0 km0 km
3 km3 km
Given: Given: dd = L= LooSeismic Inverse ProblemSeismic Inverse Problem
Find: Find: o(x,y,z)o(x,y,z)
Soln: min || LSoln: min || Loo--dd || ||22
oo = [L L] L = [L L] L ddTT TT-1-1
‘‘
L L ddTT
migrationmigration
waveformwaveforminversioninversion
OutlineOutline• Forward Acoustic Problem Forward Acoustic Problem
• Inverse Acoustic Problem Inverse Acoustic Problem
• Seismic Experiment Seismic Experiment
• Seismic Migration Seismic Migration
2-w
ay ti
me
2-w
ay ti
me
(x-(x-xx ) + y ) + y 2222
.5.5ccssrrss ==
rrss + + TToo
ZO MigrationZO Migration SmearSmear Reflections along Fat Circles Reflections along Fat Circles
xxss
rr
d(d(xx , ) , )rrssss
2-w
ay ti
me
2-w
ay ti
me
ZO MigrationZO MigrationSmearSmear Reflections along Fat Circles Reflections along Fat Circles
rrssd(d(xx , ) , )ss
xx
& & SumSum
2-w
ay ti
me
2-w
ay ti
me
ZO MigrationZO MigrationSmearSmear Reflections along Circles Reflections along Circles
rrssd(d(xx , ) , )ss
rr
& & SumSum
ZO Migration ResolutionZO Migration ResolutionIntersection of Fresnel ZonesIntersection of Fresnel Zones
Intersection of Fresnel ZonesIntersection of Fresnel ZonesVertical Res. = Near-Offset TracesVertical Res. = Near-Offset Traces
ZO Migration ResolutionZO Migration ResolutionIntersection of Fresnel ZonesIntersection of Fresnel Zones
Intersection of Fresnel ZonesIntersection of Fresnel ZonesHoriz. Res. = Far-Offset Traces Horiz. Res. = Far-Offset Traces
Why is Pt. Scatterer Response of MigrationWhy is Pt. Scatterer Response of Migrationa Blurred Version of Point?a Blurred Version of Point?
MigrationMigration:: m = m = L L ddTT
MigratedMigratedSectionSection
DataData
butbut dd = = LL rrLL rr
Migration SectionMigration Section = = Blured ImageBlured Image ofof r r
Seismic Section Seismic Section
Tim
eT
ime
12 km12 km
0 km 7 km0 km 7 km
0 km0 km
3 km3 km
0 km 7 km0 km 7 km
0 km0 km
3 km3 km
Migration Least Squares MigrationMigration Least Squares Migration
Seismic Imaging CourseSeismic Imaging Course
• Kirchhoff & Beam MigrationKirchhoff & Beam Migration
• Phase Shift-Like MethodsPhase Shift-Like Methods
• Reverse-Time MigrationReverse-Time Migration
• Full Waveform InversionFull Waveform Inversion