Geology - Phase Space Methods in Exploration Seismology.pdf

Collaborators
Phase Space Methods in Exploration Michael Lamoureux, Mathematics Prof. U Calgary
Seismology Robert Ferguson, Geophysics Prof, UT Austin
Lou Fishman, Mathematical Physicist, MDF International
PIMS Peter Gibson, Mathematics Prof, York
Inverse Theory Summer School Hugh Geiger, PDF, U Calgary
Seattle, 2005 Students: Chad Hogan, Carlos Montana, Saleh Al-
Gary F. Margrave Saleh, Richard Bale, Jeff Grossman, Yongwang Ma,
Yanpeng Mi, Linping Dong, Victor Iliescu, Peter
Manning
POTSI
Goals Part 1
• Examine some essential characteristics of
seismic wavefields and their Fourier transforms
• Understand the concept of phase space for a Seismic Data
wavefield
• Examine tools for manipulating a wavefield on its
phase space:
– raytracing, Fourier multipliers, pseudodifferential
operators, Gabor multipliers
• Two extended examples
– deconvolution: application of Gabor multipliers
– wavefield extrapolation: application of
pseudodifferential operators
Seismic Shot Record Seismic Shot Record
••• 200 geophones at 20m intervals •••••• 200 geophones at 20m intervals •••
e x e x
v v
a a
w w

t t
Re c Re c
f e f e
le r le r
c i c i
tio tio
n D n D
ψ()xzt,,= const
reflector reflector
Geophones record ψ()xz,0,= t∈
×
Want to know:
z z •Positions of reflectors
•Values of the reflection coefficients
1
Purely elastic finite-difference simulation Purely elastic finite-difference simulation
Depth Depth
Distance from source Distance from source
Surface recording of vertical motion Seismic Shot Record
Fir
st b
G re
r ak
o s
u
nd
r
o
Reflection ll
Receiver position
Seismic Shot Record Seismic Shot Record
− 104 104
2
Seismic Shot Record Seismic Shot Record
Gained Gained and clipped
Surface recording of vertical motion
Part 2
Fir
st b
G re Fourier Transforms
r ak
o s
u
nd
r
o
Reflection ll
Receiver position
Fourier Trans