shot-profile migration of gpr data
DESCRIPTION
Shot-profile migration of GPR data. Jeff Shragge, James Irving, and Brad Artman Geophysics Department Stanford University. Seismic vs. GPR Data. Seismic Elastic waves Multi-offset data Redundancy multiple offsets Localized source. GPR EM waves Single- or Multi-offset data - PowerPoint PPT PresentationTRANSCRIPT
Shot-profile migration of GPR data
Jeff Shragge, James Irving, and Brad Artman
Geophysics Department Stanford University
Seismic vs. GPR Data
Seismic• Elastic waves• Multi-offset data• Redundancy
– multiple offsets• Localized source
GPR• EM waves• Single- or Multi-offset data• Redundancy
– repeated acquisition• Localized source
GPRSeismic
Seismic vs. GPR Data
Common goal: Best possible image of subsurface reflectivity
GPRSeismic
Our aim: Transfer recent advances in multi-offset seismic migration techniques to GPR
Agenda
• Rationale– Multi-offset, prestack, wave-equation imaging
• Imaging assumptions• Methodology
– Wavefield extrapolation– Shot-profile migration – Imaging condition– Angle-domain gathers
• Field data example
Agenda
• Rationale– Multi-offset, prestack, wave-equation imaging
• Imaging assumptions• Methodology
– Wavefield extrapolation– Shot-profile migration – Imaging condition– Angle-domain gathers
• Field data example
Acquisition: Why Multi-offset?• Vast majority of GPR work involves constant offset data
– collection, processing, interpretation
• Multi-offset systems are increasingly available
Pros• Improved:
– velocity estimation, reflector imaging, S/N ratio
• Affords better subsurface characterization– AVO/AVA studies, facies and property estimates
Acquisition: Why Multi-offset?• Vast majority of GPR work involves constant offset data
– collection, processing, interpretation
• Multi-offset systems are increasingly available
Cons• More labor intensive
– Improving with new technology
• More computationally intensive
Processing: Why pre-stack wave-equation?
• Pre-stack imaging is more robust– Post-stack migration assumes that NMO-transformed traces are a
good approximation of the zero-offset trace – Significant lateral velocity variation breaks NMO approximation– Maintain angular information for AVA studies
• Wave-equation migration is more accurate– No high-frequency approximation
• Wave-based not ray-based– Accurate over full range of frequencies– Naturally handle multipathing (unlike Kirchhoff migration)
Agenda
• Rationale– Multi-offset, prestack, wave-equation imaging
• Imaging assumptions• Methodology
– Wavefield extrapolation– Shot-profile migration– Imaging condition– Angle-domain gathers
• Field data example
Imaging Assumptions
t
x
Tx Rx
• Maxwell’s equations represented by 2-D scalar wave equation • Assumptions
– Geology is 2-D
Imaging Assumptions
t
x
Tx Rx
• Maxwell’s equations represented by 2-D scalar wave equation • Assumptions
– Geology is 2-D and data is collected perpendicular to strike (TE mode)
Imaging Assumptions
t
x
Tx Rx
• Maxwell’s equations represented by 2-D scalar wave equation • Assumptions
– Geology is 2-D and data is collected perpendicular to strike (TE mode)– Heterogeneities in earth are small such that gradients in EM constitutive parameters are negligible– Isotropic scattering, no antenna radiation patterns
Governing EquationsGoverning 2-D scalar wave-equation in frequency (ω) domain
E = Electric field (component) v(x,z) = wavespeed
ε = dielectric permittivityμ = magnetic permeability σ = conductivity c = speed of lighti = sqrt(-1)
0Ez)v(x,
ωE∇2
22
σiω-εμcz)v(x,
Agenda
• Rationale– Multi-offset, prestack, wave-equation imaging
• Imaging assumptions• Methodology
– Wavefield extrapolation– Shot-profile migration– Imaging condition– Angle-domain gathers
• Field data example
Wavefield ExtrapolationWant solution to Helmholtz equation given boundary condition E(x,t,z=0)
2x2
2
z k- z)v(x,
ω±=k
Wave-equation dispersion relation
Δzikxx
ze ω)z,,E(kω)Δz,z,E(k
Wavefield propagates by advection - with solution
Ez)v(x,
ω-E∇ 2
22
Shot-profile Migration• Directly mimics the experiment by migrating the shot-record• Define source and receiver wavefields• Source wavefield – Ss(x,t,z=0)
– Idealized point source at Tx location
– Propagated causally: exp(ikzΔz)– Subscript s is the Shot-profile index
• Receiver wavefield - Rs(x,t,z=0) – Rx multi-offset data from point source at Tx location
– Propagated acausally: exp(-ikzΔz)– Subscript s is the Shot-profile index
At Z=0
Shot-profile Migration• Seed source and receiver wavefields
x
t t
x
Source Receiver
Shot-profile Migration• Seed source and receiver wavefields• Propagate S and R to all depths using wavefield extrapolation
At Z=nΔZ
x
t t
x
Source Receiver
Shot-profile Migration• Correlate Ss and Rs using imaging condition• Repeat for all shot profiles and sum
ω)z,(x,Rω)z,(x,Sz)I(x,ω
sss
Angle-domain Gathers• Compute image domain equivalent of offset: h• Have to use more advanced imaging condition
• Reflectivity at opening angle γ computed after imaging
• kh = offset wavenumber kz = vertical wavenumber• Velocity Analysis: angle gathers are flat for correct velocity
ω)z,h,(xRω)z,h,(xSh)z,I(x,ω
sss
z
h
kk
tan γ
Agenda
• Rationale– Multi-offset, prestack, wave-equation imaging
• Imaging assumptions• Methodology
– Wavefield extrapolation– Shot-profile migration– Imaging condition– Angle-domain gathers
• Field data example
Field Data Example• 2-D multi-offset GPR data set - Vancouver, BC, Canada• Geology
– Sand and gravel glacial outwash deposit– Underlain by conductive marine clay with topographically varying surface
• Data Acquisition– PulseEkko 100 GPR system– 100 MHz antennas oriented perpendicular to survey line– 30 receivers/shot gather: 0.5m-15m at 0.5m intervals– 200 shot gathers at 0.5m shot spacing
Unmigrated near-offset section
Top ofClay?
Diffractions
• Velocity model generated using semblance analysis on CMP gathers• RMS velocity picks converted into an interval velocity function• Water table ~ 4.5 meters
Layering?
Migrated near-offset section
Top ofClay
ReflectorContinuity
CollapsedHyperbolas• Clearer image after hyperbola collapse
• More laterally continuous reflectors• Top of clay readily identifiable• On-lap reflectors in sand/gravel layer visible
On-lap reflectors
ExtensionsAntenna radiation patterns
– Flexibility of Shot-profile allows for radiation patterns to be modeled into wavefields
Non-acoustic propagation– Wavefield extrapolation does not require acoustic propagation; apply
more physical operators
Anisotropic scattering– Angle gathers preserve the reflection angle information– Compensate with anisotropic scattering angle filters
Conclusions• Prestack wave-equation methods can be extended to
GPR data
• Shot-profile migration is flexible– Incorporate radiation patterns in source and receiver wavefields– Incorporate more realistic scattering physics into imaging condition
Acknowledgements
• Rosemary Knight– Stanford Environmental Geophysics
• Biondo Biondi– Stanford Exploration Project