Shot-profile migration of GPR data Jeff Shragge, James Irving, and Brad Artman Geophysics...

jeff@sep.stanford.edu

Shot-profile migration of GPR data

Jeff Shragge, James Irving, and Brad Artman

Geophysics Department Stanford University

paul@sep.stanford.edu

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

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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

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Agenda

• Rationale– Multi-offset, prestack, wave-equation imaging

• Imaging assumptions• Methodology

– Wavefield extrapolation– Shot-profile migration – Imaging condition– Angle-domain gathers

• Field data example

paul@sep.stanford.edu

Agenda

• Rationale– Multi-offset, prestack, wave-equation imaging

• Imaging assumptions• Methodology

– Wavefield extrapolation– Shot-profile migration – Imaging condition– Angle-domain gathers

• Field data example

jeff@sep.stanford.edu

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

jeff@sep.stanford.edu

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

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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)

jeff@sep.stanford.edu

Agenda

• Rationale– Multi-offset, prestack, wave-equation imaging

• Imaging assumptions• Methodology

– Wavefield extrapolation– Shot-profile migration– Imaging condition– Angle-domain gathers

• Field data example

jeff@sep.stanford.edu

Imaging Assumptions

t

x

Tx Rx

• Maxwell’s equations represented by 2-D scalar wave equation • Assumptions

– Geology is 2-D

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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)

jeff@sep.stanford.edu

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

jeff@sep.stanford.edu

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,

jeff@sep.stanford.edu

Agenda

• Rationale– Multi-offset, prestack, wave-equation imaging

• Imaging assumptions• Methodology

– Wavefield extrapolation– Shot-profile migration– Imaging condition– Angle-domain gathers

• Field data example

jeff@sep.stanford.edu

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

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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

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At Z=0

Shot-profile Migration• Seed source and receiver wavefields

x

t t

x

Source Receiver

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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

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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

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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

jeff@sep.stanford.edu

Agenda

• Rationale– Multi-offset, prestack, wave-equation imaging

• Imaging assumptions• Methodology

– Wavefield extrapolation– Shot-profile migration– Imaging condition– Angle-domain gathers

• Field data example

jeff@sep.stanford.edu

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

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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?

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Migrated near-offset section

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Unmigrated near-offset section

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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

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Flat Angle Gathers

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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

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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

jeff@sep.stanford.edu

Acknowledgements

• Rosemary Knight– Stanford Environmental Geophysics

• Biondo Biondi– Stanford Exploration Project