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 GPR Seismic

Seismic vs. GPR Data Common goal: Best possible image of subsurface reflectivity GPR Seismic 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 TxRx Maxwell’s equations represented by 2-D scalar wave equation Assumptions –Geology is 2-D

Imaging Assumptions t x TxRx 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 TxRx 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 Equations Governing 2-D scalar wave-equation in frequency (ω) domain E = Electric field (component) v(x,z) = wavespeed ε= dielectric permittivityμ=magnetic permeability σ = conductivityc=speed of light i= sqrt(-1)

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 Extrapolation Want solution to Helmholtz equation given boundary condition E(x,t,z=0) Wave-equation dispersion relation Wavefield propagates by advection - with solution

Shot-profile Migration Directly mimics the experiment by migrating the shot-record Define source and receiver wavefields Source wavefield – S s (x,t,z=0) –Idealized point source at Tx location –Propagated causally: exp(ik z Δz) –Subscript s is the Shot-profile index Receiver wavefield - R s (x,t,z=0) –Rx multi-offset data from point source at Tx location –Propagated acausally: exp(-ik z Δz) –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 S s and R s using imaging condition Repeat for all shot profiles and sum

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 k h = offset wavenumberk z = vertical wavenumber Velocity Analysis: angle gathers are flat for correct velocity

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 of Clay? 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

Unmigrated near-offset section

Migrated near-offset section Top of Clay Reflector Continuity Collapsed Hyperbolas 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

Flat Angle Gathers

Extensions Antenna 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