Seismic scattering attenuation and its applications in seismic imaging and waveform inversion Yinbin Liu Vancouver Canada

Seismic imaging: mathematics Wave localization: physics and geology Oil and gas reservoir: strongly-scattered inhomogeneous media Low frequency scattering resonance A new physical concept passive seismic monitoring and non-volcanic seismic tremor

Introduction Low frequency scattering resonance Discussions Outlines

Anderson wave localization Very few believed [localization] at the time, and even fewer saw its importance; among those who failed to fully understand it at first was certainly its author. It has yet to receiver adequate mathematical treatment, and one has to resort to the indignity of numerical simulations to settle even the simplest questions about it. -- Philip W. Anderson, Nobel lecture, 8 December 1977 Incident pulse Energy space distribution Wave in impurity band conduction Common wave phenomenon: mechanical wave, electromagenetic wave, matter wave energy trap within low velocity zone multiple scattering Random arrangements of electronic or nuclear spins

Interference and absorption Absorption has very little inference on signal Shale Sandstone shale

Well log (rock physics) Gas reservoir: strong local heterogeneity thin CBM Modified from Einsel,1992 microscope Rock physics Well log fractures Macroscope seismic response

Velocity = 3000 m/s Dominant frequency 30 Hz Wavelength = 3000 / 30 = 100 m Reservoir thickness is usually much less than wavelength Only strongly-scattered reservoir can be seen by seismic Seismic imaging resolution

Gas-bearing formation Microscopic scale heterogeneity has an important influence on seismic response Strong heterogeneity : multiple scattering Effective media and Diffusive approximation

A high frequency small-amplitude onset superposing on a low-frequency large-amplitude background Low frequency earthquake

Media: gas-oil-bearing or magam geological bodies -- strong microscopic-scale heterogeneity Seismic response: macroscopic effect Medium structure: microscopic scale Model: coupling effect (mecroscopy) it is still a challenge project in physics Strongly-scattered small-scale heterogeneity

Hyper-Airy function Similarity of different wave fields Ocean wave Microwave dispersion Pleshko and Palocz, 1969

Interference exactly include multiple scattering Fundamental laws Z1Z1 Z2Z2 Z1Z1 Z2Z2 Z1Z1

Two scatterers (m and l)

Multiple scattering theory Systematic perturbation theory (T matrix) Twesky multiple scattering theory Above two theories are not suitable for studying the high order multiple scattering in strongly scattered scale-small heterogeneity Convergence issue

15 Seismic scale effects A quasi-periodic layered model …… M=1M=2M=3 …… 2 layers4 layers6 layers M= layers RayScattering

Comparison between theory and experiment 10 MHz

Scale-dependent multiple scattering ray effective dispersion coda Low frequency enhancement

Ray theory: large scale slowing velocity Multiple low frequency scattering theory resonance coherent scattering enhancement Effective medium theory: micro-scale Inhomogeneous scale Multiple scattering

The direct wave rapidly reduces to negligible values and the multiple reflection wave becomes the first arrival. Liu and Schmitt, 2002 v=D/t Physical explanation for dispersion

1 2+3+… (scattering resonance) Physical interpretation Coda

The frequency of LFSR, which is about one order of magnitude lower than that of the natural resonance, provides higher resolution. Multiple scattering Multiple correlation Multiple iteration Passive seismic monitoring (geophones are put in borehole) Non-volcanic seismic tremor Signal is no beginning and no ending persisting for days and months Impact on wave imaging

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