Seismic scattering attenuation and Seismic scattering attenuation and

its applications in seismic imaging its applications in seismic imaging and waveform inversionand waveform inversion

Yinbin LiuVancouver 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

OutlinesOutlines

Anderson wave localizationAnderson wave localization

Very few believed [localization] at the time,and even fewer saw its importance; amongthose who failed to fully understand it atfirst was certainly its author. It has yet toreceiver adequate mathematical treatment,and one has to resort to the indignity ofnumerical 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 absorptionInterference and absorption

Absorption has very little inference on signal

ShaleSandstoneshale

Well log(rock physics)

Gas reservoir: strong local heterogeneityGas reservoir: strong local heterogeneity

thin CBM

Modified from Einsel,1992microscope

Rock physicsWell log

frac

ture

s

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 resolutionSeismic imaging resolution

Gas-bearing formationGas-bearing formation

Microscopic scale heterogeneity has an important influence on seismic response

8.8725.07.0

65.280.5

impedance gas

impedancematrix

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 earthquakeLow 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 heterogeneityStrongly-scattered small-scale heterogeneity

Hyper-Airy function

Similarity of different wave fieldsSimilarity of different wave fields

Ocean wave

Microwave dispersion

Pleshko and Palocz, 1969

Interferenceexactly include multiple scattering

Fundamental lawsFundamental laws

Z1

Z2

Z1

Z2

Z1

Two scatterers (Two scatterers (mm and and ll) )

Multiple scattering theoryMultiple 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 effectsSeismic scale effects

A quasi-periodic layered model

……

M=1 M=2 M=3

……

2 layers 4 layers 6 layers

M=256

512 layers

Ray Scattering

Comparison between theory and experiment

0 1 2 3 4 5 6 7 8-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

Calculation

Experiment

Am

plitu

de

time, us

10 MHz

Scale-dependent multiple scatteringScale-dependent multiple scattering

ray

effectivedispersion

coda

Low frequency

enhancement

Ray theory: large scale

slowing velocity

Multiple low frequency scattering

theory resonance

coherent scattering

enhancement

Effective medium theory: micro-scale

Inh

om

og

en

eou

s s

cal e

Multiple scatteringMultiple 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 dispersionPhysical explanation for dispersion

12+3+… (scattering resonance)

Physical interpretationPhysical interpretation

12

3

Coda

The frequency of LFSR, which is about one order of magnitude lower than that of the natural resonance, provides higher resolution.

Multiple scatteringMultiple correlationMultiple 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 imagingImpact on wave imaging

Thank you for your attention