AVO Modelingfor the Effects of Attenuation and Random

Scattering Using Thin-Slab Propagator

Xian-Yun Wu & Ru-Shan Wu

Modeling and Imaging Lab.University of California, Santa Cruz

Presently at URC, ExxonMobil

Outline

Introduction

Effects of scattering Effect of attenuation AVO in heterogeneous visco-elastic media Frequency-Dependent AVOs

Conclusions

Dual-domain one-way thin-slab propagator

Numerical examples

AVO analysis (elastic parameters and fluid contents)

Introduction

Significant effects of wave propagation on local true-amplitude (scattering, anelasticity, frequency-dependent, etc.)

Developing efficient AVO forward modeling tools (high efficiency, complicated models)

Dual-domain one-way thin-slab propagator and its applications

Dual-domain one-way propagator (thin-slab)

)(ku x0P

)(ku x0S

X-domain

K-domain

0S

Δzik ueSz

0P

Δzik uePz

Up

Us

0Pu

0Su

0Pu

0Su

0

0

0

elastic

0S

Δzik ueSz

0P

Δzik uePz Up

Us

+

+

updated fieldIncident

field

(x)u(x)u)( f

βfα

SPPPxik

ρ

xδρdxe x

:ˆˆ1

2

kkikμλ

xδλdxe PPxikx

(x)u

)( fα

(x)ε(x)ε

1

2

)(2 fβ

fα

SPPPxik

ikμλ

xδμdxe x

Scattered field (P wave):

Elastic thin-slab propagator

kx

dxe SSPSxikx ˆ(x)u(x)u)( f

βfα

(x)ε(x)ε

1

2

)(2 fβ

fα

SSPSxik

ik

xdxe x

Scattered field :

Elastic thin-slab propagator

Incorporate Q factors into the propagator

),2/1( , )2/1( Sp QiQi ),2/1( , )2/1( 0

000

00 SP QiQi

Complex velocities :

Elastic parameters :

0)()( xx; )()( 0 xx 0)()( xx

222 2 ; 2 2000

200

2000 2 ; 2

Perturbations :

Effects of scattering (heterogeneities)

Effect of attenuation (intrinsicity)

AVO in heterogeneous visco-elastic media

Frequency-dependent AVO

Numerical examples

Effects of scattering due to heterogeneities in elastic parameters

Type: exponential function Corrl. lengths: 100m in x and 40m in z.The rms: 2%

Plane P-wave

Homogeneous Random

Transmitted wavefront

Thin-slab

FD

Reflection amplitudes in random media

Exponential

Reflection amplitudes in random media

White-noise

Qp=Qs=50

Qp=Qs=500

Effects of attenuation

Reflection amplitudes in anelastic random media

Reflection amplitude in elastic random media

Reflection amplitudes in random media with Q

AVO in anelastic and random media

1/Q ~ frequency

Frequency-dependent AVO

shale

oil sand

*S R

Conclusions

Properties of target zones control the AVO trends; Qs mainly affect the absolute amplitudes of reflections; scatterings mainly increases local variations in reflected amplitudes.

Spatially correlated heterogeneities (even as weak as rms=1%) may produce significant effects on AVO.

In visco-elastic heterogeneous media, local reflections may be the result of interaction between Q and elastic parameters.

Table 1. Reservoir model

shale 3170 1668 2.36 0.31

gas 3350 2231 2.02 0.10Oil 3527 2131 2.22 0.21brine 3551 2109 2.27 0.23

Note: Parameters are taken from Simmons and Backus (1994).