seismology, one major aspect of waveform data that potentially is
easier to measure and analyse has generally been ignored. That
is, the information content of seismic amplitudes. Perhaps the
potential complexity has deterred most researchers from a more
thorough investigation of the practical use of seismic amplitude
data. The author of this volume presents an authoritative and
detailed study of amplitude data, as used in conjunction with
traveltime data, to provide better constraints on the variation of
seismic wave speed in the subsurface.
One of the fundamental problems in conventional reflection seismic
tomography using only traveltime data is the possible ambiguity
between the velocity variation and the reflector depth. The inclusion
of amplitude data in the inversion may help to resolve this problem
because the amplitudes and traveltimes are sensitive to
different features of the subsurface model, and thereby
provide more accurate information about the subsurface structure
and the velocity distribution. An essential goal of this monograph
is to make the amplitude inversion method work with real reflection
seismic data. Contents:
Preface. Introduction Professor G.A. Houseman.
1. Introduction to amplitude inversion.
Introduction. Velocity-depth ambiguity in
traveltime inversion. Resolving ambiguity by using amplitude
information. Overview of amplitude inversion. Analytical
expression for the geometrical spreading function for layered
structures. 2. Traveltime and ray-amplitude in heterogeneous
media.
Introduction. Bending ray tracing method. Traveltime and its
perturbations. Propagator of paraxial rays and geometrical
spreading. Ray perturbations due to model perturbations. Ray
amplitude. 3. Amplitude coefficients and approximations.
Introduction. The Zoeppritz equations. The pseudo-p
2
expressions. Quadratic expressions in terms of elastic
contrasts. Accuracy of the quadratic approximations.
Amplitude coefficients represented as a function of three
elastic parameters. Three elastic parameters from amplitude
inversion. Implication for fluid substitution modelling.
4. Amplitude inversion for interface geometry.
Introduction. Parameterization and forward
modelling. Subspace gradient inversion method. A simple
example of reflection amplitude inversion. Inversion for an
interface represented as a sum of harmonic functions. Stability of
the amplitude inversion. Strategy for the choice of ∆k and M.
Discussion. 5. Amplitude inversion for velocity variation.
Introduction. Amplitude dependence on slowness
perturbation. Inversion algorithm. Inversion example of 1-D
slowness distribution. Constraining higher wavenumber
components. Robustness of the inversion in the presence of model
error or data noise. Inversion of arbitrary smooth velocity
anomalies. Discussion. 6. Sensitivities of traveltimes
and amplitudes in joint inversion.
Introduction. The Hessian and the norm in model
space. Sensitivities to interface geometry. Sensitivities to 2-D
slowness variation. Inversion formula. Joint inversion for an
interface. Joint inversion for slowness. Discussion.
7. Amplitude inversion of a multi-layered structure.
Introduction. Forward calculation and inverse method. Preliminary
inversion test. Damped subspace method. Multi-scale scheme.
Multi-stage damped subspace method. 8. Practical approach to
application.
Introduction. Amplitudes estimated from
migrated gathers. Demigration of reflection amplitudes. Winnowing
amplitudes by LOESS. Inversion procedure. Inversion results.
9. Simultaneous inversion for model geometry and elastic
