Regularization of the AVO inverse problem by means of a ...

CHAPTER 1. INTRODUCTION 2
may show different anomalies on seismic section such as bright-spot, flat-spot and dim-spot
(McQuillin et al., 1984). ’Bright-spot’ appears where rocks-filled with gas and results in an
increased contrast i.e. it is associated with strong amplitude contrast across lithology and
their fluid content. On the contrary, ’dim-spots’ are associated with weak amplitude and
’flat-spot’ occur at fairly sharp gas-liquid contact. These anomalies on the seismic section
can be used as direct indicators of hydrocarbon. However, such anomalies can exist due to
other structural changes; for example local buildups of carbonate (old oyster reefs) (Taner
et al., 1979). This indicates that detailed information about the physical properties of the
rocks that causes the amplitude anomaly should be estimated. Those physical properties
help to predict fluid content (oil, gas, or water) and avoid the ambiguity in the interpre-
tation of the amplitude anomalies. In other words, they give additional information about
potential reservoirs or help to identify new hydrocarbon reservoirs. However, extracting
the physical model parameters from seismic data is not a simple task. It involves extensive
mathematical modeling and algorithms for seismic data inversion. In the next two sections,
I will discuss about forward and inverse problems.
1.1 Forward Problems
The method to derive information about a given system from known physical parameters is
what is called forward (direct) problem. The concern in this kind of problem is describing
a behavior of a given system in terms of the measured parameters i.e. constructing the
physics of the problem. It is an easy problem if the physical model is known. A simplified
diagram which shows a relationship between the model and the data in forward modeling
is shown in Figure 1.1.
1.2 Inverse Problems
Inverse problems are problems which arises when data measurements are obtained and one
wants to estimate unobservable property. In other words, it is a method of inferring model
parameters that characterize a system under study (see Figure 1.1). Inverse problems are
common in applied sciences such as geophysical exploration, medical tomography, remote
sensing, and astronomy. The basic step in formulating inverse problems is to write down a
system of equations (linear or non-linear) that fully describe the relationship between the
observed data, the physics model, and the unknown model parameters. Depending on the
number of equations and the unknown model parameters, the system of equations can be
classified as underdetermined, even-determined or overdetermined. For certain defined num-
ber of equations and unknowns, the problem is said to be overdetermined if the system of