Sirgue, Laurent, 2003. Inversion de la forme d'onde dans le ...

1.1. DETERMINATION OF THE MACRO-MODEL 3
More advanced techniques such as traveltime tomography have therefore been developed
and are able to handle laterally varying media (Bishop et al., 1985; Farra and Madariaga, 1988).
The traveltime tomography method consists of the resolution of an inverse problem that seeks
to minimise the mismatch between observed and calculated traveltime. The observed traveltime
are picked in the data volume and are identified by coherent events such as reflection hyperbolas
or diving/refracted arrivals. The calculated data are computed using ray tracing techniques
based on the high frequency asymptotic approximation of the wave equation ( ˘Cervený et al.,
1977; Chapman, 1985). Such modelling methods are accurate if the model varies slowly with
respect to the wavelength of the propagating wave and are therefore not adapted to simulation of
propagation within highly heterogeneous media (Chapman, 1985). For this reason, the velocity
model estimated from ray based tomography is required to be smooth; the blocky nature of
the model may however be accounted for by including velocity discontinuities (interfaces).
A widely used 2-D traveltime inversion technique is the program rayinvr developed by Zelt
and Smith (1992) that allows the simultaneous inversion of various types of ray propagation:
reflections, refractions and diving waves.The implementation of this application requires the
traveltime picking of events in time that must be identified with features in the model: for
example reflections as well as refractions must be associated with reflectors (interface). Such a
method therefore demands a strong a priori knowledge of the velocity structure as the number
of layers and lateral discontinuities must be known which may be difficult to determine in the
presence of a complex structure.
Traveltime tomography relying on the use of the first arrival traveltimes alone may also be
used (Zelt and Barton, 1998). The calculated traveltimes are computed using a finite difference
solver of the eikonal equation (Vidale, 1990; Podvin and Lecomte, 1991); diving rays are traced
by following the normal of the wavefront connecting the receiver to the source. This method
presents a great advantage: the first arrival picked traveltimes are not required to be associated
with particular horizons of the model. However, large offset data are necessary to assure the
proper illumination of the deep part of the model. Also, the exploitation of the first arrival
information is not very efficient in the determination of low velocity zones which tend to be
avoided by first arrival diving rays.
Alternative methods have emerged that aims to avoid the “hand” picking and interpretation
of coherent events in the data. Billette and Lambaré (1998) proposed the stereotomography approach
that relies on the picking of locally coherent events that may be performed automatically.
This picking does not require the association of traveltime picks with continuous reflections in