Abstract

Media containing aligned rotationally symmetrical inclusions show transverse isotropy
with respect to elastic wave propagation. The characteristics of this type of anisotropy have
been investigated in the first part of this thesis (chapters 2, 3, and 4) while its implications
on Vertical Seismic Profiling have been investigated in the second part of this
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thesis
(chapters 5, 6, and 7).
Transverse isotropy due to aligned inclusions has been studied for inclusions ranging
from flat cracks (very small aspect ratio a.) up to spheres (a. = 1) using Nishizawa's model
(chapter 2). The resultant anisotropy as described by this model (which is based on a static
approach) is identical to the anisotropy described by Hudson's crack model (based on the
scattering of elastic waves) for inclusions with aspect ratios up to 0.3. This result, which is
surprising because Hudson's model has been derived for small aspect ratios (a. < 1),
implies (assuming the validity of Nishizawa's model) that Hudson's model which is often
used to interpret anisotropy observations can be applied to much larger aspect ratios than
the aspect ratios for which it has been derived.
Another characteristic of the anisotropy as described by Nishizawa's model is that
almost spherical inclusions (a. =:: 1) result in elliptical anisotropy, which is a type of
anisotropy that can never be due to sequences of thin isotropic layers.
Sequences of isotropic layers and systems of large aligned fractures are just like
aligned inclusions possible causes of transverse isotropy. Although these fractures and
sequences of isotropic layers have a geometry that is different from the geometry of aligned
inclusions they may result in the same anisotropy as aligned inclusions (chapters 3 and 4).
The model describing the anisotropy due to large aligned fractures turns out to be identical
to Hudson's crack model, whereas the model describing the anisotropy due to fine layering
is identical to Hudson's model for ranges of aspect ratios that strongly depend on the fluid
inside the inclusions. For the situations that these models are similar observed anisotropy
can only be interpreted in terms of crack distributions if additional information shows the
existence of cracks. However, for the situations where the similarity does not hold it is
possible to distinguish between the causes of transverse isotropy (chapter 4). It should be realized, however, that other causes of transverse isotropy exist. Therefore, the 'separation'
method described in this thesis should only be considered as a first step towards
distinguishing between the causes of transverse isotropy.
Because the 'representability' of cracked media by finely layered media strongly
depends on the fluid inside the cracks, this 'representability' might not only be an
interesting way to distinguish between the causes of transverse isotropy, but might also be
an useful tool to investigate the nature of the fluid. Considering an uniformly cracked
medium monitoring the nature of the fluid as a function of time or space could be very
important for earthquake prediction or gas exploration, respectively.
Studying anisotropy observations is a powerful way to obtain information about the
internal structures of the rocks (such as aligned inclusions, thin layering) which have
dimensions much smaller than the seismic wavelength used. Studying crack-induced
anisotropy offers the possibility to monitor the stress-field that aligns the cracks. There is
evidence that a changing stress strongly affects the aspect ratio of the cracks. The results of
the first part of this thesis on the effect of a changing aspect ratio on crack-induced
anisotropy have been used to develop methods to interpret anisotropy observations in
multi-offset shear-wave VSPs in terms of a changing aspect ratio. Changes in the aspect
ratio can be monitored in such VSPs (chapter 6) by studying the changes in the direction of
wave propagation at which there is no shear-wave splitting. This technique which has been
applied to synthetic shear-wave VSPs could become important if repeated VSPs are carried
out to analyze temporal changes in anisotropy in terms of a changing stress-field.
Although shear-wave splitting is often used as a key identifier of anisotropy one
should be aware that shear-wave splitting can also be caused by transmission effects at
interfaces in isotropic media (chapter 5). This effect should be taken into account first
before shear-wave splitting is interpreted in terms of anisotropy.
Anisotropy may give valuable information about the internal structures of rocks, but it
may also lead to erroneous interpretations, when it is not properly taken into account. In
chapter 7 this has been shown for an isotropic traveltime inversion scheme which, when
applied to multi-offset VSP traveltime data in layered transversely isotropic media, may
introduce errors in the depths of the interfaces separating the layers. Therefore, anisotropy
should be included in inversion schemes. In a first attempt to develop inversion schemes
that do take anisotropy into account a transversely isotropic traveltime inversion scheme
has been developed and successfully applied to synthetic multi-offset VSP-data. The
method developed is a robust method and further research is necessary to develop more
elegant methods. Despite the robustness of the method the results of the transversely
isotropic traveltime inversion scheme show, when compared with the results of the
isotropic inversion scheme, that both an isotropic and a transversely isotropic model can
explain the same traveltime data set (consisting of the arrival times of P- and first arriving
S-waves). To attack this problem of non-uniqueness additional information (such as
polarization, shear-wave splitting) should be incorporated in the inversion.
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