Research Article
Influence of Error in Estimating Anisotropy Parameters on
VTI Depth Imaging
S. Y. Moussavi Alashloo, D. P. Ghosh, Y. Bashir, and W. Y. Wan Ismail
Center of Seismic Imaging, Universiti Teknologi PETRONAS, 32610 Seri Iskandar, Malaysia
Correspondence should be addressed to S. Y. Moussavi Alashloo; y.alashloo@gmail.com
Received 11 March 2016; Revised 5 April 2016; Accepted 20 April 2016
Academic Editor: Alexey Stovas
Copyright © 2016 S. Y. Moussavi Alashloo et al. his is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.
hin layers in sedimentary rocks lead to seismic anisotropy which makes the wave velocity dependent on the propagation angle.
his aspect causes errors in seismic imaging such as mispositioning of migrated events if anisotropy is not accounted for. One of
the challenging issues in seismic imaging is the estimation of anisotropy parameters which usually has error due to dependency on
several elements such as sparse data acquisition and erroneous data with low signal-to-noise ratio. In this study, an isotropic and
anelliptic VTI fast marching eikonal solvers are employed to obtain seismic travel times required for Kirchhof depth migration
algorithm. he algorithm solely uses compressional wave. Another objective is to study the inluence of anisotropic errors on the
imaging. Comparing the isotropic and VTI travel times demonstrates a considerable lateral diference of wavefronts. Ater Kirchhof
imaging with true anisotropy, as a reference, and with a model including error, results show that the VTI algorithm with error in
anisotropic models produces images with minor mispositioning which is considerable for isotropic one speciically in deeper parts.
Furthermore, over- or underestimating anisotropy parameters up to 30 percent are acceptable for imaging and beyond that cause
considerable mispositioning.
1. Introduction
It is well-known that hydrocarbon reservoirs and overlying
strata are commonly anisotropic [1, 2]. In reality, it is rare to
have media with elliptical or weak anisotropy properties.
However, anellipticity (deviation of wavefield from ellipse) has
been commonly observed in the Earth’s subsurface, and it is
a signiicant characteristic of elastic wave propagation [3, 4].
Another challenging issue in depth imaging is the compu-
tation of the travel time taken by a seismic wave from source
to receiver. An eicient method to compute travel times is
solving the eikonal equation by employing inite diferences
[5, 6]. Diferent techniques have been introduced to solve
the eikonal equation, such as embedding methods, single-
pass methods, sweeping methods, and iterative methods [7].
he main diference of these techniques is in how they cope
with the complication of multivalued solutions and in inding
solutions in the vicinity of cusps and discontinuities [8].
Anisotropy was initially added to an eikonal solver algorithm
by Dellinger [9]. he embedding and iterative methods
are both time consuming, particularly in heterogeneous
and anisotropic conditions [7]. Fast sweeping methods are
originally proposed for isotropic media [10]; however, a
modiication is executed to handle the anisotropic condition
[11]. Single-pass or fast marching method (FMM) is another
tool for computing travel times but is not generally applicable
for anisotropic medium [5]. his algorithm has since been
modiied to work for anisotropy [12, 13].
In this study, a prestack depth migration algorithm is
developed based on an anelliptic VTI compressional wave
equation. Fomel’s anelliptic approximation [14] for both
phase and group velocity of P-wave are employed to derive
the eikonal equation. he fast marching inite diference
approach is used as our eikonal solver since it is fast and
stable for travel time computation. In anisotropic study, four
anisotropic models are used: a true model which is exactly
similar to the model employed for forward modelling, a
model with values 30 percent less than the true model, a
model with values 40 percent less than the true model, and
a model with values 30 percent more than the true model.
Hindawi Publishing Corporation
International Journal of Geophysics
Volume 2016, Article ID 2848750, 6 pages
http://dx.doi.org/10.1155/2016/2848750