Seismic anisotropy
From 1898 till his death in 1916, Rudzki attempted to advance the theory of anisotropy, he attempted to determine the wavefront of a transversely isotropic medium (TI) in 1898 and in 1912 and 1913 he wrote on surface waves in transversely isotropic half space and on Fermat's principle in anisotropic media respectively.
Shear waves have been observed to split into two or more fixed polarizations which can propagate in the particular ray direction when entering an anisotropic medium.
The approximate expressions for the wave velocities are simple enough to be physically interpreted, and sufficiently accurate for most geophysical applications.
Anisotropy has been reported to occur in the Earth's three main layers: the crust, mantle and the core.
The presence of aligned cracks, open or filled with some different material, is an important mechanism at shallow depth, in the crust.
It is well known that the small-scale, or microstructural, factors include (e.g. Kern & Wenk 1985; Mainprice et al. 2003): (1) crystal lattice preferred orientation (LPO) of constituent mineral phases; (2) variations in spatial distribution of grains and minerals; (3) grain morphology and (4) aligned fractures, cracks and pores, and the nature of their infilling material (e.g. clays, hydrocarbons, water, etc.).
In the past two decades, the seismic anisotropy has dramatically been gaining attention from academic and industry, due to advances in anisotropy parameter estimation, the transition from post stack imaging to pre stack depth migration, and the wider offset and azimuthal coverage of 3D surveys.
In addition, the establishment of correlation between anisotropy parameters, fracture orientation, and density, lead to practical reservoir characterization techniques.
In seismic exploration, shales represent the majority of the wave propagation medium overlying the petroleum reservoir.
Seismic velocity anisotropy in shale can be estimated from several methods, including deviated-well sonic logs, walkway VSP, and core measurement.
From the context of this article, wave propagation in a vertically transverse medium can be described with five elastic constants, and ratios among these parameters define the rock anisotropy.
This anisotropy parameter can be obtained in the laboratory by measuring the velocity travel speed with transducer ultrasonic systems at variable saturation and pressure conditions.
Usually, three directions of wave propagation on core samples are the minimum requirement to estimate the five elastic coefficients of the stiffness tensor.
Another way to get the wave propagation velocity at three directions is to arrange the ultrasonic transducer onto several specific location of the core sampler.
The last technique can be used to measure the seismic anisotropy is related to the sonic logging information of a deviated well.
As a result, unlike isotropic PSDM, it is consistent with well data and provides an ideal input for reservoir characterization studies.
They can only be determined with confidence through analysis of a variety of geoscientific material – borehole data and geological history.
The logical conclusion is that, this integrated approach should extend the use of anisotropic depth imaging from complex geology only, to routine application on all reservoirs.
Ones uses azimuthal variations in the amplitude versus offset (AVO) signature when the wave is reflected from the top or base of an anisotropic material, and a second exploits the polarizing effect that the fractures have on a transmitted shear-wave.
The P-P wave reflection coefficient have the following relation with the azimuthal if anisotropy exist in the layers:
The behavior of shear waves as they pass through anisotropic media has been recognized for many years, with laboratory and field observations demonstrating how the shear wave splits into two polarized components with their planes aligned parallel and perpendicular to the anisotropy.
In this case, the operator conducted several seismic surveys on a gas field in the north sea over the period of 1993-1998 .
As can be seen in the bottom plot, more small structure features are revealed due to the reduce of error and improved resolution.
In the Earth's crust, anisotropy may be caused by preferentially aligned joints or microcracks, by layered bedding in sedimentary formations, or by highly foliated metamorphic rocks.
In active tectonic areas, such as near faults and volcanoes, anisotropy can be used to look for changes in preferred orientation of cracks that may indicate a rotation of the stress field.
Hence, shear waves naturally "split" into separate arrivals with these two polarizations; in optics this is called birefringence.
In crustal geophysics, the anisotropy is usually weak; this enables a simplification of the expressions for seismic velocities and reflectivities, as functions of propagation (and polarization) direction.
In the simplest geophysically plausible case, that of polar anisotropy, the analysis is most conveniently done in terms of Thomsen Parameters.
For receiver functions, the P-to-S converted wave displays harmonic variation with earthquake back azimuth when the material at depth is anisotopic.
Below the transition zone, the three main minerals, periclase, silicate perovskite (bridgmanite), and post-perovskite are all anisotropic and could be generating anisotropy observed in the D" region (a couple hundred kilometer thick layer about the core-mantle boundary).
