An Introduction to Seismic Anisotropy


Lithosphere is usually modeled as a layered isotropic medium. However, in reality, upper mantle is anisotropic as evidenced by the azimuthal dependence of P and S wave propagation speed. Probable causes of the observed seismic wave propagation anisotropy include the aligned crystal structure of minerals, aligned cracks and fractures. This anisotropy in the lithosphere has been greatly studied in terms of shear wave splitting, Love/Rayleigh wave incompatibility, azimuthal dependence Pn velocities (Anderson, 1989). Adequate knowledge of the deviation of deformation from the isotropic layer assumption under different boundary conditions will help explain the observed deformation of the lithosphere. The elastic stiffness tensor changes with crystal symmetry representing or associated with a given seismic anisotropy. I am going to use the stiffness tensor for different types of crystal symmetry and will investigate the changes in the deformation patterns of models with different crystal symmetry under different orientation of applied loading. The purpose of this term project is to review previous works in seismic anisotropy and its various applications in Earth’s science.


Once upon a time in the field of earth science, scientists modeled the lithosphere as a layered isotropic medium. These results from these models deviate a little from the observed measurements especially the variation of seismic wave’s arrival time (i.e. velocities) measured from different directions. Every day, these observations made scientists to further study the rocks in the earth’s lithosphere in order to understand this anomaly. One day, the scientists observed that seismic waves has different velocities as they propagate through olivine, an important mineral which made up higher percentage of mantle rocks, via different directions. Because of that, they questioned the assumption of isotropic medium in the constitutive equations relating stress and strain, and derived a new stiffness tensor relating stress and strain for anisotropic medium. They also observed that different crystals have different stiffness tensors and the mathematics was described by Anderson (1989).

Anderson (1989) also discussed the shear-wave birefringence, azimuthal anisotropy and the apparent discrepancy between Love and Rayleigh waves, all accords to the evidence of anisotropy in the earth. He also discussed the upper mantle anisotropy. Philip Wild discussed the two types of anisotropy: vertical transverse isotropy (VTI) which characterizes horizontal layering, and horizontal transverse isotropy (HTI) for vertical fracturing. He discussed the used of anisotropy in the oil and gas industry to improve seismic data and well ties which in turns improves interpretation in general and fracture interpretation. Bandyopadhyay (2009) discussed the various geological causes of anisotropy in shale and how their correction can improve interpretation of seismic data. However, there is complexity in the stiffness tensor for anisotropic mediums e.g. the orthorhombic (or orthotropic) crystals which is commonly used for fractured reservoir has nine independent elastic constants. There is a need to work on efficiency of the computations because the complexity in the stiffness tensor makes it very expensive to model reservoir rocks with orthorhombic symmetry. Tsvankin presented a method to reduce the elastic constants to two vertical (P and S) velocities and seven dimensionless parameters which can account for the anisotropy expected in the symmetry. This method also worked for orthorhombic models with strong velocity anisotropy.

The theory of seismic anisotropy has been used extensively to study the anisotropy of the mantle. Observations show that in partial molten rocks undergoing deformation, a radially inward segregation of melt fraction was observed. This segregation pattern was explained theoretically by viscous anisotropy. Qi et al. (2005) confirmed the viscous anisotropy hypothesis under torsional deformation using experimental observation and confirmed the prediction of radially inward segregation of the melt fraction.

There is also a need to incorporate independent methods to study anisotropy. Simons and Hilst (2003) combined the result of surface-wave tomography and the analysis of gravity-topography coherence to the study of anisotropy in the upper mantle beneath Australia. Tommasi et al (2004) worked on the seismic anisotropy at the top of mantle plume due to the plume-lithospheric interaction in the Ronda peridotite massif (southern Spain). They found that the interaction preserves the lithospheric seismic anisotropy rather than erasing it. They concluded that the thermo-chemical erosion of the lithospheric mantle may produce contrasting signatures for seismic velocities and anisotropy.

The theory of anisotropy wasn’t popular in the 80’s until finally when scientist have seen how the theory has helped in better understanding of the mantle, seismic data interpretation and improvement in well-tiles, anisotropy field is now growing very fast both in the industry and academics. The purpose of this term project is to review previous works in seismic anisotropy and its various applications in Earth’s science.