The idea that the propagation of elastic waves can be anisotropic, i.e., that the velocity may depend on the direction, is about 175 years old. The first steps are connected with the top scientists of that time, people such as Cauchy, Fresnel, Green, and Kelvin. For most of the 19th century, anisotropic wave propagation was studied mainly by mathematical physicists, and the only applications were in crystal optics and crystal elasticity. During these years, important steps in the formal description of the subject were made.
At the turn of the 20th century, Rudzki stressed the significance of seismic anisotropy. He studied many of its aspects, but his ideas were not applied. Research in seismic anisotropy became stagnant after his death in 1916. Beginning about 1950, the significance of seismic anisotropy for exploration seismics was studied, mainly in connection with thinly layered media and the resulting transverse isotropy. Very soon it became clear that the effect of layer-induced anisotropy on data acquired with the techniques of that time was negligible, so for the next few decades the subject was studied only by a handful of researchers.
In the last two decades of the 20th century, anisotropy changed from a nuisance to a valuable asset. Gupta and especially Crampin pointed out that cracks in a rock mass lead to observable effects from which, in principle, the orientation and density of the cracks could be deduced. Since this information has direct significance for the reservoir properties of the rock, the interest in seismic anisotropy increased considerably. Improvements in acquisition technology, with well-designed approximations that made the complicated theory manageable and with efficient algorithms running on more powerful computers, have turned the theoretical ideas of the early times into an important exploration and production tool. Although seismic anisotropy is usually weak, it nevertheless has important consequences in our modern data. Thus, today anisotropy is an important issue in exploration and reservoir geophysics, and it belongs in every exploration geophysicist's toolkit.