Velocity Ellipsoids for Crustal Seismic Anisotropy: Pumpkins and Melons Have Dimples and Bulges

Geological causes of crustal anisotropy include regional fractures and cracks, isotropic heterogeneity or layering, and material composition and textural properties. In addition, shear or metamorphic foliations in fault zones or structural terranes serve as proxies for intracrustal deformation in a manner analogous to lattice preferred orientation of olivine produced by mantle shear. The primary factor in the production of crustal seismic anisotropy is the relative angle between a seismic wave and the (dipping) symmetry axes representing the crustal material even as either change along the propagation raypath. As a result, in order to analyze observations of crustal anisotropy we must understand the behavior of compressional and shear wave velocities in all propagation directions parallel to and in-between the principal symmetry axes which represent the crustal materials. In this poster we use Christoffel equations and physical properties obtained from petrophysical lab measurements in order to examine anisotropic velocities and travel-time effects for bulk rocks representative of different crustal levels. Ellipses and ellipsoids are commonly used to represent the P- and S-wave velocity directional behavior for materials described using hexagonal and orthorhombic symmetries, respectively. While olivine and pyroxene-based mantle rocks are characteristically fast symmetry axes (the "melons" of Levin and Park, 1997), crustal rocks are typically slow symmetry axes ("pumpkins") due to the predominance of fractures or textural foliations. Careful application of Christoffel solutions indicate that for most crustal (and mantle) rocks the surfaces of their pumpkins or melons are not exact analytical ellipsoids. Rather, the surfaces in the non-axial directions have second-order deflections (bulges or dimples) which potentially may produce observable azimuthal travel-time or shear splitting effects. In the case when the P-wave surface on average is slow (dimpled), due to SV and SH crossover the travel-time of the first-arrival S will have an irregular 8-theta appearance. When the P-wave surface is on average fast (bulged), SV and SH do not cross over and a normal 2-theta S arrival time should occur. In this latter case, however, the shear wave splitting behavior has a 4-theta regularity which is maximized diagonal to the symmetry axes. The ellipsoidal deflections of dimples and bulges are related to VP as measured in non-axial directions (petrophysical diagonal measurments, for example). The deflections can exist for both crustal and mantle rocks (pumpkins and melons). In our poster we will explain the Christoffel derivation of the dimples and bulges, present examples of petrophysically-based P and S wave ellipsoids and discuss travel-time and shear wave splitting implications for observational data collected within the crust.