Computations of the complex phase-, group-, ray-velocity and attenuation for seismic ray tracing in viscoelastic anisotropic media

Abstract

Seismic imaging is still the sole reconnaissance means to provide subsurface information with no direct tangible contact. The resulting outcome of the seismic exercise greatly depends on the understanding of the sent energy, as well as the medium that the energy waves are travelling through. Too many assumptions and approximations would render the seismic depreciating in value in direct proportion to the degree of violation of reality by those assumptions. The earth is often assumed elastic and isotropic to simplify calculations while it is known that the earth is in fact attenuating and does exhibit directional trends. To accurately model Earth (through seismic surveying), it should be regarded as more complex than is being done currently. The preliminary stages of ray tracing include the calculation of complex-valued wave quantities, such as the complex phase slowness vector, the phase-, group- and ray-velocity and the ray attenuation. These parameters become complex-valued because of the viscoelasticity of the rock media which has to be taken into account because it causes amplitude decay of the wave, hence the imaginary part, which is directly linked with attenuation of the propagating wave energy. This complicates the problem. We present here three different methods which enable the computation of the wave quantities: the iterative solver method, the perturbation method, and the RSD method. The first proved satisfactory but computationally expensive due to iterations with fine steps. The second proved successful in most of the cases but failed with some highly complex media. The third and last proved efficient and fitting even at the challenging triplication of wave-fronts in vertical shear waves. Further development of such methods is needed especially for more complex media with strong anisotropy and strong attenuation, because they mimic the earth more truthfully therefore they need to be investigated. Subsequently, after obtaining such parameters, seismic ray tracing for accurate complex travel-times can be conducted.

Date of Award	May 2020
Original language	American English