Seismic Reflection, Slowness Surface, and Energy Partition Analysis in Functionally Graded Anisotropic Media with Imperfect Boundaries

Understanding wave propagation, reflection, and transmission in anisotropic

media with imperfect boundaries is essential for advancing research in both

geophysical exploration and the design of engineered materials. Motivated by

advances in reflection seismology, my recent research focuses on amplitude

analysis in a functionally graded anisotropic medium, with particular emphasis on

the reflection of three-dimensional plane wave at imperfect boundary. Seismic

amplitude-versus-angle (AVA) methods, which relate reflection amplitudes to

the angle of incidence, provide a robust framework that can be useful in the

exploration of subsurface geological materials and in advancing our

comprehension of the Earth’s interior structure. In this context, analytical

expressions for amplitude ratios as functions of incident angle are derived using

the generalized Snell’s law, along with corresponding expressions for energy

ratios and slowness surfaces. Graphical demonstrations further illustrate how

anisotropy, functional grading, and boundary conditions influence amplitude

ratios, energy partitioning, and wavefront geometry.