I am interested in predicting the periods of the Earth’s normal modes, especially those of wobble and nutation for which the observed frequencies are known. By matching the predicted and observed frequencies and adjusting the Earth models for a better fit, we strive to improve our knowledge of the material properties of the Earth’s interiors and hence help better predict the Earth’s orientation parameters.

The goal of my research program is to apply novel mathematical methods and computational tools developed in my research group to study the long period free oscillations of an elastic Earth model with a compressible and stratified fluid core. My immediate goals include:

1- To study the effects of liquid core’s non-adiabatic density stratification on the periods of the Earth’s long period internal modes, including those of wobble and nutation for which observed values are known.

2- To study the effects of elasticity of the Earth’s solid parts, especially at the core mantle and inner core boundaries, on the periods of the internal core modes.

3- To implement a non-orthogonal (Clairaut) coordinate system in order to compute the periods of the Earth’s wobble and nutation modes.

4- To compute the periods of these modes accurate to second order in the ellipticity.

5- To study the changes in the Earth’s rotation rate, change in length of day, as a result of mass displacements in the Earth’s interiors and coupling between the Earth’s interior components.

6- To study possible coupling between the fluid core’s internal modes and those of wobble and nutation.

We have developed new mathematical tools and sophisticated computer software (computational tools) for numerical solution of complicated partial differential equations describing the dynamics of these bodies, and visualization of relevant physical phenomena occurring in their interior. We have solved some of the long-standing problems in geodynamics, such as computing the rotational modes of a non-adiabatic fluid core model and nonlinear treatment of tidal instability in the Earth’s core.