1. Inertial modes of a realistic Earth Model B. Seyed-Mahmoud Physics Department, University of Lethbridge, Canada AGU 20112Fall Meetings Abstract The Earth's outer core is a rotating ellipsoidal shell of compressible, stratified and self gravitating fluid. As such, in the treatment of geophysical problems a realistic model of this body needs to be considered. The inertial modes of the core are long- period free oscillations which have the Coriolis effect as their restoring force. Historically an incompressible and homogeneous fluid is considered in order to study these modes. We consider a compressible and stratified fluid with non-zero stratification parameter in order to investigate the effects of the density stratification on the periods of these modes for spherical and spherical shell models of the core. We show that these effects may be significant and may change from model to model depending on the stratification parameters of the models. We also use a Clairaut coordinate system to compute the frequencies of some of the inertial modes of a spheroidal and spheroidal shell. Here u, p 1 and V 1 are the displacement and the perturbation in pressure and gravitational potential respectively; ρ 0 is the density, α the local speed of sound, ω the modal frequency and Ω the rotation rate of the fluid. For more information contact: Behnam Seyed-Mahmoud seyeb0@uleth.caseyeb0@uleth.ca 1-403-329-2360 Frequencies of some of the inertial modes of a neutrally stratified ellipsoid and ellipsoidal Dynamical equations:. Equilibrium Earth The displacement eigen functions for some of the inertial modes of a compressible fluid spheroid and spheroidal shell We solve the equations using a Clairaut coordinate System No need for derivatives of the material properties. Boundary conditions are implemented consistently Application of a Clairaut Coordinates The problem with truncation has been addressed (Seyed-Mahmoud et. al, 2006, 2007, 2008). Fluid Sphere Spherical Shell modeσ neutral σ -0.001 σ sine σ poly Modeσ neutral σ PREM (2,1,1)0.500 (2,1,1)0.500 (3,10)0.4560.45 (4,1,0)0.6640.66 (5,2,0)0.7660.780.77 (6,2,0)0.8330.84 (6,1,0)0.4710.480.47 (4,2,1)0.3040.31 (4,2,1)0.310-0.42 -0.41 (4,3,1)0.8520.86 (4,3,1)0.8490.86 (5,4,1)0.9320.92 (6,1,1)-0.702-0.71 -0.70 (6,1,1)-0.703-0.70 (6,4,1)0.6520.660.650.66 (6,4,1)0.6570.66 SpheroidSpheroidal Shell modeσ neutral σ shell (2,1,1)0.5013 (4,1,0)0.6570.65 (5,2,0)0.7670.775 (6,1,0)0.4710.47 (6,2,0)0.8310.832 (3,2,1)0.7580.764 (4,1,1)-0.42-0.414 (4,3,1)0.8510.864 (5,1,1)-0.6-0.587 (5,3,1)0.5230.521 (5,4,1)0.9010.904 (6,1,1)-0.71-0.706 (6,3,1)0.2240.227 (6,4,1)0.6530.659 Frequencies of some of the inertial modes of Earth models with different profiles for the stability parameter Earth Models: our models are modified PREM : PREM density P-wave velocities of PREM and modified PREM, no inner core Density of modified PREM, no inner core PREM stratification parameter Polynomial stratification for modified PREM Sinusoidal stratification for modified PREM