(W is scalar for displacement, T is scalar for traction)

Note that matrix does not depend on m

Algorithm for toroidal modes

• Choose harmonic degree and frequency

• Compute starting solution for (W,T)

• Integrate equations to top of solid region

• Is T(surface)=0? No: go change frequency and start again. Yes: we have a mode solution

T(surface) for harmonic degree 1

Radial and Spheroidal modes

Spheroidal modes

Minors

• To simplify matters, we will consider the spheroidal mode equations in the Cowling approximation where we include all buoyancy terms but ignore perturbations to the gravitational potential

Spheroidal modes w/ self grav

(three times slower than for Cowling approx)

Red > 1%; green .1--1%; blue .01--.1%

Red>5; green 1--5; blue .1--1 microHz

Mode energy densities

Dash=shear, solid=compressional energy density

Norm

alized radius

(black dots are observed modes)

All modes for l=1

(normal normal modes)

ScS --not observed

hard to compute

(not-so-normal normal modes)