Theory-of-Everything Coupling Codes

Note: REM = Reference Earth Model, in card-deck format.

Creating path-integral synthetics takes three steps:

1) calculate integration scalars for mode-mode interaction

2) use source/receiver information plus integration scalars to compute greens functions, which are output in a variant of sac format, with six data records following the header, one for each component of the moment tensor.

3) sum Greens functions with a moment tensor using sac_syndat, using either a CMT solution or a user-input solution.

2) & 3) waveform inversion codes combine steps 2 and 3 to generate synthetics to compare with "data" records.

Codes to generate integration scalars:

toe0: Theory of Everything, Rev 0 (well, almost) computes radial integrals of mode-mode interactions for path-integral coupling approximation. Input is a REM and its eigenfunctions, plus the orientation angles (psi,xi) of an axis of symmetry and parameters A,B,C,D,E along the path. Output of this routine is a big file of interaction scalars for modes that satisfy |l_1-l_2| = s. Sample input file.

toe1: Theory of Everything, Rev 1 computes radial integrals of mode-mode interactions for path-integral coupling approximation. Differs from toe0 in calculating radial integrals of coupling kernels against Legendre polynomials of order 0 thru 4. This allows the anisotropic perturbation to have radial dependence. Input is a REM and its eigenfunctions, plus the orientation angles (psi,xi) of an axis of symmetry and parameters A,B,C,D,E along the path. Output of this routine is a big file of interaction scalars for modes that satisfy |l_1-l_2| = s. Sample input file.

toeself: Computes radial integrals of self-coupling interactions in the path-integral coupling approximation. Appropriate for zero-wavenumber isotropic and transverse-isotropic perturbations. Calculates radial integrals of coupling kernels against Legendre polynomials of order 0 thru 4. This allows the perturbation to have radial dependence. Output of this routine is a big file of interaction scalars for selfcoupling. Sample input file.

Codes to generate greensfunctions

toesyn3: reads output of toe0 and generates greens-function synthetics using the path-integral coupling approximation. Uses a 'local mode' approximation of free-oscillation multiplets along the great-circle path. This is necessary to represent accurately surface-wave phase shifts caused by along-branch coupling. User supplies sacfiles with the source location and station info, and manually inputs the onset time of the event.

toesyn3_name: version of toesyn3 that accepts explicit filenames for the instrument responses, rather than constructing filenames within the code.

toesyn5: reads output of toeself *and* toe1 and generates greens-function synthetics using the path-integral coupling approximation. Allows the user to add the effects of an isotropic and TI radial perturbation (to fit surface wave phases) with a laterally varying anisotropic model, to fit coupled-mode scattered waves. Uses a 'local mode' approximation of free-oscillation multiplets along the great-circle path. This is necessary to represent accurately surface-wave phase shifts caused by along-branch coupling. User supplies sacfiles with the source location and station info, and manually inputs the onset time of the event. The version currently uses a fixed ratio of A to D (P to S wave perturbation) and B to E (P-anisotropy to S-anisotropy). For reference, Birch's Law suggests the first ratio to be 0.66, and the second ratio in PREM is roughly 2. Input is a REM and its eigenfunctions, plus the depth range and A/D and B/E ratios. Currently C=0 is hardwired.Sample input file.

Codes to perform waveform inversion

toeinv0: Code for self-coupling only, reads output of toeself. The version currently requires the user to provide a fixed ratio of A to D (P to S wave perturbation) and B to E (P-anisotropy to S-anisotropy). For reference, Birch's Law suggests the first ratio to be 0.66, and the second ratio in PREM is roughly 2. Input is a REM and its eigenfunctions, plus the depth range and A/D and B/E ratios. Currently C=0 is hardwired. Sample input file.