Included here is a variety of information about our studies of the Earth's low frequency normal modes. The information is intended mostly for other seismologists and geodynamicists who would like to use the normal mode structure coefficients in inversions for the spherical and/or aspherical elastic and/or anelastic structure of the deep Earth. Some introductory information can be found by clicking the following: 1, 2, 3.
The main point is that normal mode structure or interaction coefficients place strong constraints on the spherical and aspherical structure of the deep Earth. To date, their use has been rare in inversions for global models. However, recent advances have greatly increased their number and improved their reliability and the accuracy of the coefficient uncertainties. In addition, normal mode constraints up through and beyond degree 8 are now common and there are now constraints on odd-degree Earth structures. These factors in combination imply that the recent tabulations of structure coefficients should provide a powerful tool to investigate the deep structure of the Earth.
Like geoid coefficients, normal mode structure coefficients are quite transportable and should be able to be utilized in a wide variety of applications concerning the deep Earth. We will make an attempt to provide the necessary information, e.g., integral sensitivity kernels and related information, to facilitate use by other researchers. This information will be developing with time.
To date, we have concentrated efforts on the low frequency spectrum below 3 mHz and have estimated self-coupled and cross-coupled structure coefficients for about 90 multiplets. It is our plan to continue to apply the method to many more multiplets above 3 mHz.
Plots of even degree structure coefficient estimates and uncertainties and comparison to predictions from existing models, splitting function plots, integral sensitivity kernel plots are provided as a function of the normal mode branch: 0S, 1S, 2S, 3S, 4S, 5S, 6S, 7S, 8S, 0T, 1T, 2T, 3T, 4T. Plots of cross-coupled coefficient estimates, etc. are also provided. Tables of coefficients, uncertainties, and kernels are also provided, segregated by degree, on the main page.
If you have questions, comments or suggestions, email Mike Ritzwoller at

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