title: A Degree 8 Mantle Shear Velocity Model
       From Normal Mode Observations Below 3 mHz

authors: Joseph S. Resovsky and  Michael H. Ritzwoller


We present inversions of almost 2300 normal mode structure coefficient 
measurements and associated uncertainty estimates from 90 normal modes
below 3 mHz. These inversions produce a degree 8 shear velocity (v_s)
model, MM2_L12D8, throughout the mantle. The damping scheme described
herein penalizes misfit to these normal mode data as well as deviations
from a variety of existing mantle models. This is done to ensure that
our inversions remain consistent with models constrained  by surface
and body wave data while taking advantage of the complementary structural 
information contained in the normal mode data. The magnitude of the
allowed deviations from existing models is a function of spherical
harmonic degree and order and depth in the mantle, and is determined
from the differences between these models. The effect is to place the
largest perturbations relative to the existing models in the mid-mantle
(900-1800 km depth), where surface and body wave constraints are weakest,
where differences  between existing v_s models may be as large as the
models themselves, and where new constraints on structure from the normal
mode data set are very strong. The resulting model MM2_L12D8 is more
similar to existing  models than they are to each other, yet reduces
chi-squared misfit to normal mode structure coefficients by 58% relative
to the best existing models.  Misfits to coefficients for modes that
predominantly sample mid-mantle shear velocities are reduced by sim75%.  
MM2_L12D8 achieves corresponding improvements in the fit to high signal-
to-noise seismic spectra below 3 mHz.

The resolution of our inversions is adequate to recover reliable new images 
of long-wavelength mantle structures and to discriminate, in both amplitude 
nd geometry, between existing v_s models.  The uncertainty in structural
amplitudes in model MM2_L12D8 is less than 35% at most depths and degrees,
and this model clearly favors the amplitudes of long-wavelength structure
seen in existing models which  employ global, rather than local, basis
functions.  MM2_L12D8 displays strong images of ``slabs'' and ``plumes''
in the mid-mantle and is characterized by predominant degree 2 structure
which is more continuous with depth than in most other models. This
suggests that the mid-mantle participates in  circulation which involves
at least the whole lower mantle.  MM2_L12D8, together with our catalogue
of structure coefficients, is available at web site:
abdu.colorado.edu/geophysics/nm.dir/nm.html.


submitted to JGR, May 5, 1998