The three-dimensional shear wave structure in the mantle by overtone waveform inversion - I. Radial seismogram inversion

Summary. The three-dimensional (3-D) shear wave structure of the mantle, down to the depth of about 900 km, is obtained by inverting waveforms of radial component seismograms. Radial component seismograms contain large amplitude overtone signals which circle the Earth as wave packets and are sometimes called X1, X2, X3, … We use data which contain R1, X1 and X2 and filtered between 2 and 10mHz. It is shown that, unless each seismogram is weighted, all seismograms are not fitted uniformly. Only data from large earthquakes are fitted and the final velocity anomalies are biased by the small number of large earthquake data. Resolution is good at shallow depths, becomes worse in the intermediate depth range between about 400 and 500 km and then becomes better at greater depth ranges (600–900km). Even though we use only spheroidal mode data, velocity anomalies in the shallow structure show excellent correlation with the age of the surface rocks of the Earth. In the deeper regions, between about 600 and 900km, South America shows a fast velocity anomaly which may indicate the slab penetration beyond 700 km there. Another region which shows a fast velocity anomaly is the Mariana trench, but other subduction regions do not show such features.     

Inversion for laterally heterogeneous upper mantle S-wave velocity structure using iterative waveform inversion

In contrast to previous work, which treats the Earth's lateral heterogeneity as an infinitesimal perturbation to a spherically symmetrical starting model, we conduct iterative linearized waveform inversion for the Earth's laterally heterogeneous structure. We use the Direct Solution Method (DSM) (Geller et al. 1990a) to calculate synthetic seismograms and their partial derivatives for a laterally heterogeneous earth model. We invert surface-wave data from the IDA and GEOSCOPE networks. We expand the lateral heterogeneity of rigidity in spherical harmonics up to angular order number 8 and use three parameters to specify the depth dependence of each harmonic, giving us a total of 240 unknowns. The short-wavelength lateral heterogeneity (s = 4, 6 and 8) in the deeper part of the upper mantle obtained by this study differs significantly from M84A. The relative improvement in the variance reduction as compared with model M84A is about 20 per cent for the IDA data and more than 100 per cent for the GEOSCOPE data.     

Regional 3-D heterogeneities by waveform inversion – application to the Atlantic area

The waveform inversion method described in Woodhouse & Dziewonski (1984) was modified to retrieve regional scale 3-D heterogeneities by using the minor arc part of seismograms. The lateral heterogeneities are expanded horizontally into blocks (10°× 10°) and radially into Legendre polynomials up to order 3 (0–670 km), and thus the results show much fine details of lateral variation than previous global scale studies. We assumed that the heterogeneities produce the perturbation of eigenfrequencies which are the minor arc average of local eigenfrequency shift. We applied the method to the upper mantle beneath the Atlantic Ocean and its environments. Care was taken about the weighting of the data set. We found that the fit of each seismogram became better when the weighting of each seismogram is proportional to the inverse of initial data residuals. Resolution is good in the triangular region surrounded by South America, Europe, and North America. Resolution is not good in the South Atlantic because of the poor path coverage. Depth resolution is not clear, because of the use of Legendre polynomials, though the results suggest a broad half-width of the order of 200 km or more. We found some similarities between previous global studies and our results. For example, low velocities beneath the East Pacific Rise, Chile Rise and Azores triple junction and a high velocity Canadian shield are obtained. However, there are also differences; the high-velocity zone beneath the Brazilian shield at shallow depth is not a prominent feature in this study. Instead, we found a somewhat unexpected feature near the Romanche and Vema fracture zones where shallow positive anomalies exist. Smoothed results calculated by the spherical harmonic expansion are also shown for the purpose of comparison with global studies.