Waveform inversion of mantle Love waves:the Born seismogram approach

Summary. Normal mode theory, extended to the slightly laterally heterogeneous earth by the first-order Born approximation, is applied to the waveform inversion of mantle Love wave (200–500 s) for the Earth's lateral heterogeneity at l = 2 and a spherically symmétric anelasticity ( Q _μ) structure. The data are from the Global Digital Seismograph Network (GDSN). The l =2 pattern is very similar to the results of other studies that used either different méthods, such as phase velocity measurements and multiplet location measurements, or a different data set, such as mantle Rayleigh waves from different instruments. The results are carefully analysed for variance reduction and are most naturally explained by heterogeneity in the upper 420 km. Because of the poor resolution of the data set for the deep interior, however, a fairly large heterogeneity in the transition zones, of the order of up to 3.5 per cent in shear wave velocity, is allowed. It is noteworthy that Love waves of this period range cannot constrain the structure below 420 km and thus any model presented by similar studies below this depth are likely to be constrained by Rayleigh waves (spheroidal modes) only.
The calculated modal Q values for the obtained Q _μ model fall within the error bars of the observations. The result demonstrates the discrepancy of Rayleigh wave Q and Love wave Q and indicates that care must be taken when both Rayleigh and Love wave data, including amplitude information, are inverted simultaneously.
Anomalous amplitude inversions of G2 and G3, for example, are observed for some source-receiver pairs. This is due to multipathing effects. One example near the epicentral region, which is modelled by the obtained l = 2 heterogeneity, is shown.     

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.     

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.     

Whole mantle SH velocity model constrained by waveform inversion based on three-dimensional Born kernels

A whole mantle SH velocity model is obtained by using a unique data set and techniques. Body and surface waveforms including major and multi-orbit phases are used as a data set and are inverted by using 3-D Born kernels. The resultant model, SH18CE, reveals the different natures of the two major upwelling systems: the strong low velocity anomalies beneath Africa extend for more than 1000 km from the core–mantle boundary (CMB), whereas those beneath the Pacific are restricted to 300–400 km from the CMB. The results also show the variable natures of stagnant slabs on the 670 discontinuity around Japan: the depths of the strongest high velocity anomalies within the stagnant slabs are different region by region, which is consistent with the detailed delay time tomography model in this area.     

The accuracy of models derived by WKBJ waveform inversion

Summary . In this paper the accuracy of velocity-depth profiles derived by matching WKBJ seismograms to observations is quantitatively evaluated. Seismograms computed with the WKBJ method are generally quite reliable but possess predictable, systematic inaccuracies in the presence of strong velocity gradients. The effects of these inaccuracies on models derived through WKBJ waveform inversion are studied, using reflectivity seismograms as 'data'. The velocity structure used is an oceanic lithosphere model that contains several transition regions separated by relatively homogeneous layers, producing partially-reflected reverberations in the reflectivity synthetics that are absent from the WKBJ seismograms. The inversion incorporates the 'jumping' strategy to solve for the smoothest models consistent with the data. We find these solutions to be independent of the starting model and to have a stable basic structure that agrees well with the correct model. The differences, everywhere less than a seismic wavelength, depend on the frequency content of the seismograms. Reverberations in the reflectivity seismograms that are well separated from WKBJ arrivals are treated as 'noise' in the inversion.     

Magnitude corrections for attenuation in the upper mantle

Summary. The m _b: M _s relation for explosions at the Nevada Test Site (NTS) differs from those for explosions in other parts of the world. There is considerable evidence that this results mostly from high body-wave attenuation in the upper mantle beneath the western US. The authors have developed an empirical magnitude correction for body-wave attenuation and applied it to both source and receiver ends of the teleseismic body-wave path. The results imply that m _b values are lower for NTS explosions than for Soviet explosions of comparable yield and seismic coupling. The authors have also developed and applied a source-depth correction to account for _pP-P interference in the P -wave arrival.
The body-wave magnitude resulting from these corrections is designated m_o to distinguish it from other definitions of m _b. Values of m_Q determined for a world-wide set of large explosions show that a single m_Q : yield relation is a fair fit to the data for the explosions with high seismic coupling. However, grouping the explosions under two m_Q :yield relations gives a better fit to the data.
All the studied explosions in salt or granite or below the water table fit a common M _s:yield relation. Explosions from North America, Eurasia and Africa have a common m_Q : M _s relation.