The accuracy of event location with respect to ground truth is not a simple function of the number of free parameters or ``resolution'' of a particular velocity model. This was reported by Antolik et al. [2000], where they tested four existing P wave models.
There are several possible reasons for this result. One may be the data used in constructing higher resolution models. Most of these models make use of a somewhat limited data set (for example, only phase travel times) in order to reduce the size of the necessary computer resources (memory and CPU time). This may result in a relative lack of resolution in certain areas of the mantle (particularly at shallow depths) to which teleseismic phase travel times are not sensitive. As an example, we show the mislocation obtained from a group of explosions using only a subset of the layers of model BDP98 as a correction to PREM. Nearly all of the improvement in the locations is obtained by considering depths above 1000 km, which shows that resolution of the shallow mantle is most critical to teleseismic event location. Models which do not recover the upper mantle structure well will not provide the most accurate locations.
It is therefore important to use data in tomographic inversions which have maximum sensitivity to upper mantle structure. The figure at right shows the average value of the diagonal elements of an inner product matrix used in an inversion for S wave velocity [Gu et al., 2000]. Maximum sensitivity to the upper mantle is provided by the use of surface wave dispersion measurements and body and surface waveforms with periods longer than 45 s. Differential and direct travel times are mostly sensitive to lower mantle structure. For a P wave inversion the figure would be similar, without the Love wave measurements and with the travel times for corresponding P phases substituted. In deriving our new global mantle model, we have therefore made use of a variety of datasets.
We had several objectives in mind when constructing the new model. Among them is the easy ability to combine detailed regional models with the global model in order to use both teleseismic and regional phases in event location. The spline approach combines the advantages of using a localized parameterization with those of constructing a smmoth model, among them easy calculation of 3-D ray paths. Horizontally, the spherical splines are centered at 362 uniformly distributed knots. The number of free parameters is close to that involved in a degree-18 spherical harmonic expansion.
Perturbations to PREM in both P and S velocity are represented by:
We are currently using a large of number of datasets in the inversions as well as developing others for future use. The compressional velocity model is determined by travel times of direct P and core phases (PKP, PcP). These datasets were adopted from those of Engdahl et al. [1998] but have been improved through relocation of the earthquakes in a 3-D model (SP12; Su and Dziewonski, 1993). The relocated phase data included a correction for crustal structure at the source and receiver Mooney et al. [1998]. The travel times were then formed into summary rays with sources at the center of 2o x 2o cells. Events deeper than 50 km were grouped by depth into bins with a thickness of 100 km. Events whose epicenter moved more than 1o from the location published by Engdahl et al. [1998] were discarded. The total number of summary rays is 626,073 for P, 215,590 for PKP, and 68,473 for PcP. We also make use of the Love and Rayleigh wave dispersion measurements published by Ekström et al. [1997] in the period range 35-150 s, which have their maximum sensitivity in the upper 200-300 km of the mantle. These were previously used by Ekström and Dziewonski [1998] to derive a 3-D model of mantle shear wave velocity expanded in spherical harmonics up to degree 20 as part of an earlier phase of this project. For shear velocity inversions, we also use the direct and differential travel time datasets described in Su et al. [1994]. They consist of approximately 45,000 measurements of S, SS, ScS, SS - S, S - SKS, ScS - S, and SKKS - SKS travel times. Future models will also include the extensive dataset of body and surface waveforms compiled over the years at Harvard.
With respect to model BDP98 [Boschi and Dziewonski, 1999] , the new model shows higher amplitude velocity perturbations in the upper mantle, which may be the result of the 3-D relocation of the sources prior to inversion or the new crustal correction (see figure below). Use of the surface wave measurements produces lower velocities throughout the eastern and central Pacific than are observed using travel times alone. At the bottom of the mantle, the new model has slightly lower amplitude than BDP98 and much lower amplitude than model SP12, especially in the southern hemisphere. This may be partly due to the relatively coarse separation of the radial splines in the lower mantle in this parameterization. Since, as noted above, the upper mantle is most critical for accurate earthquake location, the new model may improve upon the location accuracy provided by BDP98 and other high-resolution models. Our new models will be tested using the dataset of calibration events compiled at Harvard and other institutions.
Antolik, M., G. Ekström, and A. M. Dziewonski, Global event location with full and sparse datasets using three-dimensional models of mantle P wave velocity, PAGEOPH, Special Volume on Monitoring a CTBT, in press, 2000.
Boschi, L. and A. M. Dziewonski, High and low-resolution images of the Earth's mantle: Implications of different approaches to tomographic modeling, J. Geophys. Res., 104, 25,567-25,594, 1999.
Ekström, G., and A. M. Dziewonski, The unique anisotropy of the Pacific upper mantle, Nature, 394, 168-172, 1998.
Ekström, G., J. Tromp, and E. W. F. Larson, Measurements and global models of surface wave propagation, J. Geophys. Res., 102, 8137-8157, 1997.
Engdahl, E. R., R. D. van der Hilst, and R. P. Buland, Global teleseismic earthquake relocation with improved travel times and procedures for depth determination, Bull. Seism. Soc. Am., 88, 722-743, 1998.
Grand, S. P., R. D. van der Hilst, and S. Widiyantoro, Global seismic tomography: A snapshot of convection in the Earth, GSA Today, 7(4), 1-7, 1997.
Gu, Y. J., A. M. Dziewonski, W. Su, and G. Ekström, Shear velocity model of the mantle and discontinuities in the pattern of lateral heterogeneities, submitted to J. Geophys. Res., 2000.
Mooney, W. D., G. Laske, and T. G. Masters, CRUST 5.1: A global crustal model at 5o x 5o, J. Geophys. Res., 103, 727-747, 1998.
Su, W. and A. M. Dziewonski, Joint 3D inversion for P- and S-velocity in the mantle, EOS, 74, 557, 1993.
Su, W., R. L. Woodward, and A. M. Dziewonski, Degree-12 model of shear velocity heterogeneity in the mantle, J. Geophys. Res., 99, 6,945-6,980, 1994.
