A.L. Hales

Parametrically simple earth models consistent with geophysical data

Abstract We present a set of three parametric earth models (PEM) in which radial variations of the density and velocities are represented by piecewise continuous analytical functions of radius (polynomials of order not higher than the third). While all three models are identical below a depth of 420 km, models PEM-O and PEM-C are designed to reflect the different properties of the oceanic and continental upper mantles, respectively. The third model PEM-A is a representation of an average earth. The data used in inversion consist of observations of eigenperiods for 1064 normal modes, 246 travel times of body waves for five different phases and regional surface-wave dispersion data extending to periods as short as 20 seconds. Agreement of the functionals derived for the PEM models with the appropriate observations is satisfactory. In particular, the fit of free-oscillation data is comparable to that obtained in inversion studies in which constraints imposed on the smoothness of structure were not as severe as in our study. Our density distribution for all depths greater than 670 km is consistent with the Adams-Williamson equation to within 0.2% maximum deviation, and these minute departures result only from the limitations imposed by the parametric simplicity of our models. We also show that the velocities in the lower mantle are consistent with the complete third-order finite-strain theory to within 0.2% for VP and 0.4% for VS (r.m.s. relative deviations). The derived pressure derivatives of the velocities are very similar to those obtained for corundum structures in laboratory experiments. We conclude that any departures from homogeneity and adiabaticity within the inner core, outer core or lower mantle must be very small, and that introduction of such deviations is not necessary on the basis of the available observational evidence.

A compressional velocity distribution for the upper mantle

Abstract A compressional wave velocity model is presented for the upper mantle at depths less than 1000 km under the stable continental region of northern Australia. The model is consistent with travel times out to about 30° obtained from a suite of events which include surface focus explosions in the U.S.A., Australia and Europe, and earthquakes with depths from 31 to 606 km that occurred to the north of Australia. It is suggested that discontinuities are present at depths of 75, 200, 325, 411, 512, 610, 630, 645 and 722 km with the uncertainties in these depths being 5 to 10 km. The possible existence of a low velocity zone between 200 and 325 km under northern Australia has been inferred from the data. The velocity model is best described as a series of steps between which the velocity is constant, or even decreases slightly with increasing depth. Insofar as the surface focus observations are concerned, it is clear that the travel times in stable continental regions show systematic deviations from the Jeffreys-Bullen travel times.

Upper-mantle travel times in Australia — A preliminary report

Abstract This paper gives a preliminary account of an experiment to determine upper-mantle travel times in Australia. A set of fifteen 14-track tape-recording units are being used along a profile from Darwin to Alice Springs in central Australia. In addition to the 14-track recorders, eleven 6-track units are being used both on-line and off-line as monitors. The sources used are natural earthquakes occurring to the north of Australia, especially Banda Sea events. Preliminary analysis of the records from the first sub-array has confirmed the high apparent velocities for P and S previously found for the distance range 800–1,800 km in central Australia. It is inferred that the high apparent velocities are due to a sharp increase in the proportion of garnet at a depth of about 90 km. Neither the P nor S arrivals from 800 to 1,800 km show any evidence of the shadow zones or offsets in the travel-time curve which would be associated with an upper-mantle low-velocity zone. It is suggested, however, that a low-velocity zone is not precluded by the observations, but that the associated offset may not occur in the first-arrival part of the travel-time curve.

The upper mantle velocity distribution

Abstract In plate tectonic theory one thinks of rigid blocks of lithosphere moving relative to one another over a weak asthenosphere. In the oceans the base of the lithosphere is associated with the top of the low velocity layer at a depth of 70–100 km. Current models of the upper mantle velocity distribution beneath continental platforms on shield regions give little indication of the depth of the base of the lithosphere in these regions. Gerver and Markusevitch (1966, 1967) have shown that, providing travel times from earthquakes covering a range of depths are available in addition to surface focus travel times, it is possible to determine the upper mantle velocity distribution even if low velocity layers are present. This paper summarizes information on surface focus travel times from controlled sources in platform or shield regions and describes a complex model of the upper mantle velocity distribution based on observations of the travel times of seismic waves from Banda Sea events covering a wide range of depth. It is pointed out that surface focus travel times in continental platform or shield regions differ significantly from the Jeffreys-Bullen travel times. The deviations from the Jeffreys-Bullen times are much larger than the differences between the deviations for different continental platform or shield regions. One of the features of the model based on the travel times from the Banda Sea events is a velocity discontinuity at a depth of about 200 km. It is difficult to account for this discontinuity in terms of a phase transformation. It is pointed out that there is supporting evidence for the existence of relatively sharp velocity discontinuities at 200, 400 and 650 km from studies of converted phases by Vinnik and Jordan and Frazer. The principal uncertainty in the upper mantle velocity distribution arises from uncertainties in the depths of foci of the earthquakes. It is in fact possible that there may be a low velocity zone in the upper mantle beneath continental platform or shield regions between depths of 150 and 200 km.

Evidence for P wave velocity discontinuities at depths greater than 650 km in the mantle

Abstract The arrival times of seismic P waves recorded at long lines of portable seismographs deployed on the shield region of central Australia show evidence of breaks in the travel-time curve at epicentral distances near 30, 39 and 43°. These breaks are additional to those at about 20 and 24° (associated with the 400- and 650-km discontinuities) and imply that the P wave velocity structure of the mantle does not increase smoothly in the depth range 650–1100 km, but rather consists of regions of nearly constant velocity separated by small but significant velocity increases at depths of approximately 770, 980 and 1080 km. These conclusions are in agreement with those previously inferred from first and later arrivals at the Warramunga Seismic Array.

Great-circle Rayleigh wave attenuation and group velocity, Part III: Inversion of global average group velocities and attenuation coefficients

Abstract Average shear-velocity models for the upper mantle have been derived by controlled Monte Carlo inversion of global average Rayleigh wave group velocity (GAGV) data for periods between 50 and 300 seconds. GAGV data have been corrected for attenuative dispersion using a method based on the theory of Liu, Anderson and Kanamori. Two types of model bounds have been used with one- or two-layer low-velocity zones beginning at depths of 70 and 100 km. All models fitting GAGV data within one standard deviation have low-velocity zones in the 100–200 km depth range. Models with low-velocity zones beginning at 70 km, as well as 100 km, fit GAGV data within one standard deviation, so the average thickness of the lithosphere (taken as the depth to the top of the low-velocity zone) cannot be determined with precision. Global average models for shear-wave attenuation (Q−1β) have been derived from global average Rayleigh wave attenuation coefficients for periods between 50 and 300 s and average shear-velocity models. Zones of high Q−1β coincide with the low-velocity zones of all shear-velocity models, however, models with low-velocity zones beginning at a depth of 70 km have the highest-attenuation layer in the lower half of the low-velocity zone. Resolution kernels for these attenuation models show that parameters for layers shallower than the lower part of the low-velocity-high-attenuation zone are strongly coupled but are distinct from the lower part of this zone. This suggests that the deeper part of the low-velocity-high-attenuation zone is the most mobile part of the zone or that on the average, the top of the zone is deeper than 70 km. The average Qβ of the lithosphere, low-velocity zone, and sub-low-velocity layer (asthenosphere) are approximately 200, 85–110 and 170–200, respectively.

Great-circle Rayleigh wave attenuation and group velocity, Part I: Observations for periods between 150 and 600 seconds for seven great-circle paths

Abstract Rayleigh wave attenuation coefficients and group velocities have been estimated for seven great-circle paths. The attenuation coefficient measurements cover the period range from 100 to 500 s, and group velocities the range from 100 to 600 s. Global average group velocities and attenuation coefficients have also been estimated for these period ranges. The spread of the individual path group velocities for 20-s averaging windows centred at 290, 250, 210, 180 and 150 s is less than 0.034, 0.028, 0.024, 0.048 and 0.071 km/s, respectively. Global average attenuation coefficients, when combined with global average group velocities, show that Q for Rayleigh waves has an approximately constant value of about 145 for periods between 150 and 220 s and slowly increases to a value of about 200 at a period of 400 s.

Great-circle Rayleigh wave attenuation and group velocity, Part II: Observations for periods between 50 and 200 seconds for nine great-circle paths and global averages for periods of 50 to 600 seconds

Abstract Great-circle group velocities and attenuation coefficients for the period range 50 to 200 s have been determined for Rayleigh waves from three Kurile Islands earthquakes ranging from magnitude 6.6 to 7.2. These data have been combined with earlier data from Mills and Hales to produce global average group velocities and attenuation coefficients for periods between 50 and 600 s. Global average phase velocities have been determined by integrating global average group velocities for periods from 50 to 340 s. Equivalent fundamental mode periods from 0 S 34 to 0 S 168 (60–240 s) are calculated and corrected for dispersion due to anelasticity. Comparison of group velocities and equivalent spheroidal mode periods with those calculated for recent earth models shows that shear velocities in the upper mantles of those models are too high to fit our data. Global average Q ′s for Rayleigh waves are slightly lower (approximately one standard deviation at most periods) than those predicted by model MM8 of Anderson, Ben-Menahem and Archambeau. Attenuation coefficients at short periods (50–100 s) agree well with similar measurements for oceanic and continental paths.

Crustal structure modelling in a spherically symmetrical earth

Abstract The choice of a crustal model for a spherically symmetrical earth presents special problems for it is important that the averaging process should correspond to that which occurs in the case of the observed free oscillations. It may not be possible to find a spherically symmetrical crustal model with velocities and densities resembling those of real earth materials.