Theory for Errors, Resolution, and Separation of Unknown Variables in Inverse Problems, with Application to the Mantle and the Crust in Southern Africa and Scandinavia

Six strain and inertial seismographs at Queen Creek, Arizona (QC-AZ), recorded six modes of surface waves from a suite of 18 earthquakes near Chiapas, Mexico. The six group-velocity dispersion curves were used in a least-squares inversion to estimate the shear velocity structure of the upper 380km of crust and mantle in central Mexico. Multiple filter analysis of 108 seismograms produced group velocity dispersion curves slower than average continental paths. The range of the average deviation from the mean dispersion curve for the fundamental modes was 0.025 to 0-160 kni s-' for Rayleigh waves and 0.025-0.281 km s-l for Love waves. The inversion models have low velocities that correspond with a representative geotherm and petrologic P-Tdiagrams to indicate partial melting. The 4layer crust is 30 km thick with a high-temperature gradient LVZ in the granitic layer and with a LVZ in the lower 8 km of a basaltic layer resulting from a high geothermal gradient or from partial melting of water saturated rock. The mantle has a 4-8 km thick solid lid and a shallow low velocity zone. The lowest velocities correspond to 10-20 per cent partial melting. A sharp velocity gradient at 70-80 km probably results from both the phase change to garnet pyrolite and the lower extreme of partial water pressure with the disappearance of amphiboles from the host pyrolite. Based on the velocities, 5 per cent anhydrous melting extends to 260 km. From 300 to 380 km temperature gradients and crystal lattice instabilities prior to the olivine-spinel phase change produce another LVZ. A hypothesis is presented that the large volume of low density magma produces a regional vertical force that creates high Aat plateaus as found in central Mexico and the Colorado Plateau. The inversion models have a 7.5s S-wave residual relative to the Canadian Shield model CANSD in agreement with observed US station anomalies.

Section: Layermentioning

confidence: 99%

Section: Layermentioning

confidence: 99%

The Crust and Upper Mantle of Central Mexico

Fix¹

1975

“…In particular the analysis will emphasize the resolution of the shear velocity and thickness of the high velocity lid of the normal ocean basin structure. The uniqueness of a structural model can be deduced using the formalism presented by Der & Landisman (1972) for inaccurate observations. The model consists of M layers with parameters P k and & (the bar indicating the undesirable parameter) with A, representing the estimate of p k .…”

Section: Uniqueness Of Earth Modelsmentioning

confidence: 99%

Rayleigh Wave Phase Velocities in the Atlantic Ocean

Weidner

1974

103

The phase velocities of Rayleigh waves are found for many paths in the north Atlantic. The single station technique is used with earthquakes in the Mid-Atlantic Ridge. The major contributor to the error in phase velocity is the uncertainty in epicentral location and origin time. Focal depth and mechanism are sufficiently well controlled for these events that they do not significantly add to the phase velocity error. The resulting uncertainty is +O-02 km s-' for the period range 20-100 s.The ocean is regionalized into ridge and basin. Both ray theory and Rytov's method are used to extract the dispersion characteristics of each region from the observations. Large lateral variations of the basin dispersion suggest a further subdivision. These variations can be explained entirely by variations in sediment thickness.The deduced upper mantle model of the ocean basin is characterized by a shear velocity reversal at 40km depth with a lid shear velocity of 4.7kms-'.The lowest shear velocities are centered at a depth of 125krn. The lid shear velocity can be reduced to 4.6kms-' only if both the thickness of the lid increases and the density increases. Phase velocities for the Mid-Atlantic Ridge imply that the upper mantle shear velocity under the ridge is significantly lower than that under the ocean basin at depths greater than 20 km.We shall find strong evidence that the first shear velocity reversal occurs at 40 km in the ocean basins. While there is a great deal of non-uniqueness in surface wave inversions, it is difficult to thicken the lid if the shear velocity is 4.7 as suggested from the S, velocities of Hart & Press (1973). We shall also find evidences for a very shallow velocity reversal underlain by low shear velocities under the Mid-Atlantic Ridge.The ocean basins can be divided into two regions with distinct dispersion relations. At longer periods (100 s) the phase velocities differ by 0.05 kms-', while at the shorter periods (20s) they differ by as much as 0.5kms-'. These differences can be entirely explained in terms of sediment thickness. Observed Rayleigh wave phase velocitiesDescription of method observed phase, $obs, through the relation The Rayleigh wave phase velocity for a frequency, o, can be determined from the

“…The European travel times agree to within 1 s with the global travel times of Enayatollah (1972b) which, in this distance interval, are derived mainly from earthquakes in South-east and South Europe recorded at stations in Sweden and Finland. These data are compared with the arrival times expected from King & Calcagnile's model KCA which is based on Der & Landisman's (1972) model SCAN down to a depth of 120 lan and on their own observations of Russian nuclear explosions at NORSAR from this depth onwards. Again, the curves differ markedly before 20' and agree quite closely beyond, but the travel times which are truly representative of old shield areas (those of the models SCAN and KCA) are considerably faster than those of this study.…”

Section: Base Linesmentioning

confidence: 99%

The travel time of P seismic waves in Europe and Western Russia

England

Worthington

1977

Over 4000 arrival times at WWSSN stations in Europe from earthquakes in the Eastern Mediterranean and from presumed Russian nuclear explosions are used to define first arrival travel-time curves for the region. Travel times within Europe show no broad regional variation and are considerably slower than those predicted by published velocity models for Fennoscandia and the Russian Platforms. The travel times from the Russian explosions differ only slightly from the European ones and it is concluded that the transition to a region of higher average velocity occurs far enough east for most of the data in this study to be representative of the lower, 'European', velocity structure.