A fast method for the solution of a system of simultaneous linear equations—A method adapted to a particular problem

Mathematical Geosciences - In mineral deposit evaluation, the estimation of block values can involve the solution of as many as 100,000 systems of linear equations. To minimize computing costs it...     

Quantitative taxonomy and biostratigraphy of Middle Cambrian trilobites from Montana and Wyoming

This study was made to revise the taxonomy and biostratigraphy of Middle Cambrian trilobites from Montana and Wyoming. Both numerical and conventional analyses were made of the taxonomic and biostratigraphic data. Numerical taxonomy was performed on a sample of 210 OTU's (Operational Taxonomic Units) using 66 characters which were determined on cranidia of Middle Cambrian ptychopariid trilobites. These characters consisted of linear measurements which were transformed to indices proportional to glabellar length, quantitative-qualitative shape or angle measurements, and multistate attributes. The similarity coefficients calculated were average taxonomic distances and Pearson's product-moment correlation coefficient. The matrices of similarity coefficients were clustered by single-linkage and unweighted pair-group algorithms. The coordinates of OTU's in a three-dimensional A-space defined by the first three principal axes also were calculated. A phenogram of the distance matrix clustered by UPGMA (which yielded the highest cophenetic correlation coefficient) and a three-dimensional pin-and-ball model were used to interpret the trilobite taxonomy. Insufficiently clear clustering in both representations of taxonomic structure necessitated also a conventional taxonomic study guided by the numerical phenetics. Numerical biostratigraphy was performed with 79 collections as OTU's and 43 trilobite genera as characters. Jaccard coefficients were used as similarity coefficients, and the results were clustered by UPGMA. The resultant phenogram was readily interpretable, and seven faunal assemblage zones (Albertella, Glossopleura, Ehmaniella, Bolaspis-Glyphaspis, Ehmania, Parehmania, and Bolaspidella)are defined for the Middle Cambrian in the study area. Two of the zones (Ehmaniellaand Parehmania)are new and replace part of the previously defined “Bathyuriscus-Elrathina”zone. Bolaspis-Glyphaspis, Ehmania,and Parehmaniazones may have only regional validity.     

Crustal structure and temporal velocity change in southern California

Summary About twenty blasts are used to determine crustal structure and to monitor temporal seismic velocity changes in southern California. The shot time is determined up to 10 msec by using a disposable pick-up placed directly on the explosive. About 17 permanent stations and 20 temporary stations are used for the recordings. With a fast paper speed (typically 1 cm/sec) and the WWVB radio signals superposed on the seismic trace, absolute timing accuracy of up to 10 msec is achieved. A representative structure thus determined consists of a 4 km thick 5.5 km/sec layer underlain successively by 23.4 km thick 6.3 km/sec layer, 5.0 km thick 6.8 km/sec layer and 7.8 km/sec half space. The details of the lower crust are somewhat uncertain. This structure can explain the travel time data, corrected for the station and source elevations and for the station delays, to ±0.15 sec. Small but systematic temporal velocity changes up to 3% have been found for some of the profiles. If the effect of the migration of the shot point is small enough, these changes are larger than experimental errors and represent real temporal change in the material property between the shot point and the stations.Contribution No. 2530, Division of Geological Sciences, California Institute of Technology, Pasadena, California.     

The Néel transition and magnetic properties of terrestrial,synthetic, and lunar ilmenites

The magnetic susceptibility of a terrestrial, synthetic and lunar ilmenite specimen has been measured from 4 to 300 K. All specimens had a single Néel temperature transition which ranged from 56 to 57.7 K. In one case the powdered specimen was partially aligned in the magnetic field prior to the susceptibility measurements and the Néel transition was observed to shift to 60 K indicating magnetic anisotropy. A study of several magnetic parameters calculated from the experimental data showed gross impurities in the terrestrial specimen, single-domain to multi-domain metallic iron in the synthetic specimen, and a small amount of superparamagnetic metallic iron in the lunar sample. No multidomain iron was observed in the lunar ilmenite. The results of electron spin resonance measurements were also in general agreement with these findings. Because of the absence of Fe³⁺ compared to most terrestrial samples it is suggested that the anisotropic magnetic parameters be determined on lunar ilmenite when a large enough single crystal becomes available.     

Volatiles from Hawaiian submarine basalts determined by dynamic high temperature mass spectrometry

Quantitative measurements of volatiles from Hawaiian submarine basalts have been made using a Knudsen cell dynamic-mass spectrometer system. The principal advantage of the technique is the ability to determine simultaneously the absolute amounts of more than one volatile released from the same sample.From mass pyrograms it was observed that the release of water was bimodal, with the major release occurring above 600°C. Water released below this temperature is believed not to have been present in the magma at the time of extrusion. Sulfur dioxide was evolved only after the bulk of the water was released and coincided with the general expansion and melting of the sample. Sulfur and carbon- containing gases which were released in surges (above 1000°C) correspond to the bursting of bubbles from the softened basalt.The molar amounts of vesicle gases were plotted as a function of extrusion depth. A change in the slope of the resulting linear curve indicates saturation of the basalt with respect to water.     

Textural recognition of mudflow deposits

A plot of median grain size against quartile deviation (after Buller and McManus) can be used to distinguish mudflow deposits. A characteristic envelope for poorly sorted streamflow deposits is also defined. Unlike most other sediment transport mechanisms, mudflows appear to deposit sediments with sorting independent of median grain size.     

Eastern Pacific spreading rate fluctuation and its relation to Pacific area volcanic episodes

Sea-floor spreading rates from four locations along the Nazca-Pacific plate boundary and one along the Juan de Fuca-Pacific plate boundary show variations over the past 2.4 m.y., with decreasing rates prior to the Jaramillo to Olduvai time interval (0.92–1.73 m.y. ago) and increasing rates since then. Other Pacific area volcanic phenomena in mid-plate and convergent-boundary settings also show minima about 1.3–1.5 m.y. ago and a maximum at present and another maximum about 5 m.y. ago: extrusion rates along the Hawaiian Ridge; volcanic episodes associated with calc-alkalic provinces of western Oregon and Central America; temporal variations in the SiO₂ content of Aleutian ash layers; and the number of deep-sea ash layers. These phenomena may fluctuate in response to changing spreading rates. During times of more rapid spreading increased shear and melting along lithospheric boundaries may occasion increased volcanic activity, whereas during times of less rapid spreading volcanic activity may be less intense.     

Holocene displacement along branch and secondary faults in the San Andreas fault zone, southern California

Detailed geologic mapping of the San Andreas fault zone in Los Angeles County since 1972 has revealed evidence for diverse histories of displacement on branch and secondary faults near Palmdale. The main trace of the San Andreas fault is well defined by a variety of physiographic features. The geologic record supports the concept of many kilometers of lateral displacement on the main trace and on some secondary faults, especially when dealing with pre-Quaternary rocks. However, the distribution of upper Pleistocene rocks along branch and secondary faults suggests a strong vertical component of displacement and, in many locations, Holocene displacement appears to be primarily vertical. The most recent movement on many secondary and some branch faults has been either high-angle (reverse and normal) or thrust. This is in contrast to the abundant evidence for lateral movement seen along the main San Andreas fault. We suggest that this change in the sense of displacement is more common than has been previously recognized.The branch and secondary faults described here have geomorphic features along them that are as fresh as similar features visible along the most recent trace of the San Andreas fault. From this we infer that surface rupture occurred on these faults in 1857, as it did on the main San Andreas fault. Branch faults commonly form “Riedel” and “thrust” shear configurations adjacent to the main San Andreas fault and affect a zone less than a few hundred meters wide. Holocene and upper Pleistocene deposits have been repeatedly offset along faults that also separate contrasting older rocks. Secondary faults are located up to 1500 m on either side of the San Andreas fault and trend subparallel to it. Moreover, our mapping indicates that some portions of these secondary faults appear to have been “inactive” throughout much of Quaternary time, even though Holocene and upper Pleistocene deposits have been repeatedly offset along other parts of these same faults. For example, near 37th Street E. and Barrel Springs Road, a limited stretch of the Nadeau fault has a very fresh normal scarp, in one place as much as 3 m high, which breaks upper Pleistocene or Holocene deposits. This scarp has two bevelled surfaces, the upper surface sloping significantly less than the lower, suggesting at least two periods of recent movement. Other exposures along this fault show undisturbed Quaternary deposits overlying the fault. The Cemetery and Little Rock faults also exhibit selected reactivation of isolated segments separated by “inactive” stretches.Activity on branch and secondary faults, as outlined above, is presumed to be the result of sympathetic movement on limited segments of older faults in response to major movement on the San Andreas fault. The recognition that Holocene activity is possible on faults where much of the evidence suggests prolonged inactivity emphasizes the need for regional, as well as detailed site studies to evaluate adequately the hazard of any fault trace in a major fault zone. Similar problems may be encountered when geodetic or other studies, Which depend on stable sites, are conducted in the vicinity of major faults.