Statistical self-affinity, fractal dimension, and geologic interpretation

Properties of statistical self-affinity are explored and explained. Semi-variogram analysis can be used for identifying statistical self-affine behavior. This is, however, not the only method available for such an analysis. Some error and interpretation is involved; therefore, estimating the Hurst dimension (and from this the fractal dimension) from the semi-variogram can be misleading. Simulations based on statistical self-affine properties are alternatively used to develop an empirical approach to assessing statistical self-affine behavior. Analyzing simulations using semi-variograms, and comparing these semi-variograms to those from actual data, offers an alternate and perhaps superior approach to the understanding of the statistical self-affine properties of a geologic phenomenon. This empirical approach offers a method of reverse modeling for verifying estimates of Hurst dimension from semi-variograms.     

Atrazine in a Stream-Aquifer System: Estimation of Aquifer Properties from Atrazine Concentration Profiles

Lincolns municipal wellfield consists of 44 wells developed in an alluvial aquifer adjacent to the Platte River near Ashland, Nebraska Induced recharge from the river is the primary source of water for the wellfield. Wafer samples were collected on a periodic basis from the Platte River arid two transects of monitoring wells. These samples were analyzed for the herbicide atrazine, which was used as a tracer of induced recharge in this stream-aquifer system. Atrazine concentrations in the river and aquifer were much less than 1.0 ppb during late fall and winter, but increased to as high as 18.9 ppb during spring and summer, associated with runoff from upgradient agricultural lands. There was approximately a 21-day lag time from the first detection of increasing atrazine concentration in the river to the first detection in monitoring wells immediately adjacent to the river. This lag time was relatively constant throughout the year and from one year to the next, even with major fluctuations of river stage and wellfield production. This consistency of lag time indicated that the travel times from the river to the first set of monitoring wells immediately adjacent to the river were fairly constant.
Paths of preferential flow were identified in the aquifer at a depth of 25 to 35 feet below land surface. This aquifer zone appeared to play a significant role in movement of water from beneath the river into the wellfield.
Aquifer dispersivity was calculated using a method described by Hoehn and Santschi (1987). Macrodispersivity (A_L) was shown to increase linearly over the scale of the wellfield. Calculated values of A_L were within limits of other reported values for this type of aquifer material and agreed well with values reported by Hoehn and Santschi (1987); These findings will be extremely beneficial for planning and management of the municipal wellfield.     

Incompatible element and isotopic evidence for tectonic control of source mixing and melt extraction along the Central American arc

The Sr and Nd isotopic ratios of Central American volcanics can be described by the mixing of four components, marine sediment from DSDP Site 495, MORB-source mantle (DM), EMORB-source mantle (EM), and continental crust. Most of the isotopic data define a trend between EM and a modified mantle (MM) formed as a mixture of DM and less than 0.5% marine sediment, or fluid derived there from. The MM to EM trend is equally apparent in the incompatible-element data and is most clearly seen in a Ba/La versus La/Yb plot. A hyperbolic trend connects high Ba/La and low La/Yb at the MM end of the trend to low Ba/La and high La/Yb at the EM end. Smooth regional variations in incompatible-element and isotopic ratios correlate with the dip of the subducted slab beneath the volcanic front and the volume of lava erupted during the last 100,000 years (volcanic flux). Steep dip and low flux characterize the MM end-member and shallow dip and high flux characterize the EM end-member. The simplest model to explain the linked tectonic and geochemical data involves melting in the wedge by two distinct mechanisms, followed by mixing between the two magmas. In one case, EM magma is generated by decompression of EM plus DM asthenosphere, which is drawn in and up toward the wedge corner. EM mantle is preferentially melted to small degrees because of the presence of low melting components. The second melt is formed by release of fluid from the subducted slab beneath the volcanic front to form MM magma. Mixing between EM and MM magmas is controlled by subduction angle, which facilitates delivery of EM magma to the volcanic front at low-dip angles and impedes it at steep-dip angles.     

Application of universal kriging for estimation of earthquake ground motion: Statistical significance of results

Universal kriging is compared with ordinary kriging for estimation of earthquake ground motion. Ordinary kriging is based on a stationary random function model; universal kriging is based on a nonstationary random function model representing first-order drift. Accuracy of universal kriging is compared with that for ordinary kriging; cross-validation is used as the basis for comparison. Hypothesis testing on these results shows that accuracy obtained using universal kriging is not significantly different from accuracy obtained using ordinary kriging. Tests based on normal distribution assumptions are applied to errors measured in the cross-validation procedure;t andF tests reveal no evidence to suggest universal and ordinary kriging are different for estimation of earthquake ground motion. Nonparametric hypothesis tests applied to these errors and jackknife statistics yield the same conclusion: universal and ordinary kriging are not significantly different for this application as determined by a cross-validation procedure. These results are based on application to four independent data sets (four different seismic events).     

Seasonal changes in surface level of a salt marsh creek

Nineteen surveys were carried out over a two-year period to determine the surface height of a salt marsh creek located on the north side of the River Esk, Cumbria, England. An AGA 112 electromagnetic distance measurer mounted on a Wild TI theodolite was used in conjunction with acrylic reflectors to follow the form of the ground. The results showed that there were no significant net trends in surface level, although seasonal variations of the order of 2 cm occurred. Vegetated areas responded in similar fashion to bare surfaces. It is thought that the elevational changes were attributable to the swelling of clay particles during the winter months rather than the effects of erosion and accretion.     

An indicator kriging model for investigation of seismic hazard

Time domain probabilistic techniques most often are used for assessment of seismic hazard. Such techniques are based on the historic frequency of ground motion. Hazard is expressed as a probability of experiencing a particular level of seismic activity over a given length of time. One of these techniques utilizes frequency of extreme values for assessment of hazard. The major disadvantage of this technique, however, becomes evident when maximum seismic activity for two consecutive years occurs only a few weeks or months apart. In this case, the extreme value approach overestimates seismic hazard. A new approach for hazard assessment is founded on principles of indicator kriging. This technique evaluates seismic hazard as a simple frequency record, which is more realistic for regions of little to moderate seismicity.     

Mercury as a pathfinder in exploration geochemistry — Case history studies

Mercury has long been regarded as a potential pathfinder for base and precious metals, and for mercury deposits per se. The earliest work was done in Russia (e.g. Saukov, 1946; Ozerova, 1962) and was followed up in North America, the UK and Australia. However, results were generally unsatisfactory. While the earlier data related to high-mercury systems, the methodology was adapted for sulphide deposits in general when it was recognized that these also carried mercury as a trace component. However, few case history studies have been published which demonstrate the usefulness of mercury in exploration geochemistry, especially in comparison to the more commonly analyzed target and indicator elements copper, lead, zinc, silver, gold and arsenic (Hawkes, 1982).     

Carbon isotopes in submarine basalts

High-sensitivity stepped extraction reveals two isotopically distinct forms of carbon in submarine basalt glasses: an isotopically light carbon component released by combustion from 200 to 600°C and an isotopically heavy CO₂ liberated from vesicles (magmatic carbon) from 600 to 1200°C. The δ¹³C_PDB of the low release temperature carbon varies from −24 to −30‰ and is believed to be surficial organic contamination. A survey of various types of oceanic glasses demonstrates that the δ¹³C of magmatic CO₂ varies from −4.2 to −7.5‰ in mid-ocean ridge basalt (MORB), from −2.8 to −6.7‰ in glasses from Hawaii and Explorer Seamount and from −7.7 to −16.3‰ in glasses from the Scotia Sea and Mariana Trough. Magmatic CO₂ in back-arc basin basalts (BABB) is on average 5‰ lighter than equivalent CO₂ in MORB and can be explained by the mixing in the source regions for BABB magmas of juvenile (MORB-like) CO₂ with an organic carbon component from subducted pelagic sediments. It is inferred that significant amounts of pelagic carbonate carbon (δ¹³C 0‰) must be recycled into the mantle.