Geology Reports⌕ Search
Home/Archive/USGS

USGS · 70031923

Are fractal dimensions of the spatial distribution of mineral deposits meaningful?

G. L. Raines
View original source ↗Export metadata ↓

Abstract

It has been proposed that the spatial distribution of mineral deposits is bifractal. An implication of this property is that the number of deposits in a permissive area is a function of the shape of the area. This is because the fractal density functions of deposits are dependent on the distance from known deposits. A long thin permissive area with most of the deposits in one end, such as the Alaskan porphyry permissive area, has a major portion of the area far from known deposits and consequently a low density of deposits associated with most of the permissive area. On the other hand, a more equi-dimensioned permissive area, such as the Arizona porphyry permissive area, has a more uniform density of deposits. Another implication of the fractal distribution is that the Poisson assumption typically used for estimating deposit numbers is invalid. Based on datasets of mineral deposits classified by type as inputs, the distributions of many different deposit types are found to have characteristically two fractal dimensions over separate non-overlapping spatial scales in the range of 5-1000 km. In particular, one typically observes a local dimension at spatial scales less than 30-60 km, and a regional dimension at larger spatial scales. The deposit type, geologic setting, and sample size influence the fractal dimensions. The consequence of the geologic setting can be diminished by using deposits classified by type. The crossover point between the two fractal domains is proportional to the median size of the deposit type. A plot of the crossover points for porphyry copper deposits from different geologic domains against median deposit sizes defines linear relationships and identifies regions that are significantly underexplored. Plots of the fractal dimension can also be used to define density functions from which the number of undiscovered deposits can be estimated. This density function is only dependent on the distribution of deposits and is independent of the definition of the permissive area. Density functions for porphyry copper deposits appear to be significantly different for regions in the Andes, Mexico, United States, and western Canada. Consequently, depending on which regional density function is used, quite different estimates of numbers of undiscovered deposits can be obtained. These fractal properties suggest that geologic studies based on mapping at scales of 1:24,000 to 1:100,000 may not recognize processes that are important in the formation of mineral deposits at scales larger than the crossover points at 30-60 km. ?? 2008 International Association for Mathematical Geology.

Explore related subjects

Natural Resources ResearchArticle

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

G. L. Raines. 2008-05-14. Are fractal dimensions of the spatial distribution of mineral deposits meaningful?. https://doi.org/10.1007/s11053-008-9067-8

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related USGS reports

USGS2026

Quantitative mineral resource assessment of lithium pegmatite deposits in the southern Appalachian orogen

The first quantitative mineral resource assessment for undiscovered lithium pegmatite deposits in the southern Appalachian region of the United States was conducted. Permissive tracts for lithium pegmatite deposits were delineated by integrating lithological, tectonic, geochemical, geophysical and mineral occurrence data. Lithium pegmatite prospectivity of the tracts was ranked with simplified mappable criteria, including proximity to Paleozoic felsic intrusions and major lithotectonic structures, stream sediment geochemical anomalies, and pegmatite occurrence data. The geospatial data and permissive tracts were used to estimate the number of undiscovered lithium pegmatite deposits. These estimates were integrated into probabilistic simulations along with a new global lithium pegmatite grade and tonnage dataset to quantify potential contained undiscovered lithium resources. An economic filter was applied to convert the probabilistic estimates of contained lithium into recoverable material. The identified lithium pegmatite resources for the Carolina Lithium and Kings Mountain deposits, North Carolina, contain 1589 thousand tons (kt) of Li 2 O. The median contained undiscovered resource for the southern Appalachian orogen was estimated to be 2240 kt Li 2 O. At 90% confidence, the region contains at least 130 kt Li 2 O, and 10,700 kt at 10% confidence. After applying economic filters, the median recoverable contained resource was 1430 kt Li 2 O, corresponding to approximately 201 years of current lithium imports for consumption in the United States. North and South Carolina are likely to contain most of these resources. Coarse data resolution and intra-state variations in the geological data contribute to uncertainty of undiscovered lithium pegmatite resources. Continued efforts to harmonize disparate geospatial datasets with updated or new information can improve the accuracy and precision of estimated undiscovered lithium pegmatite resources in the study area and at broader scales.

Alabama, Georgia, Maryland, North Carolina, South ↗
USGS2026

Quantitative mineral resource assessment of lithium pegmatite deposits in the northern Appalachian orogen, USA

Lithium demand is projected to increase more than 48 times by 2040 due to electric vehicle production and other energy storage needs. Most lithium production is outside of the USA, thereby increasing supply chain vulnerability. The combined end use importance and heightened supply risk of lithium make this lightest metallic element a critical commodity to the USA. To mitigate this supply risk, the US Geological Survey is actively assessing lithium deposits in the USA. Herein, we detail an assessment for lithium-mineralized pegmatites in the US northern Appalachian Mountains. Permissive tracts were generated by cross-referencing tectonic and geologic maps and mineral occurrence data with mappable criteria derived from generalized and region-specific lithium pegmatite ore deposit models; tracts were then ranked as having high, medium, or low permissibility. Available geophysical and geochemical data were found to be of minimal utility for this deposit type at the scale of the assessment. The number of undiscovered deposits were estimated and integrated into probabilistic simulations, which included an expanded and updated global grade and tonnage model of pegmatite-hosted lithium ore. The estimated total amount of undiscovered resources for the northern Appalachian Orogen has a median value of 1,410,000 metric tons of Li 2 O when considering moderate correlation across sub-regions. At a confidence level of 90%, a resource of at least 90,000 metric tons of Li 2 O remains undiscovered, and at a 10% confidence level, a resource of as much as 7,380,000 metric tons Li 2 O remains undiscovered. After applying an up-to-date economic filter to convert median contained lithium to recoverable material, a correlated total of 900,000 metric tons of Li 2 O may be economically extractable, equating to enough Li 2 O to provide the current annual US lithium supply deficit (presently obtained through net imports) for 127 years at 2025 rates of apparent consumption. This period of provision will inevitably shorten with projected increasing consumption rates, emphasizing that further research could be completed to better delineate regions of high lithium resource potential and support exploration and domestic production.

Connecticut, Delaware, Maine, Massachusetts, New H↗
USGS2024

How quickly do oil and gas wells “Water Out”? Quantifying and contrasting water production trends

Water production from petroleum (oil and natural gas) wells is a topic of increasing environmental and economic importance, yet quantification efforts have been limited to date, and patterns between and within petroleum plays are largely unscrutinized. Additionally, classification of reservoirs as “unconventional” (also known as “continuous”) carries scientific and regulatory importance, but in some cases the distinction from "conventional" wells is unclear. Using water, oil, and gas production data, we calculated a set of quantitative metrics that elucidate trends in the water-to-petroleum ratio over the life of each producing well. The percent growth of the water-to-petroleum ratio quantifies the degree to which a well “waters out” over time; values calculated for 153,900 wells in 18 oil and gas plays show generally much higher values for conventional wells than for continuous/unconventional wells. Analysis of the percent growth along with the slope and median metrics reveals greater variation between conventional plays and between continuous (unconventional) plays than previously recognized. Further, an example from the Bakken Formation in the Williston Basin, USA, illustrates that, within a single play, the metrics provide insight into spatial variation of water production trends, as influenced by geology and reservoir characteristics. By quantifying the variability of water production trends within individual plays and between plays, including differences between conventional and continuous (unconventional) plays, these results provide a more nuanced view of water production from oil and gas wells than has previously been possible and they illustrate the degree to which water management considerations vary spatially and temporally.

Natural Resources Research↗