Book Review of "Mathematical Geosciences: Hybrid Symbolic-Numeric Methods", by Joseph L. Awange, Béla Paláncz, Robert H. Lewis, and Lajos Völgyesi
No abstract available.
Pure and Applied Geophysics↗
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Mineral deposit densities for estimating mineral resources
Estimates of numbers of mineral deposits are fundamental to assessing undiscovered mineral resources. Just as frequencies of grades and tonnages of well-explored deposits can be used to represent the grades and tonnages of undiscovered deposits, the density of deposits (deposits/area) in well-explored control areas can serve to represent the number of deposits. Empirical evidence presented here indicates that the processes affecting the number and quantity of resources in geological settings are very general across many types of mineral deposits. For podiform chromite, porphyry copper, and volcanogenic massive sulfide deposit types, the size of tract that geologically could contain the deposits is an excellent predictor of the total number of deposits. The number of mineral deposits is also proportional to the type’s size. The total amount of mineralized rock is also proportional to size of the permissive area and the median deposit type’s size. Regressions using these variables provide a means to estimate the density of deposits and the total amount of mineralization. These powerful estimators are based on analysis of ten different types of mineral deposits (Climax Mo, Cuban Mn, Cyprus massive sulfide, Franciscan Mn, kuroko massive sulfide, low-sulfide quartz-Au vein, placer Au, podiform Cr, porphyry Cu, and W vein) from 108 permissive control tracts around the world therefore generalizing across deposit types. Despite the diverse and complex geological settings of deposit types studied here, the relationships observed indicate universal controls on the accumulation and preservation of mineral resources that operate across all scales. The strength of the relationships ( R 2 =0.91 for density and 0.95 for mineralized rock) argues for their broad use. Deposit densities can now be used to provide a guideline for expert judgment or used directly for estimating the number of most kinds of mineral deposits.
Mathematical Geosciences↗
Using sequential self-calibration method to identify conductivity distribution: Conditioning on tracer test data
An iterative inverse method, the sequential self-calibration method, is developed for mapping spatial distribution of a hydraulic conductivity field by conditioning on nonreactive tracer breakthrough curves. A streamline-based, semi-analytical simulator is adopted to simulate solute transport in a heterogeneous aquifer. The simulation is used as the forward modeling step. In this study, the hydraulic conductivity is assumed to be a deterministic or random variable. Within the framework of the streamline-based simulator, the efficient semi-analytical method is used to calculate sensitivity coefficients of the solute concentration with respect to the hydraulic conductivity variation. The calculated sensitivities account for spatial correlations between the solute concentration and parameters. The performance of the inverse method is assessed by two synthetic tracer tests conducted in an aquifer with a distinct spatial pattern of heterogeneity. The study results indicate that the developed iterative inverse method is able to identify and reproduce the large-scale heterogeneity pattern of the aquifer given appropriate observation wells in these synthetic cases. ?? International Association for Mathematical Geology 2008.
Mathematical Geosciences↗
Generalized bootstrap method for assessment of uncertainty in semivariogram inference
The semivariogram and its related function, the covariance, play a central role in classical geostatistics for modeling the average continuity of spatially correlated attributes. Whereas all methods are formulated in terms of the true semivariogram, in practice what can be used are estimated semivariograms and models based on samples. A generalized form of the bootstrap method to properly model spatially correlated data is used to advance knowledge about the reliability of empirical semivariograms and semivariogram models based on a single sample. Among several methods available to generate spatially correlated resamples, we selected a method based on the LU decomposition and used several examples to illustrate the approach. The first one is a synthetic, isotropic, exhaustive sample following a normal distribution, the second example is also a synthetic but following a non-Gaussian random field, and a third empirical sample consists of actual raingauge measurements. Results show wider confidence intervals than those found previously by others with inadequate application of the bootstrap. Also, even for the Gaussian example, distributions for estimated semivariogram values and model parameters are positively skewed. In this sense, bootstrap percentile confidence intervals, which are not centered around the empirical semivariogram and do not require distributional assumptions for its construction, provide an achieved coverage similar to the nominal coverage. The latter cannot be achieved by symmetrical confidence intervals based on the standard error, regardless if the standard error is estimated from a parametric equation or from bootstrap.
Mathematical Geosciences↗
Aggregation methodology for the circum-arctic resource appraisal
This paper presents a methodology that intends to aggregate the results of a recent assessment of undiscovered conventional oil and gas resources of the Arctic by the U.S. Geological Survey. The assessment occurred in 48 geologically defined regions called assessment units. The methodology includes using assessor specified pair-wise correlations as the basis to construct a correlation matrix. Sampling from this matrix generates more realistic uncertainty estimates of aggregated resources than if assumptions of total independence or total dependence are made. The latter two assumptions result in overly narrow or overly broad estimates. Aggregation results for resources in regions north of the Arctic Circle are presented.
Mathematical Geosciences↗
Comparison of two methods used to model shape parameters of Pareto distributions
Two methods are compared for estimating the shape parameters of Pareto field-size (or pool-size) distributions for petroleum resource assessment. Both methods assume mature exploration in which most of the larger fields have been discovered. Both methods use the sizes of larger discovered fields to estimate the numbers and sizes of smaller fields: (1) the tail-truncated method uses a plot of field size versus size rank, and (2) the log–geometric method uses data binned in field-size classes and the ratios of adjacent bin counts. Simulation experiments were conducted using discovered oil and gas pool-size distributions from four petroleum systems in Alberta, Canada and using Pareto distributions generated by Monte Carlo simulation. The estimates of the shape parameters of the Pareto distributions, calculated by both the tail-truncated and log–geometric methods, generally stabilize where discovered pool numbers are greater than 100. However, with fewer than 100 discoveries, these estimates can vary greatly with each new discovery. The estimated shape parameters of the tail-truncated method are more stable and larger than those of the log–geometric method where the number of discovered pools is more than 100. Both methods, however, tend to underestimate the shape parameter. Monte Carlo simulation was also used to create sequences of discovered pool sizes by sampling from a Pareto distribution with a discovery process model using a defined exploration efficiency (in order to show how biased the sampling was in favor of larger fields being discovered first). A higher (more biased) exploration efficiency gives better estimates of the Pareto shape parameters.
Mathematical Geosciences↗
Time-lapse analysis of methane quantity in Mary Lee group of coal seams using filter-based multiple-point geostatistical simulation
Coal seam degasification and its success are important for controlling methane, and thus for the health and safety of coal miners. During the course of degasification, properties of coal seams change. Thus, the changes in coal reservoir conditions and in-place gas content as well as methane emission potential into mines should be evaluated by examining time-dependent changes and the presence of major heterogeneities and geological discontinuities in the field. In this work, time-lapsed reservoir and fluid storage properties of the New Castle coal seam, Mary Lee/Blue Creek seam, and Jagger seam of Black Warrior Basin, Alabama, were determined from gas and water production history matching and production forecasting of vertical degasification wellbores. These properties were combined with isotherm and other important data to compute gas-in-place (GIP) and its change with time at borehole locations. Time-lapsed training images (TIs) of GIP and GIP difference corresponding to each coal and date were generated by using these point-wise data and Voronoi decomposition on the TI grid, which included faults as discontinuities for expansion of Voronoi regions. Filter-based multiple-point geostatistical simulations, which were preferred in this study due to anisotropies and discontinuities in the area, were used to predict time-lapsed GIP distributions within the study area. Performed simulations were used for mapping spatial time-lapsed methane quantities as well as their uncertainties within the study area. The systematic approach presented in this paper is the first time in literature that history matching, TIs of GIPs and filter simulations are used for degasification performance evaluation and for assessing GIP for mining safety. Results from this study showed that using production history matching of coalbed methane wells to determine time-lapsed reservoir data could be used to compute spatial GIP and representative GIP TIs generated through Voronoi decomposition. Furthermore, performing filter simulations using point-wise data and TIs could be used to predict methane quantity in coal seams subjected to degasification. During the course of the study, it was shown that the material balance of gas produced by wellbores and the GIP reductions in coal seams predicted using filter simulations compared very well, showing the success of filter simulations for continuous variables in this case study. Quantitative results from filter simulations of GIP within the studied area briefly showed that GIP was reduced from an initial ∼73 Bcf (median) to ∼46 Bcf (2011), representing a 37 % decrease and varying spatially through degasification. It is forecasted that there will be an additional ∼2 Bcf reduction in methane quantity between 2011 and 2015. This study and presented results showed that the applied methodology and utilized techniques can be used to map GIP and its change within coal seams after degasification, which can further be used for ventilation design for methane control in coal mines.
Alabama↗
Accurate ocean bottom seismometer positioning method inspired by multilateration technique
The positioning of ocean bottom seismometers (OBS) is a key step in the processing flow of OBS data, especially in the case of self popup types of OBS instruments. The use of first arrivals from airgun shots, rather than relying on the acoustic transponders mounted in the OBS, is becoming a trend and generally leads to more accurate positioning due to the statistics from a large number of shots. In this paper, a linearization of the OBS positioning problem via the multilateration technique is discussed. The discussed linear solution solves jointly for the average water layer velocity and the OBS position using only shot locations and first arrival times as input data.
Mathematical Geosciences↗
Compositional data analysis of coal combustion products with an application to a Wyoming power plant
A mathematically sound approach for summarizing chemical analyses of feed coal and all its combustion products (bottom ash, economizer fly ash, and fly ash) is presented. The nature of the data requires the application of compositional techniques when conducting statistical analysis, techniques that have not been applied before to the study of partitioning of elements between the coal that enters the boiler and the associated coal combustion products. A collection of descriptive and inferential compositional techniques was used to analyze the coal combustion products from a Wyoming power plant burning Paleocene Wyodak–Anderson coal. The significance of the fluctuation in ash composition is determined by using a Hotelling’s T -squared test and bootstrapping. Tree displays allow for visualization of the progressive effect of filters in removal of chemical species based on their geochemical composition. Results indicate that, in general, as the suspended combustion products entrained in the flue gases move closer to the stack, chemical species are removed from the combustion gas, starting with minerals associated with elements having the lowest volatility.
Mathematical Geosciences↗
Implications of aggregating and smoothing daily production data on estimates of the transition time between flow regimes in horizontal hydraulically fractured Bakken oil wells
The level to which data are aggregated or smoothed can impact analytical and predictive modeling results. This paper discusses findings regarding such impacts on estimating change points in production flow regimes of horizontal hydraulically fractured shale oil wells producing from the middle member of the Bakken Formation. Change points that signal transitions in flow regimes are important because they subsequently affect estimates of ultimate recovery from wells producing from shale plays. Extending our earlier work, we employ two different statistical approaches, Bacon–Watts Bayesian regression and nonlinear constrained least squares regression, and a designed computational experiment to estimate the time of transition from the transient to the boundary-dominated flow regime for 14 different wells using daily production data rather than aggregated monthly data, as previously considered. The daily data were also smoothed to reduce noise. Computational experiments suggest that both statistical approaches can lead to plausible estimates of the transition point under different data aggregation or smoothing regimes, but that daily data are likely too granular to produce credible estimates. Although the expected value of transition points using smoothed daily data and monthly disaggregated data are generally comparable, the confidence intervals bounding the estimates based on smoothed daily data are generally wider. Our results not only inform the operational practices of oil producers engaged in economic evaluation of their shale resources and additional play development activities, but also the activities of petroleum research groups, government agencies, and financial organizations seeking to improve the trustworthiness of resource projections.
Mathematical Geosciences↗
A Bayesian nonparametric approach to unmixing detrital geochronologic data
Sedimentary deposits constitute the primary record of changing environmental conditions that have acted on Earth’s surface over geologic time. Clastic material is eroded from source locations (parents) in sediment routing systems and deposited at sink locations (children). Both parents and children have characteristics that vary across many different dimensions, including grain size, chemical composition, and the geochronologic age of constituent detrital minerals. During transport, sediment from different parents is mixed together to form a child, which in turn may serve as the parent for other sediment farther down-system or later in time when buried sediment is exhumed. The distribution of detrital mineral ages observed in parent and child sediments allows for investigation of the proportion of each parent in the child sediment, which reflects the properties of the sediment routing system. To model the proportion of dates in a child sample that comes from each of the parent distributions, we use a Bayesian mixture of Dirichlet processes. This model enables us to estimate the mixing proportions with associated uncertainty while making minimal assumptions. We also present an extension to the model whereby we reconstruct unobserved parent distributions from multiple observed child distributions using mixtures of Dirichlet processes. The model accounts for uncertainty in both the number of mineral formation events that constitute each parent distribution and the mixing proportions of each parent distribution that constitutes a child distribution. To demonstrate the model, we perform analyses using simulated data where the true age distribution is known as well as using a real-world case study from the coast of central California, USA.
Mathematical Geosciences↗
Uncertainty quantification of geologic energy storage in depleted gas reservoirs using material balance equations embedded in a hierarchical errors-in-variables model
The storage potential for gas in geologic settings, such as depleted hydrocarbon reservoirs and solution-mined salt caverns, is becoming salient to future energy infrastructure planning. Technologies such as carbon capture, utilization, and storage, carbon dioxide-enhanced oil recovery, and natural gas and hydrogen storage help meet growing energy demands, reduce carbon emissions to meet climate goals, and provide energy security amid geopolitical uncertainties. Therefore, estimates of underground gas storage capacity could be useful for efficiently navigating the energy transitions. Material balance is a fundamental method in reservoir engineering for estimating original gas in place and potential storage capacity at the scale necessary for national assessments of subsurface pore space resources. However, the deterministic method cannot accommodate multiple data sources or quantify uncertainty in predictions. In this study, a method that embeds material balance equations within a hierarchical errors-in-variables model is proposed which allows the estimation of the distributions of reservoir properties needed for assessments. Uncertainties associated with these reservoir properties have traditionally been expert-elicited, whereas the uncertainty estimates from the proposed models are data-driven. Capacity and uncertainty estimates can be used in a probabilistic resource assessment, supplementing information traditionally used by assessors or even replacing this expert elicitation step when data are unavailable. Various regression models are compared in a case study of the Michigan Basin, a large contributor to the United States’ current natural gas storage capacity. In particular, errors-in-variables models help ameliorate regression dilution and can quantify uncertainty in predictions of pressure in addition to storage capacity. Overfitting is addressed by quantifying generalization error and model averaging in simple and stratified cross-validation against reported working gas capacity, representing the varying quality and quantity of available data. Incorporating a statistical framework into existing numerical methods in reservoir engineering can improve the quality of estimation, and in particular, this method brings rigor to uncertainty quantification as part of a larger effort by the U.S. Geological Survey to assess domestic energy gas storage resources in depleted hydrocarbon reservoirs.
Mathematical Geosciences↗
The Appalachian Geo-STEM Camp: Learning about geology through experiential adventure recreation
The inaugural Appalachian Geo-STEM Camp (AGC) was a partnership between West Virginia University (WVU), the U.S. Geological Survey (USGS) and the West Virginia Geological and Economic Survey (WVGES). Designed to engage high school students in geoscience-oriented Science, Technology, Engineering and Mathematics (STEM) activities through adventure-based outdoor recreation, the inaugural AGC took place in June 2018, with its base operations at the WVU Natural Resources Center (NRC), located northeast of Morgantown, West Virginia. The goals of the AGC are to increase the knowledge of the teenaged campers about the geological formations and biodiversity in the region, to acquaint them with geologic mapping technology used by USGS, WVGES, and WVU, and to foster interest in STEM-based careers. Nine students participated, with a cadre from the USGS, WVGES, and WVU teaching lessons in local geology and ecology. Inaugural-year efforts were focused on development and logistics of the camp and what activities best complimented the STEM research. Post-evaluations by the participants were generally favorable. Year-two goals are to fully develop a curriculum, and conduct a thorough pre-camp and post-camp participant survey to quantify learning objectives and guide the sustainability of the effort.
West Virginia↗
Undergraduate research projects help promote diversity in the geosciences
A workforce that draws from all segments of society and mirrors the ethnic, racial, and gender diversity of the United States population is important. The geosciences (geology, hydrology, geospatial sciences, environmental sciences) continue to lag far behind other science, technology, engineering and mathematical (STEM) disciplines in recruiting and retaining minorities (Valsco and Valsco, 2010). A report published by the National Science Foundation in 2015, “Women, Minorities, and Persons with Disabilities in Science and Engineering” states that from 2002 to 2012, less than 2% of the geoscience degrees were awarded to African-American students. Data also show that as of 2012, approximately 30% of African-American Ph.D. graduates obtained a bachelor’s degree from a Historic Black College or University (HBCU), indicating that HBCUs are a great source of diverse students for the geosciences. This paper reviews how an informal partnership between Tennessee State University (a HBCU), the U.S. Geological Survey, and Mammoth Cave National Park engaged students in scientific research and increased the number of students pursuing employment or graduate degrees in the geosciences.
Conference Paper↗
SSA task force on diversity, equity, and inclusion: Toward a changing, inclusive future in earthquake science
In the United States, a wide variety of studies show that the geoscience community does not reflect the broader societal makeup (e.g., Velasco and Jaurrieta de Velasco, 2010; Dutt, 2020; Howley, 2020). In fact, only about 10% of all Science, Technology, Engineering, and Mathematics (STEM) Ph.D. degrees are awarded to people of color, although they represent more than a third of the population (Dutt, 2020). These numbers have changed little over the past 40 yr (e.g., Bernard and Cooperdock, 2018; Dutt, 2020). Recent events in the United States have again raised awareness of this discrepancy in many fields; similar divergences may be present throughout the world. This discrepancy represents a tremendous loss of talent and contributes to ongoing bias and racism. As the premier international seismological professional society, Seismological Society of America (SSA) is committed, as stated in its ethics policy, to “freedom and transparency in research and education, which should be conducted in a supportive, inclusive, and respectful environment, free from any discrimination, harassment or bullying.” SSA convened the SSA Diversity, Equity, and Inclusion (DEI) Task Force to identify specific and actionable recommendations that the Society can take to start to address the significant issues surrounding the systematic underrepresentation in seismology and related geosciences by marginalized groups on both short- and long- term time horizons. This report, written by the Task Force, outlines actionable items that SSA can undertake as well as a framework by which progress can be measured to help guide the Society and its members forward as a community to make earthquake science more just, equitable, diverse, and inclusive. We recognize that this document cannot address the multiple individual, cultural, and historical barriers that some members may face (e.g., Núñez et al., 2020), nor can it reflect all possibilities or all recommended practices (e.g., Ali et al., 2021). What this document does represent, however, is the beginning of what we hope to be a significant cultural change in how we conduct earthquake science as an organization, not the end of this process as the Task Force fulfills its charter. As a note, some of the recommendations that the Task Force has outlined here have already been implemented within SSA or are actively being considered. For completeness, we still include them here because this highlights the commitment to change that SSA leadership has embraced.
Seismological Research Letters↗
Typing mineral deposits using their associated rocks, grades and tonnages using a probabilistic neural network
A probabilistic neural network is employed to classify 1610 mineral deposits into 18 types using tonnage, average Cu, Mo, Ag, Au, Zn, and Pb grades, and six generalized rock types. The purpose is to examine whether neural networks might serve for integrating geoscience information available in large mineral databases to classify sites by deposit type. Successful classifications of 805 deposits not used in training - 87% with grouped porphyry copper deposits - and the nature of misclassifications demonstrate the power of probabilistic neural networks and the value of quantitative mineral-deposit models. The results also suggest that neural networks can classify deposits as well as experienced economic geologists. ?? International Association for Mathematical Geology 2006.
Mathematical Geology↗
lasertram: A Python library for time resolved analysis of laser ablation inductively coupled plasma mass spectrometry data
Laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) data has a wide variety of uses in the geosciences for in-situ chemical analysis of complex natural materials. Improvements to instrument capabilities and operating software have drastically reduced the time required to generate large volumes of data relative to previous methodologies. Raw data from LA-ICP-MS, however, is in counts per unit time (typically counts per second), not elemental concentrations and converting these count ratesto concentrations requires additional processing. For complex materials where the ablated volume may contain a range of material compositions, a moderate amount of user input is also required if appropriate concentrations are to be accurately calculated. In geologic materials such as glasses and minerals that potentially have numerous heterogeneities (e.g., microlites or other inclusions) within them, this is typically determiningwhether the total ablation signal should be filtered to remove these heterogeneities. This necessitates that the LA-ICP-MS data processing pipeline is one that is not automated, but is also designed to enable rapid and efficient processing of large volumes of data. Here we introduce , a Python library for the time resolved analysis of LA-ICP-MS data. We outline its mathematical theory, code structure, and provide an example of how it can be used to provide the time resolved analysis necessitated by LA-ICP-MS data of complex geologic materials. Throughout the pipeline we show how metadata and data are incrementally added to the objects created such that virtually any aspect of an experiment may be interrogated and its quality assessed. We also show, that when combined with other Python libraries for building graphical user interfaces, it can be utilized outside of a pure scripting environment. can be found at https://doi.org/10.5066/P1DZUR3Z
Applied Computing and Geosciences↗
Using an analytical geometry method to improve tiltmeter data presentation
The tiltmeter is a useful tool for geologic and geotechnical applications. To obtain full benefit from the tiltmeter, easy and accurate data presentations should be used. Unfortunately, the most commonly used method for tilt data reduction now may yield inaccurate and low-resolution results. This article describes a simple, accurate, and high-resolution approach developed at the Illinois State Geological Survey for data reduction and presentation. The orientation of tiltplates is determined first by using a trigonometric relationship, followed by a matrix transformation, to obtain the true amount of rotation change of the tiltplate at any given time. The mathematical derivations used for the determination and transformation are then coded into an integrated PC application by adapting the capabilities of commercial spreadsheet, database, and graphics software. Examples of data presentation from tiltmeter applications in studies of landfill covers, characterizations of mine subsidence, and investigations of slope stability are also discussed.
Environmental & Engineering Geoscience↗