THREE NONHOMOGENEOUS POISSON MODELS FOR THE PROBABILITY OF BASALTIC VOLCANISM: APPLICATION TO THE YUCCA MOUNTAIN REGION


CHARLES B. CONNOR and BRITTAIN E. HILL

Center for Nuclear Waste Regulatory Analyses, Southwest Research Institute, Bldg. 189

6220 Culebra Rd, San Antonio, Texas, 78238-5166, USA


Reference: Connor, C.B., and B.E. Hill, 1995, Three nonhomogeneous Poisson models for the probability of basaltic volcanism: Application to the Yucca Mountain region, Journal of Geophysical Research 100 (B6): 10,107-10,125.

 

TABLE OF CONTENTS


ABSTRACT
INTRODUCTION
Patterns in cinder cone volcanism

MODELING VENT DISTRIBUTIONS
method 1: nearest neighbor
method 2: kernel
method 3: hybrid kernel

APPLICATION TO THE YUCCA MOUNTAIN REGION
Basaltic volcanism in the Yucca Mountain region
Data Used in Models
Application of Method 1
Application of Method 2
Application of Method 3

DISCUSSION
Comparison of the Models
Probability of Volcanic Eruptions through Repository

CONCLUSIONS
ACKNOWLEDGEMENTS
REFERENCES

List of Figures


Figure 1: Location of basaltic volcanis in the YMR
Figure 2: Results of a cluster analysis

Figure 3: Recurrence rate for the formation of new volcanoes in the YMR - method 1
Figure 4: Estimated probability of disruption of the HLW repository - method 1
Figure 5: Probability maps of a new volcano forming during the next 10,000 years - method 1
Figure 6: Spatial recurrence rate of volcanism estimated for the location of the proposed repository using method 2
Figure 7: The probability of volcanic disruption of the proposed repository, estimated using method 2
Figure 8: Maps showing the variation in probability of volcanic eruptions across the YMR calculated using method 2
Figure 9: Spatial recurrence rate of volcanism estimated for the location of the proposed repository using method 3
Figure 10: The probability of volcanic disruption of the proposed repository, estimated using method 3
Figure 11: Maps showing the variation in probability of volcanic eruptions across the YMR calculated using method 3

List of Tables

Table 1: Data used in models


ABSTRACT

Distribution and timing of areal basaltic volcanism, including migration and abrupt shifts in the locus of volcanism, volcano clustering, and development of regional vent alignments, are modeled using three nonhomogeneous methods: spatio-temporal nearest-neighbor, kernel, and nearest-neighbor kernel.These models give nonparametric estimates of spatial or spatio-temporal recurrence rate, based on the positions and ages of cinder cones and related vent structures. The three methods are advantageous because (i) recurrence rate and probability maps can be made, facilitating comparison with other geological information, (ii) the need to define areas or zones of volcanic activity, required in homogeneous approaches, is eliminated, and (iii) the impact of uncertainty in the timing and distribution of individual events is particularly easy to assess. The three methods are applied to the Yucca Mountain region (YMR), Nevada, the site of a proposed high-level radioactive waste disposal facility. Application of a Hopkins F-test indicates volcano clustering in the YMR (> 95% confidence). Weighted-centroid cluster analysis indicates that Plio-Quaternary volcanoes are distributed in four clusters, three of these clusters including cinder cones formed < 1 Ma. Probability of disruption within the 8 km2 area of the proposed repository by formation of a new basaltic vent is calculated to be between 1 x 10-4and 3 x 10-4 in 104 yr (the kernel and nearest-neighbor kernel methods give a maximum probability of 3 x 10-4 in 104 yr), assuming regional recurrence rates of 5-10 volcanoes/million years, values comparable to previously published estimates. An additional finding, illustrating the strength of nonhomogeneous methods, is that maps of the probability of volcanic eruptions for the YMR indicate the proposed repository lies on a steep probability gradient: volcanism recurrence rate varies by more than 2 orders of magnitude within 20 km of the repository. Insight into this spatial scale of probability variation is a distinct benefit of application of these methods to hazard analysis in areal volcanic fields.


INTRODUCTION

The distribution and timing of volcanism in areal basaltic volcanic fields has been the focus of numerous studies, primarily with the aim of better understanding the processes that govern magma supply and the role of crustal structure in influencing magma ascent [Settle, 1979; Nakamura, 1977; Wadge and Cross, 1988; Connor, 1990; Lutz and Gutmann, 1994]. Three basic aspects of cinder cone distribution have been described through these and related studies: (i) shifts in the location of cinder cone volcanism are a common phenomenon in volcanic fields; (ii) cinder cones cluster within these fields, often on several scales; and (iii) vent alignments are ubiquitous, including short local alignments of several vents and more regional alignments, usually more than 20 km in length and consisting of numerous vents. Patterns in the distribution and timing of basaltic volcanism also have been used to assess hazards. For example, Wadge et al. [1994] made a quantitative analysis of the distribution of lava boccas on Mt. Etna as part of their assessment of lava flow hazards.
Here, we develop three spatial and spatio-temporal near-neighbor models to describe areal patterns in basaltic volcanism, and then apply these models to the probability of volcanic eruptions occurring in the Yucca Mountain region (YMR), Nevada. We propose this approach primarily in recognition of several characteristics of near-neighbor methods which make them amenable to volcano distribution studies and hazard analysis in areal volcanic fields. First, volcanic eruptions, such as the formation of a new cinder cone, are discrete in time and space. Using near-neighbor methods, the probability surface is estimated directly from the location and timing of these past, discrete volcanic events. As a result, near-neighbor models are sensitive to the patterns generally recognized in cinder cone distributions. Furthermore, the resulting probability surfaces are continuous, rather than consisting of abrupt changes in probability that must be introduced in spatially homogeneous models. Continuous probability surfaces can be readily compared to other geologic data, such as the distribution of faults, that may influence volcano distribution. Near-neighbor methods also eliminate the need to define areas or zones of volcanic activity as is required by all spatially homogeneous Poisson models. Finally, uncertainty in the ages of individual volcanic events and the distribution of older, usually pre-Quaternary volcanoes, are important limitations on the usefulness of all probability approaches. The impact of uncertainty in the timing and distribution of individual events is particularly easy to assess using near-neighbor models.
Volcanism in the YMR has been the topic of numerous previous studies focusing on the probability of disruption of a proposed high-level radioactive waste repository by volcanic activity [Crowe et al., 1982; Ho, 1991; Ho et al., 1991; Crowe et al., 1992a; Sheridan, 1992]. These studies are pursued largely because the proposed waste repository is located within 10 to 20 km of at least five Quaternary cinder cones and the high-level radioactive waste must be isolated from the surrounding environment for a period of at least 10,000 yr (Figure 1). Most models assessing the probability of future volcanism in the YMR and the likelihood of a repository-disrupting event rely on the assumption that Plio-Quaternary basaltic volcanoes are distributed in a spatially uniform random manner over some bounded area [e.g., Crowe et al., 1982; Crowe et al., 1992a; Ho et al., 1991; Margulies et al., 1992]. However, as in other volcanic fields, patterns in the distribution and age of basaltic volcanoes in the YMR make the choice of these bounded areas somewhat subjective. The locus of basaltic volcanism has shifted in the YMR from E to W since the cessation of caldera-forming volcanism in the Miocene Southern Nevada Volcanic Field [Crowe and Perry, 1989].
Crowe et al. [1992a] and Sheridan [1992] also noted that basaltic vents appear to cluster in the YMR. Sheridan [1992] suggests that one parametric method of accounting for spatial heterogeneity in vent distribution is to assume that post 4-Ma volcanoes located close to the proposed repository are formed as a result of steady-state activity, and that the dispersion of these vents represents two standard deviations on an elliptical Gaussian probability surface. Using this assumption, Sheridan [1992] modeled the probability of repository disruption by Monte Carlo simulation for both volcanic events and dike intrusions, noting that variations in the shape of the probability surface significantly alter the probability of igneous disruption of the proposed repository.
An alternative approach used to assess volcanic hazards in the YMR has been to define specific areas in which the recurrence rate of igneous events is increased. Smith et al. [1990] and Ho [1992] define NNE-trending zones within which average recurrence rates exceed that of the surrounding region. These zones correspond to cinder cone alignment orientations, which Smith et al. [1990] and Ho [1992] hypothesize may occur as a result of structural control. The objectives of our application of near-neighbor methods in the YMR are to (i) account for observed patterns in volcano distribution in our estimate of the probability of volcanism in the area, and within the boundaries of the proposed repository; (ii) use this model to map variation in probability of volcanism across the region for the first time, thus placing the probability of volcanic eruptions occurring at or near the repository in a more regional context; and (iii) compare the three near-neighbor estimates, and previous estimates, of the probability of volcanic eruptions in the area.
back to top
back to table of contents

PATTERNS IN CINDER CONE VOLCANISM

Patterns in the distribution and timing of cinder cone volcanism in the YMR are similar to patterns identified in other, often more voluminous volcanic fields. For example, abrupt shifts or migration in the location of volcanism over periods of millions of years have been documented in many basaltic volcanic fields. In the Coso Volcanic Field, California, Duffield et al. [1980] found that basaltic volcanism has taken place in essentially two-stages. Eruption of basalts took place over a broad area in what is now the northern and western portions of the Coso Volcanic Field from approximately 4 to 2.5 Ma. In the Quaternary the locus of volcanism shifted; the youngest basalts erupted in the southern portion of the Coso field. Condit et al. [1989] noted the tendency for basaltic volcanism to gradually migrate from west to east in the Springerville Volcanic Field between 2.5 Ma to 0.3 Ma. Other examples of volcanic fields in which the location of cinder cone volcanism has migrated include the San Francisco Volcanic Field, Arizona [Tanaka et al., 1986], the Lunar Crater Volcanic Field, Nevada [Foland and Bergman, 1992], the Michoacán-Guanajuato Volcanic Field, Mexico [Hasenaka and Carmichael, 1985], and the Cima Volcanic Field, California [Dohrenwend et al., 1984; Turrin et al., 1985]. In some instances, migration is readily explained by plate movement, as is the case in the San Francisco and SpringervilleVolcanic Fields [Tanaka et al., 1986; Condit et al., 1989; Connor et al., 1992]. In other areas, the direction of migration or shifts in the locus of volcanism does not correlate with the direction of plate movement. In any case, models developed to describe the recurrence rate of volcanism, or to predict locations of future eruptions in volcanic fields, need to be sensitive to these shifts in the location of volcanic activity.
On a slightly finer scale, cinder cones are known to cluster within many volcanic fields [Heming, 1980; Hasenaka and Carmichael, 1985; Tanaka et al., 1986]. Spatial clustering can be recognized through field observation, or through the use of exploratory data analysis or cluster analysis techniques [Connor, 1990]. Clusters identified using the latter approach in the Michoacán-Guanajuato and the Springerville volcanic fields were found to consist of 10 to 100 individual cinder cones. Clusters in these fields are roughly circular to elongate in shape with diameters of 10 to 50 km. The simplest explanation for the occurrence, size, and geochemical differences between many clusters is that these areas have higher magma supply resulting from persistent partial melting or higher rates of partial melting. Factors affecting magma pathways through the upper crust, such as fault distribution, appear to have little influence on cluster formation [Connor, 1990; Connor and Condit, 1994]. In some volcanic fields, the presence of silicate melts in the crust may influence cinder cone distribution by impeding the rise of basaltic magma [Eichelberger and Gooley, 1977; Bacon, 1982] and result in the formation of clusters.
Tectonic setting, strain-rate and fault distribution all may influence the distribution of basaltic vents within clusters, and sometimes across whole volcanic fields [Nakamura, 1977; Smith et al., 1990; Parsons and Thompson, 1992; Takada, 1994]. Kear [1964] discussed local vent alignments, in which vents are of the same age and easily explained by a single episode of dike injection, and regional alignments, in which vents of varying age and composition are aligned over distances of 20 to 50 km or more. Numerous mathematical techniques have been developed to identify and map vent alignments on different scales, including the Hough transform [Wadge and Cross, 1988], two-point azimuth analysis [Lutz, 1986], and frequency-domain map filtering techniques [Connor, 1990]. Regional alignments identified using these techniques are commonly colinear or parallel to mapped regional structures. For example, Draper et al. [1994] mapped vent alignments in the San Francisco Volcanic Field which are parallel to, or colinear with, segments of major fault systems in the area. About 30% of the cinder cones and maars in the San Francisco Volcanic Field are located along these regional alignments [Draper et al., 1994]. Lutz and Gutmann [1994] identified similar patterns in the Pinacate Volcanic Field, Mexico. Although alignments can clearly form due to episodes of dike injection [Nakamura , 1977] and therefore are sensitive to stress orientation [Zoback, 1989], there are also examples of injection along pre-existing faults [e.g., Kear, 1964; Draper et al., 1994] oblique to maximum horizontal compressional stress.
Cumulatively, these studies indicate that models describing the recurrence rate, or probability, of basaltic volcanism should reflect the clustered nature of basaltic volcanism and shifts in the locus of basaltic volcanism through time. Models should also be amenable to comparison with basic geological data, such as fault patterns and neotectonic stress information, which may impact vent distributions on a comparatively more detailed scale. In addition, probability models should incorporate uncertainties in the distribution and timing of volcanism. Uncertainty in the distribution of volcanoes is particularly important for pre-Quaternary volcanoes. These volcanoes may be buried as a result of subsequent volcanic activity [e.g., Condit et al., 1989] or sedimentation [e.g., Langenheim et al., 1993], or have been so deeply eroded that vent locations can not be recognized. Uncertainty in the ages of volcanoes is the result of variations in the precision and accuracy of different techniques used to date the volcanoes and open-system behavior.
Finally, it is possible to define a volcanic event in various ways. A simple definition that can be applied to young cinder cones, spatter mounds, and maars is based on morphology: an individual edifice represents an individual volcanic event. In the literature, volcanic events used in distribution analyses are defined as mapped vents [Condit et al., 1989; Connor et al., 1992, Lutz and Gutmann, 1994; Wadge et al., 1994], or volcanic edifices of a minimum size [Hasenaka and Carmichael, 1985; Connor, 1990; Bemis and Smith, 1993]. In older, eroded systems, evidence of the occurrence of vents, such a near-vent breccias or radial dikes, is required. However, several edifices can form in single, essentially continuous, eruptive episodes. For example, three closely spaced cinder cones formed during the 1975 Tolbachik fissure eruption [Tokarev, 1983; Magus'kin et al., 1983]. In this case, the three cinder cones represent a single eruptive event, that is distributed over a larger area than is represented by a single cinder cone. The three 1975 Tolbachik cinder cones have very different morphologies, and erupted adjacent to three older (late? Holocene) cinder cones [Braytseva et al., 1983]. Together this group forms a 5 km-long N-trending alignment. Without observing the formation of this alignment, it would likely be difficult to resolve the number of volcanic events represented by these six cones. This type of eruptive activity results in uncertainty in the number of volcanic events represented by individual cones, even where these are well-preserved.
These uncertainties represent a serious problem in most, if not all volcanic fields, because often there is no clear way to resolve them. An alternative approach is to ascertain the impact of this uncertainty on the probability model. We adopt this approach here, by developing several data sets for basaltic volcanism in the YMR that likely bound the uncertainties associated with the age, distribution, and number of volcanic events in the area.
back to top
back to table of contents

MODELING VENT DISTRIBUTION

Aherne and Diggle [1978] define two measures of intensity (expected number of points (in this case volcanoes) per unit area):

 
 

where ui and vi are areas of circles whose radii are the distance from the ith randomly chosen point to the nearest volcano, and the ith volcano to its nearest neighbor, respectively; m is the number of near neighbors and in this case is equal to the number of volcanoes; lpis the intensity estimated from m point-to-volcano measurements; and lvis the intensity estimated from m volcano-to-volcano measurements. Aherne and Diggle [1978] used these measures of intensity to distinguish between homogeneous Poisson point distributions, for which  lp and lv should be approximately equal, and clustered distributions, for which lv tends to measure the intensity within clusters, and  lp is a measure of cluster intensity [Ripley, 1981]. The Hopkins F-test [Ripley, 1981] uses the ratio:
tested against a Fisher F(2m,2m) distribution [Byth and Ripley, 1980], the null hypothesis being that HopF = 1 and volcanoes have a Poisson distribution. Assuming that some area can be identified in which all points, p, are located, HopF provides one means of distinguishing clustered and random volcano distributions. Numerous similar tests exist, including the Clark-Evans test [Clark and Evans, 1955] and the K-function [Ripley, 1977]. Calculation of these statistics, coupled with a spatial cluster analysis [Späth, 1980; Connor, 1990] provides an effective means of characterizing the spatial distribution.
The expected recurrence rate per unit area [Diggle, 1977; 1978; Ripley, 1977; 1981; Cressie, 1991], must be estimated in most volcanic fields because clustering causes a marked departure of recurrence rate per unit area from the average recurrence rate. Here, we describe three near-neighbor estimates of recurrence rate and describe the assumptions in each. All three methods are nonparametric and the recurrence rate estimates are controlled by the distribution and timing of past volcanism.


back to top
back to table of contents

Method 1: spatio-temporal nearest-neighbor estimate

The first method provides a spatial and temporal estimate of recurrence rate:
(4)
where near-neighbor volcanoes are determined as the minimum, uiti, ti is the time elapsed since the formation of the ith nearest neighbor volcano, and ui is defined as before [Eq. 1], with ui >1 km2.
 
The relationship between this estimate of recurrence rate and homogeneous Poisson models, in which the recurrence rate is a constant over time and within a specified area, can be illustrated by describing the behavior of lr(x,y) when a completely spatially and temporally random process is sampled. Modifying equation 4 slightly:
(5)
(6)
where E(Z) is the expected value of z. If volcanoes form as the result of a completely spatially and temporally random process, E(Z) can be thought of as the expected time and area within which n volcanoes will form, and z must have a gamma density distribution [Ripley, 1981]. Therefore the probability density function for z is:
(7)
 
where l is the average recurrence rate within some specified area and over some specified time interval. The expected value of z, given this probability density function, becomes:
(8)
(9)
In order to compare E(Z) with the recurrence rate per unit area, as defined in equation 6, E(Z) is evaluated for n = 1, that is, the expected time and area within which one new volcano will form. Combining equations 6 and 9,
(10)
for completely spatially and temporally random distributions. The near-neighbor estimate of recurrence rate, lr(x,y), becomes a constant equal to the average recurrence rate over some specified area if the underlying distribution is completely spatially and temporally random. This near-neighbor nonhomogeneous Poisson model is simply a general form of homogeneous Poisson models.One distinct advantage of using the more general near-neighbor nonhomogeneous Poisson models rather than homogeneous Poisson models is that regions within which l is taken to be constant need not be defined.
Therefore, it is reasonable to compare the expected regional recurrence rate calculated using various near-neighbors [equation 4]:
with the observed regional recurrence rate. In practice, recurrence rates,lr(x,y), are calculated on a grid and these values are summed over the region of interest:
where, in this case, Dx and Dy are the grid spacing used in the calculations, and q and n are the number of grid points used in the X and Y directions, respectively.
In summary of the first method, several assumptions are made in the application of equation 4 to estimate the intensity of volcanism, and the probability of volcanic eruptions, in a particular volcanic field. The most important assumption is that the appropriate number of near-neighbor volcanoes can be estimated from the regional recurrence rate. In areas of concentrated volcanism, such as the Springerville Volcanic Field, the frequency of vent-forming eruptions is high enough to make recurrence-rate estimates fairly straightforward [Connor and Condit, 1994]. In other areas, such as the YMR, greater uncertainty exists in estimates of the recurrence rate because of the comparatively fewer number of events [Crowe et al., 1982; Ho et al., 1991]. In addition, the use of equation 4 assumes that ui and ti have been adequately determined for each volcano. Here, ti is taken to represent the time of formation of the volcano. Finally, it is assumed that each volcano is adequately represented as a point. However, as described below, various area terms may be used to alleviate this assumption. In practice, it is relatively simple to test the sensitivity of results to both uncertainty in the ages of volcanoes and estimates of the regional recurrence rate of volcanism by computing the recurrence rate using a range of parameters.


back to top
back to table of contents

Method 2: kernel estimate

Lutz and Gutmann [1994] applied a kernel method [Silverman, 1986] for estimation of the spatial recurrence rate of volcanism in their study of vent alignment distribution in the Pinacate Volcanic Field. In the kernel estimation technique, spatial variation in estimated recurrence rate is a function of distance to nearby volcanoes and a smoothing constant, h. The kernel function is a probability density function which is symmetric about the locations of individual volcanoes. Following the example of Lutz and Gutmann [1994], an Epanechnikov kernel is used [Cressie, 1991]. For a purely spatial, bivariate distribution:
(13)
where h is the smoothing constant, used to normalize the distance between point p, the location for which recurrence rate is estimated, and volcano vi. The spatial recurrence rate at point p is then:
(14)
where n volcanoes are used in the analysis and eh(p) is an edge correction [Diggle, 1985; Cressie, 1991]. In the case of a volcanic field, integrating lh(p) over some large area, A, relative to the size of the field and the smoothing constant, h, should yield n. For the Epanechnikov kernel, letting :

Therefore, if
 
 

then

,

where the units of lh(p)are volcanoes/km2. Using this value for eh(p), lh(p) can be multiplied by an estimate of the temporal recurrence rate, lt, to calculate the expected number of volcanoes per unit area per time. The value of lh(p) at a given point p depends on the number of volcanoes found within a distance h of p. If no volcanoes are located within h of a point p, then lh(p) = 0.
 

Eruptions will have a high probability close to existing volcanoes if h is chosen to be small. Conversely, a large value of h will result in a more uniform probability distribution. Clearly, utility of the kernel model depends on the assumption that the smoothing constant can be estimated in a geologically meaningful way. Silverman [1986] recommends using a wide range of smoothing constants in density calculations, an approach adopted by Lutz and Gutmann [1994]. We use an identical approach here. However, we further constrain the range of reasonable smoothing constants by using a spatial cluster analysis. The shape of the kernel function is an additional assumption in the model. Alternative kernel functions include uniform random and normal density distributions. Although Cressie [1991] and Lutz and Gutmann [1994] indicate that the choice of the kernel function is not as important as the choice of an appropriate smoothing constant, we used several different kernels in our analysis of volcano distribution in the YMR. Even with this limited number of volcanic events, we also found that the kernel function has a trivial impact on probability calculations compared with the choice of a smoothing constant.
back to top
back to table of contents

Method 3: nearest-neighbor kernel estimate

In method 3 a value rm(p) is substituted for the smoothing constant, h, in equation 14, where rm(p)is the distance between point p and the mth nearest-neighbor volcano [Silverman, 1986]. In this case, we determine the nearest-neighbor on the basis of distance only, rather than using the measure uitiused in method 1. For m > 1, lr(p) > 0 everywhere. Thus, this nearest-neighbor kernel method produces smoother variation in the probability surface than is calculated for all but the largest values of a smoothing constant in method 2. Nonetheless, the estimated recurrence rate will be higher near the center of clusters than is estimated using the large values for the smoothing constant in method 2. As in method 1, the number of near neighbors used to estimate lr(p) will strongly impact the results and experimentation using a range of near-neighbors is necessary to identify the resulting variation in lr(p) .
Commonality between the three methods lies in the fact that each method depends fundamentally on the distribution of past volcanic events in order to estimate the probable locations of future volcanism. In the case of methods 1 and 3, the m nearest-neighbor volcanoes are used, defined by the distance to, or distance to and time since, past eruptions in the area. In method two, only nearby volcanoes are used in the estimate of recurrence rate, where "nearby" is defined by the smoothing constant. Furthermore, in all three methods the calculation of a probability of future volcanism at a given location within a volcanic field depends on an estimate of the regional recurrence rate, lt, which is generally not known with certainty [McBirney, 1992; Ho, 1991].
back to top
back to table of contents

APPLICATION TO THE YUCCA MOUNTAIN REGION

The proposed geological repository for high-level radioactive waste at Yucca Mountain, Nevada, provides one example of the increasing need to evaluate hazards due to areal basaltic volcanism. The objective of the repository is to isolate high-level radioactive waste from the accessible environment for at least the next 10,000 years, through deep (about 300 m) burial in Tertiary ignimbrites situated in the unsaturated zone several hundred meters above the local water table [DOE, 1988]. Volcanic eruptions at or near the repository could potentially release high-level radioactive waste into the accessible environment [DOE, 1988]. Therefore, determining the probability of a volcanic eruption in the repository area during the next 10,000 years is an important step in evaluating the potential risks associated with the Yucca Mountain site. The near-neighbor models described above provide one means of calculating these probabilities and evaluating their uncertainties. In the following sections the basics of YMR basaltic volcanism are reviewed, the near-neighbor models are applied, and the results are discussed in the context of previously proposed models of the probability of volcanic disruption of the repository.
back to top
back to table of contents

Basaltic Volcanism in the Yucca Mountain area

The YMR contains more than 30 Miocene-Quaternary basaltic volcanoes distributed over approximately 2500 km2. The region has been the site of recurring basaltic volcanism since the cessation of Miocene caldera-forming activity in the Southwestern Nevada Volcanic Field [e.g., Sawyer et al., 1994]. Basalts younger than about 9 Ma are petrogenetically distinct from older basalts, and better represent the mafic system that produced Quaternary eruptions in the YMR [Crowe et al., 1983; 1986]. Figure 1 illustrates the location of mapped and inferred basaltic vents younger than about 9 Ma. Several subdivisions have been proposed for YMR post-caldera basaltic volcanism. The Crater Flat Volcanic Zone (CFVZ) of Crowe and Perry [1989] is a NNW-trending zone that includes all YMR Quaternary volcanoes, most Pliocene volcanoes, and the Amargosa Valley aeromagnetic anomalies. The Area of Most Recent Volcanism (AMRV) of Smith et al. [1990] includes all Pliocene and younger YMR volcanoes. Both the CFVZ and AMRV are expanded from their original boundaries to include all of the aeromagnetic anomalies of Amargosa Valley (Figure 1).
The recognition of vent locations is particularly difficult for many Pliocene and older volcanic centers. Vent locations in  Table1 were generally reported as such on geologic maps and in reports [Byers et al., 1966; Ekren et al., 1966; Carr and Quinlivan, 1966; Byers and Barnes, 1967; Byers and Cummings, 1967; Hinrichs et al., 1967; Noble et al., 1967; Tschanz and Pampeyan, 1970; Cornwall, 1972; Crowe and Perry, 1991; Crowe et al., 1983, 1986; 1988; Carr, 1984; Swadley and Carr, 1987; Faulds et al., 1994], or interpreted in the field from the presence of feeder dikes, vent agglutinate, or cinder cone remnants. Some of the Miocene volcanic centers have been eroded to hundreds of meters below the paleosurface, removing most of the evidence for vent locations. The number of vents reported for Pliocene and older volcanic centers should be regarded as a minimum estimate. This may impact estimated cluster size, shape and longevity, but has little impact on spatial of spatio-temporal recurrence rate when data are weighted by age.
Over 200 isotopic age determinations have been published for YMR basaltic rocks younger than about 9 Ma. Many of the older analyses have relatively low degrees of precision and are occasionally inaccurate. For example, dates as old as 10.4±0.4 Ma are reported for the basalt of Pahute Mesa [Crowe et al., 1983], which overlies the 9.40±0.03 Ma Rocket Wash Tuff [Sawyer et al., 1994]. Following the example of Crowe [1994], we selected age estimates reported in Table 1 from more recent analyses, which are generally regarded as more precise and accurate than older analyses [Sinnock and Easterling, 1983; Vaniman and Crowe, 1981; Vaniman et al., 1982]. For units with multiple analyses, the age estimates represent the mean and one standard deviation of the data set and in cases where there is apparent discrepency between two recent dates, both are incorporated in the analyses.
Several of the age estimates reported in Table 1 require further explanation. The dipolar aeromagnetic anomalies in Amargosa Valley [Kane and Bracken, 1983; Langenheim et al., 1993] have both normal (Figure 1, sites B and C) or reversed (Figure 1, sites D and E) magnetic polarities. Anomaly B has been drilled, and samples of this basalt unit dated at 4.3±0.1 [Turrin, 1992] and 3.8±0.1 Ma [Perry, 1994]. Magnetic polarities are used to constrain the ages of the other anomalies, which have not been drilled but are interpreted to be caused by buried basaltic centers [Langenheim et al., 1993]. The aeromagnetic anomaly in southern Crater Flat likely represents a buried basaltic unit with normal magnetic orientation [Kane and Bracken, 1983; Crowe et al., 1986]. The age of this unit is problematic, as all of the other basalts in Crater Flat have reversed magnetic orientations [Crowe et al., 1986]. We chose not to include this possible volcanic center in our analyses. Over 100 age determinations are published for the Lathrop Wells volcano, which range from about 0.4 Ma to younger than 0.01 Ma and represent numerous analytical methods such as 40Ar/39Ar [Turrin et al., 1991], U-series disequilibrium [Crowe et al., 1992b], and cosmogenic isotopes [Poths and Crowe, 1992; Zreda et al., 1993; Poths et al., 1994]. Some of the variation in the Lathrop Wells dates may represent polycyclic activity [e.g., Crowe et al., 1992b], the evaluation of which is beyond the scope of this paper. In an attempt to encompass many of the higher-precision age determinations for Lathrop Wells, we use an estimated age of 0.1±0.05 for this volcano. A posteriori experimentation indicates that the age of Lathrop Wells may be varied from 0.01 to 0.4 Ma with little impact on probability of volcanic eruptions at the location of the repository.

 

back to top
back to table of contents

Data Used in Models

Based on the abundant geological and geochronological data available for the YMR, we use two data sets throughout the following analyses. These two data sets are meant to encompass most of the uncertainty the number and timing of volcanoes formed in the YMR. Data set 1 [ Table 1] maximizes the number of events in the YMR. For example, closely spaced cinder cones, like Little Cone NE and Little Cone SW are treated as distinct events in data set 1. Furthermore, minimum ages are used in data set 1. These minimum ages are defined by one-sigma uncertainty reported for age determinations. In cases where there is no overlap between two recent age determinations, such as is the case for Black Cone [Table 1], we use the younger of the dates in data set 1. Data Set 2 excludes several mapped vents from the analysis because these vents are closely spaced with others, and therefore may represent a single eruptive event. For example, Little Cone NE is not included in data set 2 because of its proximity to Little Cone SW. Also, several undrilled aeromagnetic anomalies are not included in data set 2. Older volcano ages are used in data set 2 [Table 1]. We believe that these two data sets bound current estimates of the timing and distribution of post-caldera basaltic volcanic events in the YMR, noting that alternative data sets may certainly be developed and ages may be revised as additional geochronological analyses are reported.
In addition, these two data sets are further sub-divided throughout the analyses that follow by volcano age. Each analysis is made for all volcanoes in the data set (i.e. all mapped post-caldera basalts), volcanoes less than 5 Ma, and volcanoes less than 2 Ma. This is done in recognition of the nonstationary character of cinder cone volcanism. Inspection of Figure 1, for example, reveals that Miocene clusters have little spatial relationship to Pliocene and Quaternary cluster distribution. However, Pliocene clusters have certainly reactivated in the Quaternary. Thus, further division of the two data sets preferentially weights the distribution of younger volcanoes.
Estimate of the regional recurrence rate, lt, of volcanism for the YMR during the Quaternary has received a great deal of study. These estimates range from about 1 volcano per million years (v/my) to 8 v/my [e.g., Ho, 1991; Ho et al., 1991; Crowe et al., 1992a]. This range of estimates is based on the application of various averaging techniques and statistical estimators. For example, one approach has been to consider the number of volcanoes that have formed in the last 1.8 m.y. [Crowe et al., 1982]. A total of eight volcanoes formed during that time interval and lt = 4 v/my [Crowe et al., 1982]. However, the YMR Quaternary volcanoes are all less than approximately 1 Ma, so, averaging over the last one million years, lt = 7 - 8 v/my. For all post-caldera basalts, lt = 3 v/my. Using a maximum likelihood estimator, Ho et al. [1991] calculated lt  = 5 - 6 v/my. Finally, based on a Poisson-Weibull model, Ho [1992] calculated that lt = 2 v/my to 13 v/my with 90% confidence. We do not attempt to refine these estimates here. Rather, our probability estimates assume lt = 5 - 10 v/my in order to encompass most previous estimates.
back to top
back to table of contents

 

Probability Models

As a first step in analysis of volcano distribution in the YMR, the presence of volcano clusters is tested using data sets 1 and 2 [Table 1] and Equations 1 and 2. Random points within the AMRV are used to calculate volcano intensity, lp [equation 1] [Aherne and Diggle, 1978]. The value of lp may change depending on the position of the m random points. We calculate lp and HopF, average the results of 100 simulations [Cressie, 1991] and report the standard error on the mean.
Considering all volcanoes in the AMRV (data set 1), HopF = 2.6±0.1. Considering only Quaternary volcanoes within the AMRV (data set 2), HopF = 7.1±0.3. In either case, the null hypothesis that volcanoes are randomly distributed in the AMRV is rejected with greater than 95% confidence. Hopkins F-test may be applied to smaller regions also. The CFVZ is approximately 70 km long and 20 km wide and is a minimum area which includes Quaternary cinder cones of the YMR and the Amargosa Valley vents. Even using areas as small as the CFVZ [Figure 1], HopF = 3.1±0.2 (data set 1) and clustering is significant with greater than 95% confidence. Application of similar measures of clustering, including the Clark-Evans test [Clark and Evans, 1955] and the K-function [Ripley, 1977] yield the same result. Consequently, we conclude that the recurrence rate of volcanism varies across the YMR, and therefore application of near-neighbor estimates of spatial and spatio-temporal variation in recurrence rate are appropriate.
A weighted-centroid cluster analysis [Späth, 1980] of vent distribution in the YMR helps illustrate vent clustering and provides additional insight into vent distribution. The results of the cluster analysis are shown by a dendrogram [Figure 2], which plots the distance at which individual cones and clusters link, where the linkage distance is the distance between the centers of clusters [Späth, 1980]. The dendrogram shown was calculated using data set 1 and volcanoes formed less than 5 Ma. The cluster analysis was repeated using both data sets, sub-divided by age, and a variety of clustering algorithms with very similar results to those plotted [Figure 2]. The weighted centroid cluster analysis shows that 4 clusters of volcanoes less than 5 Ma exist in the YMR. These include the Amargosa Valley cluster, including Lathop Wells, the Crater Flat Cluster, Sleeping Butte Cluster, including Hidden Cone, Little Black Peak, and Thirsty Mesa [Figure 1], and the Buckboard Mesa Cluster, which consists of only two closely spaced vents.These four clusters are complete and self-contained at linkage distances of 15 kmor less. The four clustersbegin forming groups at 23 km, when the Amargosa Valley and Crater Flat Valley Clusters form a single group [Figure 2]. Together these volcanoes are isolated from the Sleeping Buttes and Buckboard Mesa Clusters. The Amagosa Valley and Crater Flat Clusters are less distinct using a single linkage clustering algorithm because of the comparatively intermediate position of Lathrop Wells [Figure 1]. Vent pairs which are grouped as single events in data set 2, such as the Little Cones, link at distances of less than 2 km. The absence of these vent pairs in the Amargosa Valley Cluster is evident comparing linkage distances in this cluster with Crater Flat. This may indicate the comparatively low resolution of aeromagnetic methods for the delineation of buried vent pairs, or reflect a difference in the style of volcanism between the two clusters. Adding a hypothetical volcanic event at the location of the candidate repository [Figure 1] alters the cluster analysis very little. The hypothetical repository event links with Northern Cone at a distance of 8.2 km; this group then links with the rest of the Crater Flat Cluster at a distance of approximately 11 km.
In summary, the analysis of volcano distribution yields several observations that are useful for interpretation of the near-neighbor analyses. First, vents form statistically significant clusters in the YMR. Volcanoes less than 5 Ma form four clusters, the Crater Flat and Amargosa Valley Clusters overlapping somewhat due to the position of Lathrop Wells. Second, a volcanic event located at the repository would be part of, albeit near the edge of, the Crater Flat Cluster, rather than forming between or far from clusters in the YMR. Third, three of the four clusters contain Quaternary basalts, indicating that these clusters are long-lived and provide some indication of the likely areas of future volcanism. Finally, the cluster analysis provides one means of estimating the smoothing constant, h, used in method 2. If h is chosen to be less than 15 km, then significant, perhaps unwarranted, variation in recurrence rate will be predicted within clusters. If h is chosen to be greater than 25 to 30 km, recurrence rate will be comparatively high between clusters. Choosing h between 15 km and 25 km, therefore, will best capture the clustered nature of volcano distribution in the YMR.


back to top
back to table of contents

Application of Method 1.

Regional recurrence rate is calculated using equation [3] and then compared with expected regional recurrence rate, lt, using equation [12]. The calculations are repeated using the two data sets, further subdivided by age [Figure 3]. For data set 1, 6 to 11 nearest-neighbor volcanoes give regional recurrence rates of 5 to 10 v/my. Data set 2 models this range of recurrence rates with 6 to 8 nearest-neighbor volcanoes. Limiting the analysis to younger volcanoes results in lower regional recurrence rates at a given number of nearest neighbors because Quaternary volcanoes are tightly clustered.Ten to thirteen near-neighbor volcanoes are required to model recurrence rates similar to the estimated post-caldera recurrence rate of <4 v/my.
The probability of volcanic disruption of the potential repository site is calculated for various estimates of lr(x,y) [equation 4],
where the limits of integration define the area of the repository. This relation is closely approximated in discretized form:
where Dx and Dy each are one kilometer and a is the area within which a volcanic eruption may occur and intersect the repository. These probabilities are very close to the probability of one volcanic event because the probability of two or more events is vanishingly small (P[N(10,000 yr) > 1] = 1 x 10-9), although it is noted that a single event using data set 2 may form more than one volcanic vent. The probabilities of volcanic disruption of the repository using a range of near-neighbor models are given in Figure 4, calculated of t = 10,000yr and a = 8 km2. The area of the actual repository is currently estimated to be approximately 6 km2. Larger area terms (i.e., 8 km2) are presented to indicate the effects of an increase in repository size, and, more importantly, to account for the subsurface area directly affected by the emplacement of a new volcanic center. For example, emplacement of a cinder cone 500 m outside the repository boundary may result in dike injection within the repository itself. Using lt= 5v/my to 10 v/my anda = 8 km2, the probability of disruption during a 10,000 year isolation period is between 1.3 x 10-4 and 3.3 x 10-4 [Figure 4]. Altering the area term a from 6 km2 to 10 km2 has little impact on these probabilities. The probability of volcanic disruption of the proposed repository in greater than 1 x 10-4 for all but the lowest proposed values of lt (< 3 v/my).
One way to illustrate spatial variation in estimated recurrence rate in the YMR, and hence the probability of volcanic eruptions, is to map probabilities calculated from nonhomogeneous Poisson models. Applying equation 4, the expected recurrence rate is estimated at points on a grid (grid-node spacing 2 km) using varying numbers of near neighbors. Probabilities of at least one event occurring within one repository area (8 km2) about each grid point during the next 10,000 years are then calculated (equation 16). Two such maps are illustrated in Figures 5a-5b.Using m = 9 nearest-neighbor volcanoes and data set 1 (Figure 5) the clustered nature of volcanism in the YMR is captured by the probability surface, with the most significant mode in probability being centered on the Crater Flat Cluster. Modes in probability are also preserved at Miocene clusters in the eastern part of the YMR, although probabilities of eruptions are estimated to be more than one order of magnitude lower than in Crater Flat. None of the maps shown indicate increased probability of volcanic eruptions in the Sleeping Butte Cluster because of the few vents that comprise this cluster.Probability contours on all three maps [Figures 5] are elongate NNW-SSE, reflecting the overall distribution of Quaternary cones in the CFVZ [Crowe and Perry, 1989].


back to top
back to table of contents

Application of Method 2.

Spatial recurrence rate lh(p) [equation 14] is calculated for the repository using the same data sets for a range of smoothing constants [Figure 6]. For h = 15 to 30 km, lh(p)= 1.3 x 10-4 to 3.6 x 10-4 v/km2at the repository with a maximum at h = 20 km for most data sets. At h < 15 km the recurrence rate drops with decreasing h to 0 at h = km, the approximate distance between Northern cone and the repository site. Letting lt = 5 v/my to 10 v/my, the probability of volcanic disruption of the repository (a = 8 km2 and t = 10,000 yr) is calculated in Figure 7 for data set 1 (volcanoes formed < 5 Ma) and data set 2 (volcanoes formed < 2 Ma), other calculations falling at intermediate values. Taking 15 km < h < 25 km, based on interpretation of the cluster analysis, the probability of volcanic disruption of the repository in 10,000 yr is between 1 x 10-4 and 3 x 10-4 Maps of the probability of volcanic eruptions throughout the region are plotted in Figures 8a and 8b. The clustered nature of volcanism in the YMR is clearly illustrated on these maps, as is the overall NNW-trend in vent distribution. The probability of volcanic eruptions drops to zero very close to the log P[n = 1, a = 8km2, t = 10,000yr] = -4.5 contour, for h = 20 km.


back to top
back to table of contents

Application of Method 3.

Spatial recurrence rate, lk(p), is calculated at the repository site using equation 14 where the smoothing constant h is replaced by the distance to the mth nearest-neighbor volcano. The maximum value of lk(p)at the repository is estimated to be 3.75 x 10-4 v/km2, for data set 2 [Figure 9], volcanoes less than 2 Ma and the fifth nearest-neighbor. Each of the data sets goes through a maximum, the value of lk(p) at the maximum depending on the number of volcanoes included in the analysis. Data sets of volcanoes less than 5 Ma and all volcanoes have maxima at the same number of nearest-neighbors because the nearest-neighbors to the repository are all less than 5 Ma. Nearly all estimates of lk(p) > 1 x 10-4 v/km2. The probability of volcanic disruption of the repository site largely varies fromP[n = 1, a = 8km2, t = 10,000yr] = 5 x 10-5 to 1.5 x 10-4, with a maximum probability of 3 x 10-4[Figure 10], based on the distribution of Quaternary volcanoes and lt= 10 v/my. Maps showing the variation in probability of volcanic eruptions across the YMR calculated using lk(p) are plotted in Figures 11a and 11b.


back to top
back to table of contents

DISCUSSION

The three nonhomogeneous methods are sensitive to basic patterns in cinder cone distribution to varying degrees. These patterns include shifts in the location of cinder cone volcanism in time, cinder cone clustering, and the presence of vent and regional volcano alignments. These features of areal volcanic fields make nonhomogeneous models useful for modeling volcano distributions and calculating the probability of future volcanic eruptions within these areas.

Comparison of the Three Methods

Method 1 is most sensitive to shifts in the locus of cinder cone volcanism through time because equation [4] incorporates time since volcano formation directly into the recurrence rate estimate. Thus, using all post-caldera basalts in the calculation of probability of future volcanic eruptions in the YMR, method 1 produces a small mode in probability at Miocene clusters, but this mode is distinctly smaller than the Crater Flat mode [Figure 5a]. Using methods 2 and 3 and the same data, modes at Crater Flat and in Miocene clusters are of nearly equal amplitude. However, application of method 1 to many other volcanic fields is also more difficult because the ages of all volcanoes in the region must be known with reasonable precision. In areas where shifts in the locus of volcanism are as temporally distinct as they are in the YMR, methods 2 and 3 are easily adapted by subdividing the volcano data set on the basis of age, as we have done for the YMR. Method 2 is least sensitive to shifts in the location of volcanism because the probability of volcanic eruptions is zero at distances greater than the smoothing constant if the Epanechnikov kernel is used [equation 13].
The occurrence of cinder cone clusters is commonplace and well-documented in basaltic volcanic fields [e.g., Heming, 1980; Connor, 1990]. This clustering may be the result of various geologic controls on cinder cone emplacement, including the size, distribution, and longevity of partial melt zones, or possibly the heterogeneity of extension rates within the crust [Heming, 1980; Connor, 1990]. Geological factors such as these suggest a mechanistic basis for application of temporally and spatially nonhomogeneous Poisson probability models. The three methods treat clusters using different criteria, with varying results. Method 2 presupposes that volcano density and distance between volcanoes best defines clustering. As a result, for example, method 2 effectively identifies the Sleeping Butte area as a cluster of three volcanoes (Hidden Cone, Little Black Peak, and Thirsty Mesa), in a manner quite consistent with the cluster analysis [Figures 8a and 8b]. Method 1 and method 3 presuppose that the number of volcanoes, or volcanic events, is the predominant characteristic defining clusters. Therefore, these methods weight rates of volcanic activity between clusters much more heavily than does method 2. For example, methods 1 and 3 do not identify a separate cluster in the Sleeping Butte area, because only three volcanoes define the cluster [e.g., Figure 5a and Figure 11a]. Rather, contour lines tend to elongate between the Sleeping Butte Cluster and the Crater Flat Cluster when recurrence rate is determined using methods 1 and 3, and probability of volcanic eruptions in the center of the Crater Flat Cluster is calculated to be comparatively high.
All three methods respond to the presence of regional volcano alignments. In the YMR, the NNW trend of the CFVZ is reflected in the overall shape of the probability surfaces calculated using the three methods [Figure 5b, Figure 8a, and Figure 11a]. It is possible to model existing local vent alignments, such as the vent alignments within the Crater Flat Cluster, by decreasing the smoothing constant, h, in method 2 [Lutz and Gutmann, 1994] or decreasing the number of nearest-neighbors used in methods 1 and 3. In the case of the YMR, this is achieved by choosing h < 5 km or m < 3 nearest-neighbor volcanoes.


back to top
back to table of contents

Probability of Volcanic Disruption of the Proposed Yucca Mountain Repository

Volcano clustering in the YMR is statistically significant at the 95% confidence level. Probability models based on a homogeneous Poisson density distribution will overestimate the likelihood of future igneous activity in parts of the YMR far from Quaternary centers and underestimate the likelihood of future igneous activity within and close to Quaternary volcano clusters.
The probability of volcanic disruption of the proposed HLW repository site calculated using the three near-neighbor methods is consistently between 1 x 10-4 and 3 x 10-4, in 10,000 yr for an 8 km2 area. This range is close to, or slightly higher than, ranges indicated by most calculations based on homogeneous Poisson models.For example, Crowe et al. [1982] propose a range of probability of disruption between 3.3 x 10-6 and 4.7 x 10-4 in 10,000 yr, noting that only a "worst case" model leads to probabilities in excess of 1 x 10-4.Other reported ranges of between 1 x 10-6 and 1 x 10-4 in 10,000 yr [Crowe et al., 1992a] are close to the probabilities calculated using near-neighbor nonhomogeneous models.Differences, especially at the lower bound, arise because the candidate repository site is relatively close to the youngest large volcano cluster in the YMR. More recently, Crowe et al. [1993] proposed a range of models and calculated a range of probabilities of disruption between 9 x 10-5 and 2.6 x 10-4 in 10,000 yr using various area terms. "Worst case" models of repository disruption in which structural controls, such as those that may have resulted in the alignment of cinder cones in Crater Flat, are assumed to focus magmatism [Smith et al., 1990; Ho, 1992] include probabilities as high as 1 x 10-3 in 10,000 yr. The nonhomogeneous models developed here do not support such high probabilities because they do not include this kind of mechanistic control. It is noted that the nonhomogeneous methods do give probabilities as high as 1 x 10-3 near the center of the Crater Flat Cluster.
The basic agreement between many of these estimates of the probability of volcanic disruption of the proposed repository must be tempered, however, by a fundamental result of the spatial and spatio-temporal nonhomogeneous techniques developed here. All three nonhomogeneous methods indicate that the proposed repository is positioned on a probability gradient due to its proximity to Crater Flat. Immediately west of the proposed site, the probability of volcanism within the next 10,000 years increases by about one order of magnitude due to the presence of Quaternary volcanoes in Crater Flat Valley. The probability of volcanism within the next 10,000 years decreases east of the proposed repository site; 20 km east of the site, the probability of a new volcano forming within an 8 km2 area is on the order of 1 x 10-5 in 10,000 yr or less.This rapid change in probability, resulting from clustering in volcano distribution, has important implications for the uncertainty associated with the use of probability models.Within 20 km of the proposed site, the probability of volcanism during the next 10,000 yr and within a given 8 km2 area varies by more than two orders of magnitude. Given the rapid change in probability across the area, it seems likely that additional geologic information, such as the role of pre-existing structure [Smith et al., 1990; McDuffie et al., 1994] or strain rate [Parsons and Thompson, 1993], may alter estimates of the probability of future volcanic activity at the proposed repository site.


back to top
back to table of contents

CONCLUSIONS

Near-neighbor estimates of spatial and spatio-temporal variation in recurrence rate of basaltic volcanism can account, to varying degrees, for several basic features of volcano distribution in areal basaltic fields. These features include spatial shifts in the locus of volcanism, clustering of volcanoes within the field, and the occurrence of volcano alignments. A strength of near-neighbor methods is that uncertainty can be estimated, both by mapping variation in the probability surface across the region of interest and through experimentation encompassing the precision and accuracy of geochronological information.
Application of the Hopkins F-test and related methods shows that cinder cones cluster in the YMR with greater than 95% confidence. Assuming a regional Quaternary recurrence rate of 5 to 10 v/my, these models estimate probabilities of disruption of between 1 x 10-4 and 3 x 10-4 in 10,000 yr, in close agreement with some other recent estimates. However, spatial variation in estimated recurrence rate is substantial across the YMR, with probability of volcanic eruptions varying by more than two orders of magnitude within 20 km of the proposed repository site. This variation indicates that refinement of models, primarily through the incorporation of additional geological information, may alter these probability estimates.


back to top
back to table of contents

Acknowledgements:

Budhi Sagar and William M. Murphy made important contributions to this work. Careful reviews by Tim Lutz, Geoff Wadge, Eugene Smith, Bruce Crowe, Ken Foland and an anonymous reviewer are greatly appreciated. Tim Lutz first suggested the use of method 2. Careful C and PERL programming by Laura Connor and DEM work by Brent Henderson is gratefully acknowledged. This manuscript is the result of work performed at the Center for Nuclear Waste Regulatory Analyses (CNWRA) for the U.S. Nuclear Regulatory Commission (NRC) under contract No. NRC-02-93-005. This report is an independent product of the CNWRA and does not necessarily reflect the views or regulatory position of the NRC.


back to top
back to table of contents

 

REFERENCES

Aherne, W.A., and P.J. Diggle. 1978. The estimation of neuronal population density by a robust distance method. Journal of Microscopy 114:285-293.
 
Bacon, C.R. 1982. Time-predictable bimodal volcanism in the Coso Range, California. Geology 10: 65-69.
 
Bemis, K.G., and D.K. Smith. 1993. Production of small volcanoes in the Superswell region of the South Pacific. Earth and Planetary Science Letters 118: 251-262.
 
Braytseva, O.A., I.V. Melekestev, and V.V. Ponomareva. 1983. Age divisions of the Holocene volcanic formations of the Tolbachik Valley. The Great Tolbachik Fissure Eruption, Geological and Geophysical data, 1975-1976. S.A. Fedotov and Ye. K. Markhnin, eds. Cambridge University Press, Cambridge. 83-95.
 
Byers, F.M., and H. Barnes. 1967. Geologic Map of the Paiute Ridge Quadrangle, Nye County, Nevada. U.S. Geological Survey Geological Quadrangle Map GQ-577. Reston, VA: U.S. Geological Survey.
 
Byers, F.M., and D. Cummings. 1967. Geologic Map of the Scrugham Peak Quadrangle, Nye County, Nevada. U.S. Geological Survey Geological Quadrangle Map GQ-695. Reston, VA: U.S. Geological Survey.
 
Byers, F.M., C.L. Rogers, W.J. Carr, and S.J. Luft. 1966. Geologic Map of the Buckboard Mesa Quadrangle, Nye County, Nevada. U.S. Geological Survey Geological Quadrangle Map GQ-552. Reston, VA: U.S. Geological Survey.
 
Byth, K., and B.D. Ripley. 1980. On sampling spatial patterns by distance methods. Biometrics 36:279-284.
 
Carr, W.J. 1984. Regional and Structural Setting of Yucca Mountain, Southwestern Nevada, and Late Cenozoic Rates of Tectonic Activity in Part of the Southwestern Great Basin, Nevada and California. USGS Open-File Report 84-854. Reston, VA: U.S. Geological Survey.
 
Carr, W.J., and W.D. Quinlivan. 1966. Geologic Map of the Timber Mountain Quadrangle, Nye County, Nevada. U.S. Geological Survey Geological Quadrangle Map GQ-503. Reston, VA: U.S. Geological Survey.
 
Clark, P.J., and F.C. Evans. 1955. On some aspects of spatial pattern in biological populations. Science 121:397-398.
 
Condit, C.D., L.S. Crumpler, J.C. Aubele, and W.E. Elston. 1989. Patterns of volcanism along the southern margin of the Colorado Plateau: the Springerville Field. Journal of Geophysical Research 94: 7,975-7,986.
 
Connor, C.B. 1990. Cinder cone clustering in the TransMexican volcanic belt: structural and petrologic implications. Journal of Geophysical Research 95:19,395-19,405.
 
Connor, C.B., and C.D. Condit. 1994. Estimating recurrence rate of volcanism in the Springerville volcanic field, Arizona. Geological Society of America, Abstracts with Programs, Seattle, Washington, A-115.
 
Connor, C.B., C.D. Condit, L.S. Crumpler, and J.C. Aubele. 1992. Evidence of regional structural controls on vent distribution: Springerville volcanic field, Arizona. Journal of Geophysical Research 97:12,349-12,359.
 
Cornwall, H.R. 1972. Geology and Mineral Deposits of Southern Nye County, Nevada. Nevada Bureau of Mines and Geology Bulletin 77. Reno, NV: Nevada Bureau of Mines and Geology.
 
Cressie, N.A.C. 1991. Statistics for Spatial Data, John Wiley and Sons, New York. 900 pp.
 
Crowe, B.M. 1990. Basaltic volcanic episodes of the Yucca Mountain region. High-Level Radioactive Waste Management, International Conference, April 8-12, 1990, Las Vegas, Nevada. American Nuclear Society 1:65-73.
 
Crowe, B.M. 1994. Probabilistic volcanic risk assessment. Presentation to the Advisory Committee on Nuclear Waste. April 20, 1994, Bethesda, Maryland.
 
Crowe, B.M.and F.V. Perry. 1989. Volcanic probability calculations for the Yucca Mountain site: estimation of volcanic rates. Proceedings Nuclear Waste Isolation in the Unsaturated Zone, Focus '89, American Nuclear Society, 326-334.
 
Crowe, B., and F. Perry. 1991. Preliminary geologic map of the Sleeping Butte Volcanic Centers. Los Alamos National Laboratory Report LA-12101-MS. Los Alamos, NM: Los Alamos National Laboratory.
 
Crowe, B.M., M.E. Johnson, and R.J. Beckman. 1982. Calculation of the probability of volcanic disruption of a high-level nuclear waste repository within southern Nevada, USA. Radioac­tive Waste Management and the Nuclear Fuel Cycle 3:167-190.
 
Crowe, B.M., D.T. Vaniman, and W.J. Carr. 1983. Status of Volcanic Hazard Studies for the Nevada Nuclear Waste Storage Investigations. Los Alamos National Laboratory Report LA-9325-MS. Los Alamos, NM: Los Alamos National Laboratory.
 
Crowe, B.M., K.H. Wohletz, D.T. Vaniman, E. Gladney, and N. Bower. 1986.Status of Volcanic Hazard Studies for the Nevada Nuclear Waste Storage Investigations.LA-9325-MS, Vol. II.Los Alamos, NM:Los Alamos National Laboratory.
 
Crowe, B.M., C. Harrington, L. McFadden, F. Perry, S. Wells, B. Turrin, and D. Champion.1988. Preliminary Geologic Map of the Lathrop Wells Volcanic Center. Los Alamos National Laboratory Report LA-UR-88-4155.
 
Crowe, B.M., R. Picard, G. Valentine, and F.V. Perry. 1992a. Recurrence Models for Volcanic Events: Applications to Volcanic Risk Assessment. Third Conference on Radioactive Waste Manage­ment, April 14-16, Las Vegas, NV, American Nuclear Society, 2:2344-2355.
 
Crowe, B., R. Morley, S. Wells, J. Geissman, E. McDonald, L. McFadden, F. Perry, M. Murrell, J. Poths, and S. Forman. 1992b. The Lathrop Wells volcanic center:Status of field and geochronology studies. Proceedings of the Third International High Level Radioactive Waste Management Conference. La Grange Park, IL: American Nuclear Society. 1,997–2,013.
 
Crowe, B.M., F.V. Perry, G.A. Valentine, P.C. Wallmann, and R. Kossik. 1993. Simulation modeling of the probability of magmatic disruption of the potential Yucca Mountain site. Proceedings, Site Characterization and Model Validation, Focus '93, September 26-29, Las Vegas, Nevada, American Nuclear Society. 182-191.
 
Diggle, P.J. 1977. A note on robust density estimation for spatial point patterns. Biometrika 64:91-95.

Diggle, P.J. 1978. On parameter estimation for spatial point patterns. Journal of the Royal Statistical Society B 40:178-181.
 

Diggle, P.J. 1985. A kernel method for smoothing point process data. Applied Statistics 34: 138-147.
 
DOE. 1988. Site Characterization Plan: Yucca Mountain Site, Nevada Research and Development Area, Nevada. DOE/RW-0199. U.S. Department of Energy, Office of Radioactive Waste Management, Washington D.C.
 
Dohrenwend, J.C., L.D. MacFadden, B.D. Turrin, and S.G. Wells, 1984. K-Ar dating of the Cima volcanic field, eastern Mojave Desert, California: Late Cenozoic volcanic history and landscape evolution. Geology 12: 163-167.
 
Draper, G., Z. Chen, M. Conway, C.B. Connor, and C.D. Condit. 1994. Structural control on magma pathways in the upper crust: insights from the San Francisco volcanic field, Arizona. Geological Society of America, Abstracts with Programs, Seattle, Washington, A-115.
 
Duffield, W.A., C.R. Bacon, and G.B. Dalrymple. 1980. Late Cenozoic volcanism, geochronology, and structure of the Coso Range, Inyo County, California. Journal of Geophysical Research 85: 2381-2404.
 
Eichelberger, J.C., and R. Gooley. 1977. Evolution of silicic magma chambers and their relationship to basaltic volcanism. The Earth's Crust, Heacock, J.G., ed., American Geophysical Union Monograph 20: 57-77.
 
Ekren, E.B., R.E. Anderson, P.P. Orkild, and E.N. Hinrichs. 1966. Geologic Map of the Silent Butte Quadrangle, Nye County, Nevada. U.S. Geological Survey Geological Quadrangle Map GQ-493. Reston, VA: U.S. Geological Survey.
 
Faulds, J.E., J.W. Bell, D.L. Feuerbach, and A.R. Ramelli. 1994. Geologic Map of the Crater Flat Area, Nevada. Nevada Bureau of Mines and Geology Map 101. Reno, NV: Nevada Bureau of Mines and Geology.
 
Fleck, R.J., B.D. Turrin, D.A. Sawyer, R.G. Warren, D.E. Champion, M.R. Hudson, and S.A. Minor. 1994. Age and character of basaltic rocks of the Yucca Mountain region, southern Nevada. Journal of Geophysical Research, submitted.
 
Foland, K.A. and S.C. Bergman. 1992. Temporal and spatial distribution of basaltic volcanism in the Pancake and Reveille ranges north of Yucca Mountain. High-Level Radioactive Waste Management. Proceedings of the Third International Conference, La Vegas, NV, 12-16 April 1992. American Nuclear Society and American Society of Civil Engineers, 2366-2371.
 
Hasenaka, T., and I.S.E. Carmichael. 1985. The cinder cones of Michoacán-Guanajuato, central Mexico, their age, volume, distribution, and recharge rate. Journal of Volcanology and Geothermal Research 25:195 -204.
 
Heizler, M.T., W.C. McIntosh, F.V. Perry, and B.M. Crowe. 1994. 40Ar/39Ar results of incompletely degassed sanidine: age of Lathrop Wells volcanism. Abstracts of the Eighth International Conference on Geochronology, Cosmochronology, and Isotope Geology, Berkeley, California, June 5 - 11, 1994. U.S. Geological Survey Circular 1107: 133.
 
Heming, R.F. 1980. Patterns of Quaternary basaltic volcanism in the northern North Island, New Zealand. New Zealand Journal of Geology and Geophysics 23:335-344.
 
Hinrichs, E.N., Krushensky, R.D., and S.J. Luft. 1967. Geologic Map of the Ammonia Tanks Quadrangle, Nye County, Nevada. U.S. Geological Survey Geological Quadrangle Map GQ-638. Reston, VA: U.S. Geological Survey.
 
Ho, C.-H. 1992. Risk assessment for the Yucca Mountain high-level nuclear waste repository site: estimation of volcanic disruption. Mathematical Geology 24: 347-364.
 
Ho, C.-H., 1991. Time trend analysis of basaltic volcanism at the Yucca Mountain site. Journal of Volcanology and Geothermal Research 46:61-72.
 
Ho, C.-H., E.I. Smith, D.L. Feurbach, and T.R. Naumann. 1991. Eruptive probability calculation for the Yucca Mountain site, USA: statistical estimation of recurrence rates. Bulletin of Volcanology 54:50-56.
 
Kane, M.F., and R.E. Bracken. 1983. Aeromagnetic map of Yucca Mountain and surrounding regions, southwest Nevada. U.S. Geological Survey Open-File Report 83-616, 19 pp.
 
Kear, D. 1964. Volcanic alignments north and west of New Zealand's central volcanic region, New Zealand Journal of Geology and Geophysics 7: 24-44.
 
Langenheim, V.E., K.S. Kirchoff-Stein, and H.W. Oliver. 1993. Geophysical investigations of buried volcanic centers near Yucca Mountain, southwestern Nevada. Proceedings of Fourth International Conference on High-Level Radioactive Waste Management. La Grange Park, IL: American Nuclear Society: 1,840-1846.
 
Lutz, T.M. 1986. An analysis of the orientations of large scale crustal structures: A statistical approach based on areal distributions of pointlike features. Journal of Geophysical Research 91: 421-434.
 
Lutz, T.M., and J.T. Gutmann. 1994. An improved method of determining alignments of point-like features and its implications for the Pinacate volcanic field, Mexico. Journal of Geophysical Research, in press.
 
Magus'kin, V.B. Enman, and V.S. Tselishchev, 1983. Changes in the height, volume, and shape of the New Tolbachik volcanoes of the Northern Breakthrough, The Great Tolbachik Fissure Eruption, Geological and Geophysical data, 1975-1976. S.A. Fedotov and Ye. K. Markhnin, eds. Cambridge University Press, Cambridge. 307-315.
 
Margulies, T., L. Lancaster, N. Eisenberg, and L. Abramson. 1992. Probabilistic analysis of magma scenarios for assessing geologic waste repository performance. 92-WA/SAF-11, American Society of Mechanical Engineers, New York, NY.
 
McBirney, A.R. 1992. Volcanology. In: Techniques for Determining Probabilities of Geologic Events and Processes, R.L. Hunter and C.J. Mann, eds., International Association for Mathematical Geology, Studies in Mathematical Geology No. 4, Oxford University Press, New York: 167-184.
 
McDuffie, S., Connor, C.B., and Mahrer, K.D., 1994.A simple model of fault-dike interaction. Eos, Transactions of the American Geophysical Union, Spring Meeting.
 
Nakamura, K. 1977. Volcanoes as possible indicators of tectonic stress orientation - principles and proposal. Journal of Volcanology and Geothermal Research 2:1-16.
 
Noble, D.C.., Krushensky, R.D., E.J. McKay, and J.R. Ege. 1967. Geologic Map of the Dead Horse Flat Quadrangle, Nye County, Nevada. U.S. Geological Survey Geological Quadrangle Map GQ-614. Reston, VA: U.S. Geological Survey.
 
Parsons, T., and G.A. Thompson, 1991. The role of magma overpressure in suppressing earthquakes and topography: worldwide examples. Science, 253: 1399-1402.
 
Perry, F.M. 1994. Update on characterization of volcanic features. Presentation to the Advisory Committee on Nuclear Waste. April 20, 1994, Bethesda, Maryland.
 
Poths, J., and Crowe, B.M. 1992. Surface exposure ages and noble gas components of volcanic units at the Lathrop Wells volcanic center, Nevada. EOS, Transactions of the American Geophysical Union 73: 610.
 
Poths, J., F. Perry, and B.M. Crowe. 1994. 3He surface exposure ages at the Lathrop Wells, NV, Volcanic Center. U.S. Geological Survey Circular 1107, p. 255. Reston, VA: U.S. Geological Survey.
 
Ripley, B.D. 1977. Modelling spatial patterns. Journal of the Royal Statistical Society B39: 172-212.
 
Ripley, B.D. 1981. Spatial Statistics. Wiley Series in Probability and Mathematics. New York: John Wiley and Sons: 252.
 
Sawyer, D.R., R.J. Fleck, M.A. Lanphere, R.G. Warren, D.E. Broxton, and M.R. Hudson. 1994. Episodic caldera volcanism in the Miocene southwestern Nevada volcanic field: Revised stratigraphic framework, 40Ar/39Ar geochronology, and implications for magmatism and extension. Geological Society of America Bulletin 106:1,304-1,318.
 
Settle, M. 1979. The structure and emplacement of cinder cone fields. American Journal of Science 279: 1089-1107.
 
Sheridan, M.F. 1992. A Monte Carlo technique to estimate the probability of volcanic dikes. High Level Radioactive Waste Management: Proceedings of the Third International Conference, Las Vegas, Nevada, April 12-16, 1992, American Nuclear Society, 2: 2033-2038.
 
Silverman, B.W. 1986. Density Estimation for Statistics and Data Analysis. Chapman and Hall, London, 175 pp.
 
Sinnock, S., and R.G. Easterling. 1983. Empirically Determined Uncertainty in Potassium-Argon Ages for Plio-Pleistocene Basalts from Crater Flat, Nye County, Nevada. Sandia National Laboratory Report SAND 82-2441. Albuquerque, NM: Sandia National Laboratory.
 
Smith, E.I., T.R. Feuerbach, and J.E. Faulds. 1990. The area of most recent volcanism near Yucca Mountain, Nevada: implications for volcanic risk assessment. High-level Radioactive Waste Meeting. Proceedings of the International Topical Meeting.LaGrange Park, IL. American Nuclear Society 1:81-90.
 
Späth, H. 1980. Clustering Algorithms. John Wiley and Sons, New York. 226 p.
 
Swadley, W.C, and W.J. Carr. 1987. Geologic Map of the Quaternary and Tertiary Deposits of the Big Dune Quadrangle, Nye County, Nevada, and Inyo County, California. U.S. Geological Survey Miscellaneous Investigations Series Map I-1767. Reston, VA: U.S. Geological Survey.
 
Takada, A. 1994. The influence of regional stress and magmatic input on styles of monogenetic and polygenetic volcanism. Journal of Geophysical Research 99: 13,563-13,574.
 
Tanaka, K.L., E.M. Shoemaker, G.E. Ulrich. and E.W. Wolfe. 1986. Migration of volcanism in the San Francisco volcanic field, Arizona. Geological Society of America, Bulletin 97: 129-141.
 
Tokarev, P.I. 1983. Calculation of the magma discharge, growth in the height of the cone and dimensions of the feeder channel of Crater I in the Great Tolbachik Fissure Eruption, July 1975. The Great Tolbachik Fissure Eruption, Geological and Geophysical data, 1975-1976. S.A. Fedotov and Ye. K. Markhnin, eds. Cambridge University Press, Cambridge. 27-35.
 
Tschanz, C.M, and E.H. Pampeyan 1970. Geology and Mineral Deposits of Lincoln County, Nevada. Nevada Bureau of Mines and Geology Bulletin 73. Reno, NV: Nevada Bureau of Mines and Geology.
 
Turrin, B., 1992. New high-precision 40Ar/39Ar step heating results from basalts near Yucca Mountain. U.S. Nuclear Waste Technical Review Board, Panel on Structural Geology and Engineering Meeting on Volcanism, September 14-16, 1992, Las Vegas Nevada.
 
Turrin, B.D., J.C. Dohrenwend, R.E. Drake, and G.H. Curtis. 1985. K-Ar ages from the Cima volcanic field, eastern Mojave Desert, California, Isochron West 44: 9-16.
 
Turrin, B.D., D. Champion, and R.J. Fleck. 1991. 40Ar/39Ar age of the Lathrop Wells volcanic center, Yucca Mountain, Nevada. Science 253: 654-657.
 
Vaniman, D.T., and B.M. Crowe. 1981. Geology and Petrology of the Basalts of Crater Flat: Applications to Volcanic Risk Assessment for the Nuclear Waste Storage Investigations. Los Alamos National Laboratory Report LA-8845-MS.
 
Vaniman, D.T., B.M. Crowe, and E.S. Gladney. 1982. Petrology and geochemistry of Hawaiite lavas from Crater Flat, Nevada. Contributions in Mineralogy and Petrology 80: 341-357.
 
Wadge, G., and A. Cross. 1988. Quantitative methods for detecting aligned points: An application to the vents of the Michoacán-Guanajuato volcanic field, Mexico. Geology 16:815-818.
 
Wadge, G., P.A.V. Young, and I.J. McKendrick. 1994. Mapping lava flow hazards using computer simulation. Journal of Geophysical Research 99: 489-504.
 
Zoback, M.L. 1989. State of stress in the northern Basin and Range Province. Journal of Geophysical Research 94: 7,105-7,128.
 
Zreda, M.G., F.M. Phillips, P.W. Kubik, P. Sharma, and D. Elmore. 1993. Cosmogenic 36Cl dating of a young basaltic eruption complex, Lathrop Wells, Nevada. Geology 21: 57-60.
 


back to top
back to table of contents