(1)
C.D. CONDIT
C.B. CONNOR
CENTER FOR NUCLEAR WASTE REGULATORY ANALYSES, SOUTHWEST RESEARCH
INSTITUTE, SAN ANTONIO, TX, 78238
1.0 Abstract
2.0 Introduction
2.1 Purpose
2.2 The
Springerville Volcanic Field
3.0 Defining Volcanic Events
3.1 Mapping
volcanic events
3.2 Dating
volcanic events
4.0 Temporal Trends in Volcanism
4.1 Cumulative
number of volcanic events
4.2 Cumulative
area affected by volcanic eruptions
4.3 Cumulative
number of volcanic events by petrologic type
5.0 Spatial Trends in Volcanism
5.1 The
interval 1.75 to 1.5 Ma
5.2 The
interval 1.5 to 1.25 Ma
5.3 Younger
intervals
6.0 Modeling Petterns in Basaltic Volcanism
7.0 Recurrence Rate and Probability Maps
8.0 Discussion
8.1
Hazard models
8.2 Patterns
of volcanism in the SVF
9.0 Conclusions
10.0 Acknowledgements
11.0 References
Figure 1: regional setting of the SVF
Figure 2: vent distribution in the SVF
Figure 3: Geologic map of part of the SVF
Figure 4: Age chart for part of the SVF
Figure 5: Cumulative number of volcanic
events
Figure 6: Cumulative area / volume
Figure 7: Cumulative percent volcanic events
by petrologic type
Figure 8: Density map of volcanic eventsby
petrologic type
Figure 9: Comparision of recurrence rate
models
Figure 10: Comparison of modified recurrence
rate models
Figure 11: Waxing and aning volcanism in
the SVF
Figure 12: Probability maps
Figure 13: Comparison of model results
A spatio-temporal near-neighbor model is used to identify and map variations in recurrence rate of volcanism in the Springerville Volcanic Field (SVF), Arizona, a large Colorado Plateau boundary field. Detailed mapping of individual lava flows and their associated vents, together with radiometric and paleomagnetic dating, demonstrates that 366 volcanic events comprise the SVF. These volcanic events consist of mapped eruptive units between 2.1 to 0.3 Ma over an area of 3,000 km2. Cumulatively, the SVF experienced waxing rates of vent formation prior to 1.5 Ma, near steady-state rates of vent formation 1.5 to 0.75 Ma, and waning rates of vent formation since 0.75 Ma. The increase in rate of vent formation at about 1.5 Ma coincided with a shift in the locus of magmatism from west to east in the SVF and an increase in magma alkalinity, including eruption of mugearites and benmoreites. Volume of erupted magmas, inferred from lava flow areas, was steady-state 1.75 to 0.75 Ma. A near-neighbor spatio-temporal recurrence rate model using seven near-neighbor volcanoes and a 0.5 m.y. time window reveals that areas of waxing and waning magmatism in the SVF are much more localized and volcanic activity within these areas is much more intense than implied by field-wide temporal trends. These volcano clusters are 10 to 20 km in diameter and are commonly active for less than 0.25 Ma. Mugearites and benmoreites are limited to these areas of high recurrence rate. This clustered and petrologically distinctive, rather than distributed or random, volcanic activity suggests that individual magma source regions also are localized and short-lived compared with the area and longevity of the entire field. Because volcanic activity is spatially and temporally clustered, forecasting subsequent activity is more successful using the spatio-temporal model than using average recurrence rates. This success indicates that spatio-temporal recurrence rate models are useful tools for the quantification of long-term volcanic hazards in basaltic volcanic fields.
back to top
back to table of contents
Models of volcanism recurrence rate are used to evaluate long-term volcanic hazards and to suggest mechanisms for the formation of volcanic fields (Bacon, 1982; Kuntz and others, 1986; Ho, 1992; McBirney, 1992; Wadge and others, 1994; Connor and Hill, 1995). Assessment of long-term hazards related to the development of volcanic fields is an increasingly important issue, primarily because of the changing demands society places on hazard analysis. Some types of modern facilities require siting in areas of very low geologic risk. Such critical facilities include nuclear power plants (e.g., McBirney, 1992), or the proposed high-level radioactive waste repository at Yucca Mountain, Nevada, which is located within 20 km of six Quaternary cinder cones (Crowe and others, 1982; Ho, 1991; Connor and Hill,1995). For such facilities, acceptable probabilities of high consequence events are often considered to be 10-5/yr - 10-8/yr (e.g., Griesmeyer and Okrent, 1981; IAEA, 1991; CFR, 1994) during the lifetime of the facility. In volcanic hazard assessment, estimation of such low probabilities involves characterization of patterns of volcanic activity for time periods on the order of 104-106 yr. Furthermore, population density is increasing near many volcanic fields. For example, southern Mexico City is encroaching on the Sierra Chichinautzin Volcanic Field (Bloomfield, 1975; Martin del Pozzo, 1982), increasing the exposure of the population to hazards associated with future small-volume basaltic volcanism. Recurrence-rate estimation and related probabilistic methods can play an important role in evaluating long-term volcanic hazards in these areas.
Many recurrence rate models depend on temporal patterns of volcanism observed in individual volcanic fields. Bacon (1982) observed that cumulative erupted volume in the Coso Volcanic Field since about 0.4 Ma is remarkably linear in time. Successive eruptions occur at time intervals that depend on the cumulative volume of the previous eruptions. This linear relationship was used by Bacon (1982) to forecast the timing of future eruptions and to speculate about processes, such as strain rate, that may govern magma supply and output in the Coso Volcanic Field. Kuntz and others (1986) successfully applied a volume-predictable model to several areas on the Snake River Plain, where recurrence rates of late Quaternary volcanism are much higher than in the Coso Volcanic Field but cumulative volumetric rate of basaltic magmatism is nonetheless linear in time. Other recurrence rate models depend on the number of volcanoes formed, or number of volcanic events, through time. Ho (1991) and Ho and others (1991) describe a set of models based on several statistical estimators of recurrence rate, including maximum likelihood estimators and the Weibull-Poisson distribution. In this approach, the recurrence rate of volcanism depends on the time elapsed between successive eruptions within some specified time interval. Statistical estimators are used to evaluate whether volcanism within a specific region is temporally waxing, waning, or steady-state, and to place bounds on the certainty with which these trends in activity can be estimated.
The broad and comparatively uniform temporal trends identified in some volcanic fields are in marked contrast to spatial patterns that reveal the clustered, episodic character of small-volume basaltic volcanism. Cinder cones and related basaltic vents are not randomly distributed within continental volcanic fields, but form clusters and alignments (Connor, 1990; Lutz and Gutmann, 1995). Shifts in the locus of volcanism within these fields also appear to be common (Duffield and others, 1980; Tanaka and others, 1986; Condit and others, 1989a; Foland and Bergman, 1992). These spatial patterns exist because recurrence rate is not uniform across a volcanic field at a given time even if volumetric output in the field as a whole is steady-state. Such spatial patterns reflect basic geologic controls on magma generation and ascent processes.
Recurrence rate models can account for changing temporal and spatial patterns in volcanic activity. For example, zones may be defined within which the recurrence rate of volcanism is thought to be greater than elsewhere in the field (Smith and others, 1990). Alternatively, recurrence-rate models can incorporate spatial information directly. These spatial and spatio-temporal models evaluate recurrence rate as a function of area, or time and area, on subregional scales. Wadge and others (1994) used this technique to estimate the probable locations of future lava-flow boccas on Mt. Etna. Connor and Hill (1995) used three sets of spatial and spatio-temporal models to map the probability of future volcanism in the region around a proposed high-level radioactive waste repository at Yucca Mountain. In these models, both the timing and distribution of past volcanic events are used to estimate the long-term volcanic hazard.
back to top
back to table of contents
In this paper, temporal and spatial patterns of volcanism in the Springerville Volcanic Field (SVF), Arizona, are analyzed using a spatio-temporal recurrence rate model. The model is used to track the Plio-Quaternary development of this large Colorado Plateau volcanic field (Figure 1) and to quantify the relationship between rate of vent formation, volume measured as magma output rate, and changes in the major petrologic characteristics of basalts. By constraining the spatio-temporal model with a robust data set, we are able to map areas of waxing and waning volcanism within the SVF for specific areas during discrete time intervals. This approach provides a more complete view of the development of the SVF than is possible using conventional analysis of field and geochronological data. The utility of the recurrence rate model as a tool in hazard analysis is then evaluated by forecasting subsequent volcanic events within the SVF at discrete time intervals.
back to top
back to table of contents
The lavas of the SVF are distributed over an area of about 3,000 km2. Approximately 409 vents in the area consist mostly of cinder cones and include five maars, four fissure vents, two shield volcanoes, and several spatter mounds. Mapping at the 1:24,000 scale by Condit and others (in press) and Condit (1995) shows that of the 3,000 km2 area of the field, 2,166 km2 is volcanic outcrop (Figure 2).
The SVF provides excellent possibilities for evaluation of both probability models of volcanism and uncertainties inherent in the application of these models. The SVF is one of the few continental cinder cone fields that has been mapped (Condit, 1991, 1995; Condit and others, in press) using criteria designed to identify units as individual flow fields and correlate units with source vents (Aubele and others, 1987; Condit and others, 1989b; Ulrich and others, 1989; Crumpler and others, 1994). Forty-two K-Ar age determinations (Table 1) have been obtained on the basalts in the SVF. In addition, extensive stratigraphic and magneto-stratigraphic studies further constrain the ages of flows for which radiometric age determinations have not been made (Condit, 1984, 1991,1995).
The geology and geochemistry of SVF basalts have been discussed by Condit (1984, 1995), Condit and others (1989a), and Ulrich and others (1989). The distributions of the six oldest lavas in the SVF suggest that older Pliocene and Miocene basaltic volcanism may have been substantial. Two flows found on the southwest edge of the field and dated at 8.66 to 0.19 and 8.97 to 0.19 Ma (Condit, and Shafiqullah, 1985) have a source on the Mount Baldy shield volcano (Condit, 1984; Nealey, 1989). A 50 km2 tholeiitic flow in the northern SVF is dated at 5.31 to 0.11 Ma (Cooper and others, 1990; Cooper, 1991). Other older Pliocene flows range in age from 7.6"0.4 Ma (R.J. Miller, pers. comm., 1991) to 2.94 to 0.14 Ma (Laughlin and others, 1979) and are tholeiites to hawaiites in composition. Voluminous tholeiites erupted early in the latest episode (about 2.1 to 0.3 Ma) of volcanism in the field, followed by increasing volumes of transitional and olivine-alkaline basalts (Condit and others, 1989a). The eruption of more evolved alkaline rocks, including hawaiite, mugearite and benmoreite, reached a maximum at 1.5 to 1.0 Ma. Condit and others (1989a) noted that a west-east shift in the locus of volcanism occurs through time in the field at rates consistent with rates of plate motion (1 to 3 cm/yr), but they identified little or no other systematic spatial variation in basalt geochemistry. However, additional geochronological data (e.g., Cooper and others, 1990), coupled with spatial analysis of vent distribution (Connor and others, 1992) suggested spatio-temporal geochemical trends exist and are important in the development of the SVF. Analysis of geochemical data in light of spatio-temporal recurrence rates elucidates these trends.
back to top
back to table of contents
It is critical to define the event used to describe volcanic activity in any recurrence rate model. Definitions of volcanic events vary widely in the literature (Condit and others, 1989a; Bemis and Smith, 1993; Lutz and Gutmann, 1995; Connor and Hill, 1995). Ideally, volcanic events would correspond to eruptions. Unfortunately, subsequent geologic processes often obliterate evidence of previous eruptions from the geologic record (e.g., Walker, 1993). Consequently, volcanic events in the SVF are defined as mappable eruptive units, each unit being an assemblage of volcanic products having internal stratigraphic features that indicate a cogenetic origin and eruption from a common vent.
back to top
back to table of contents
By definition, identification of volcanic events is based on mapping of eruptive units. Each of these units was distinguished using lithologic (type, size, and abundance of phenocrysts) and morphologic criteria that are detailed in Condit (1995) and Condit and others (in press). Mapping included correlation of flows to source vents, which are most commonly cinder cones, but also include maar craters and tuff rings, fissures that fed flows, and shield volcanoes. Vents on some of the older units include isolated spatter mounds that form distinctive topographic highs.
Stratigraphic and volcanologic relationships are essential to determine the number of volcanic events represented by eruptive units. Most flow units could be traced to their source at a single cone; these flow-vent units are inferred to represent single volcanic events. Seventy-four isolated vents could not be associated with flows. Each of these vents is taken to represent a single volcanic event.
Often, multiple vents correlate with single lava flow units, some of which have multiple flow lobes. A total of 26 lava flow units correlate to vent pairs. Other lava flow units correlate with up to six vents. Units that are a composite of multiple flow lobes were defined because discontinuous flow fronts or flow edges were recognized within an area of otherwise uniform lithology and flow morphology. Both volcanological relationships and historical analogy suggest that these flow units are likely little separated in time. For example, three vents (V9523, V9514A, and V9514C) form a short alignment within a single flow field (Figure 3). The 1975 Tolbachik cinder cones are a modern example of a brief episode of dike injection resulting in the formation of a similar alignment of several closely spaced vents and associated composite lava flows (Tokarev, 1983). In a few cases, composite units consist of different flow-lobe lithologies that could not be broken out as discrete units because of poor exposures or other complicating factors. Some composite units of mixed lithologies may represent a magma of varied phenocryst content emplaced during a single eruptive episode (Wilcox, 1954), although these types of composite units are probably rare in the SVF. In all cases in which more than one vent has been assigned to a single map unit, vents are assigned the same age (Figure 3) and each of these vents is defined as a volcanic event. In the most extreme case, six vents correlate with a single flow unit. This represents six discrete events, all of which are assigned the age of the dated lava flow.
Conversely, in some cases multiple flow lobes are clearly traceable back to a single vent. Seven vents within the SVF erupted more than one mappable flow lobe (e.g., Figure 3). Where these flow lobes could be distinguished, single vents appear more than once in the data set as volcanic events, each correlated in time with its mapped eruptive unit. A total of six of these vents erupted two distinct, mappable units, representing a total of twelve volcanic events. One vent (V9525A, Figure 3) has four distinct eruptive units, and therefore produced four events. Based on radiometric age determinations, stratigraphy, flow morphology, and paleomagnetic data, it is likely that little time elapsed between the emplacement of any of these flow lobes. One example of this style of eruptive activity is Cerro Negro, Nicaragua, which has erupted 10 lava flows since 1850 A.D. (McKnight and others, 1994; Simkin and Siebert, 1994). Although these vents are weighted more in the analysis because they include more than one volcanic event, they are few in number and do not significantly alter recurrence-rate estimates.
In the following discussions, we include 357 vents documented in the mapped area. As discussed above, more than one flow unit is associated with some of these vents, giving a total of 366 volcanic events. These volcanic events correspond to mapped units that are less than 2.1 Ma. Fifty-two additional known vents in the SVF have been identified based on topographic expression in the unmapped area in the southern part of the field (Figure 2). Because we have no age control on these vents, they are not included as volcanic events in the following analysis. In an area of intense magmatism, such as the SVF, subsequent activity buries or destroys vents. This means that recurrence-rate estimates based on mapped features will be lower than actual recurrence rates. Units older than 2.1 Ma are excluded from the analysis, primarily because of substantial burial of these units and loss of event details in the geologic record.
back to top
back to table of contents
Given the number of units in the SVF, it was not tenable to obtain radiometric age determinations for each unit. However, map and stratigraphic information coupled with radiometric age determinations on key stratigraphic units constrain the chronological development of the field. Thirty-four K/Ar age determinations (Table 1) have been made on flows <2.1 Ma that cover slightly more than 30% of the SVF. The possible age ranges of the remaining units <2.1 Ma can be inferred using stratigraphic, magneto-stratigraphic, and to a lesser degree, geomorphologic correlation with dated flows. In some cases, age ranges of undated flow units are estimated quantitatively, for example, where a unit is bounded solely by magnetic polarity reversals. Where possible, further attempt was made to bound flow and vent ages using geomorphologic data. For example, the degree of soil development between flows provides indication of the time elapsed between successive eruptions. Thus, age range-charts for all flows and their associated vents were developed for subregions within the SVF. Detailed unit descriptions and details of the stratigraphic correlation are available in Condit (1995).
It is assumed that there is equal probability of a vent forming early, late, or in the middle of its estimated age range, with the expected age being the average age within the range. Undated units may have erupted at any time within their estimated age range. Under these circumstances a uniform random distribution provides a consistent approach to estimate ages of stratigraphically bounded units and allows assignment of a confidence interval for the age of each flow unit and vent.
The Morgan Mountain area illustrates the procedure of estimating ages. In the Morgan Mountain area, a lava flow and vent sequence of 18 units lies stratigraphically between two other dated flows: Qme and QTsf (Figure 4). QTsf is a reversely polarized composite unit dated at 1.90 to 0.06 Ma and 2.00 to 0.11 Ma in the Morgan Mountain area. Elsewhere in the SVF, K-Ar dates on the composite QTsf lavas indicate slightly younger ages (Table 1). Thus, this unit is assigned a mean estimated age of 1.95 to 0.13 Ma, based on radiometric age determinations and rock magnetic polarity. Qme erupted at 0.49 to 0.03 Ma. In addition, two intermediate units in the Morgan Mountain area are dated radiometrically and seven units sampled for magnetic polarity.
These age data are used to estimate the permissible age range for each flow in the Morgan Mountain area. For example, unit Qmc4 directly overlies QTsf, underlies Qme, and is reversely polarized. No other stratigraphic information definitively bounds the age of this unit, and it may have formed at any time between 1.95 and 0.73 Ma, with the exception of during the Jarmillo and Olduvai normal-polarity subchrons (Figure 4). Parenthetically, lavas upslope of Qmc4 vent V9313 indicate that an additional Qmc4 vent must be present but buried beneath Qme or Qmb6; this inferred vent is not included in the analysis. Unit Qmb4 is reversely polarized, also overlies QTsf and underlies both Qmh and Qmg. Units Qmb4, Qmh, and Qmg are all overlain by Qmb6, which is dated at 1.01 to 0.02 Ma (Figure 4). Each of these units (Qmb4, Qmh and Qmg ) may have erupted between 1.95 to 0.13 and 1.01 to 0.02 Ma. However, differences in soil development at the contact, and flow surface morphology, indicate that Qmb4 is considerably older than either Qmh or Qmg. Using these geological criteria, Qmb4 is assigned an age range of 1.95 to 1.25 Ma, exclusive of the Olduvai isochron, and Qmh and Qmg are each assigned an age range of 1.5 to1.01 Ma.
After determining the permissible age range for each vent and lava flow in the mapped area, the data were subdivided into 0.25 Ma intervals. Subdividing the development of the SVF into 0.25 Ma intervals yields a relatively equal number of radiometric age determinations per interval. Between 2 Ma and 0.75 Ma, four to eight lava flows and their associated vents per interval have radiometric age determinations; three flows between 0.5 to 0.75 Ma and two lava flows between 0.25 to 0.5 Ma are dated. Errors associated with placing units in specific intervals are easily propagated through the analysis. For example, the mean estimated age of Qmb5 is 1.4 Ma, but this unit has a large age range (Figure 4). Based on the age range of Qmb5, there is a 34% chance that Qmb5 erupted between 1.25 and 1.5 Ma. Also, there is a 32% chance that Qmb5 erupted 1.0 and1.25 Ma; a 23% chance, 1.5 and1.75 Ma; and an 11% chance, 1.75 and 2.0 Ma. The cumulative impact of these uncertainties is evaluated in the following section.
back to top
back to table of contents
One way to represent the temporal pattern of volcanism in the SVF is by plotting the cumulative number of volcanic events through time (Figure 5). This plot was made at 0.25 Ma intervals and used expected, minimum, and maximum ages for the 366 volcanic events. Despite the uncertainty in the age determinations, it is clear that the SVF has gone through a waxing stage, prior to about 2 Ma, a steady-state phase, in which the numbers of volcanic events were relatively constant, and a waning stage since 0.75 Ma. The youngest dated vents are approximately 0.3 Ma.
Based on mean estimates of the ages of volcanic events, recurrence rate of volcanism was highest between 1.5 and 1.0 Ma, and averaged approximately 3.0 x 10-4 volcanic events/yr (v/yr). Using maximum vent ages, the highest recurrence rate of vent formation in the field occurred between 2.0 and 1.5 Ma and averaged 3.7 x 10-4 v/yr. Using minimum vent ages, the highest recurrence rate of vent formation in the field occurred between 1.0 and 0.5 Ma and averaged 3.6 x 10-4 v/yr. The timing of the maximum recurrence rate of volcanic events for the SVF lies within the envelope defined by these two extremes and, given the large number of vents, likely occurred close to 1.5 - 1.0 Ma.
back to top
back to table of contents
The areal extent of lava flows and vents is used to estimate magma output rate, rather than flow volume. Lava flow thickness is highly variable for individual flows and is a difficult parameter to estimate from outcrop mapping. Flow and vent areas, on the other hand, are well known through mapping. Cumulative area covered by lava flows is plotted in Figure 6. Total area covered by lavas with mapped vents less than 2.1 Ma is approximately 1,700 km2. These data suggest that the magma output rate in the field is remarkably steady through time. The magma output rate in the SVF is essentially constant between 1.75 and 0.75 Ma, a long period compared with steady-state volumetric trends identified previously in other volcanic fields (e.g., Bacon, 1982). In contrast, the frequency of volcanic events, or vent formation, increases later in this interval at approximately 1.5 Ma. Thus, rates of magma output and rate of vent formation are not equivalent during the development of the SVF.
back to top
back to table of contents
Major-element analyses exist for 257 of the mapped eruptive units (volcanic events) between approximately 2.1 and 0.3 Ma (Condit, 1995). These 257 eruptive units are further classified (Condit and others, 1989a; modified from LeBas and others, 1986) by petrologic type as: tholeiite, transitional basalt, alkali-olivine basalt, hawaiite, mugearite, and benmoreite. Temporal patterns in the eruption of these basalts are striking (Figure 7). The eruption of transitional, alkali-olivine basalts, and hawaiites, that together make up about 80% of the total units, closely follows the trend defined by the cumulative number of volcanic events (Figure 5). In contrast, tholeiites, roughly 10% of the volcanic events, erupted at a comparatively high rate than other lava types between 1.75 and 1.5 Ma.
Eruption of the most evolved basalts in the field increased after 1.5 Ma, reaching a maximum at 1.25 to1.0 Ma. These highly evolved basalts can be characterized by their alkalinity index, the difference between sample alkalinity (Na2O + K2O) and the alkaline - subalkaline boundary of Irvine and Baragar (1971) at the same SiO2 concentration (Condit and others, 1989a). Roughly 10% of the 257 units analyzed in the SVF are highly alkaline. Of these highly alkaline vents, 50% formed 1.5 to 1.25 Ma. This increase in the rate of highly alkalic, predominantly mugearitic and benmoreitic, volcanic events correlates well with the decrease in the rate of eruption of tholeiites, and with an increase in the rate of volcanic events overall (Figure 7). The total volumetric output of the field remained constant during this transition (Figure 6).
back to top
back to table of contents
The relationship between the occurrence of volcanic events, volumetric output, and petrology of basalts is further elucidated by mapping vent density in the field for individual 0.25 Ma time intervals. Vent density is quantified using a kernel estimation technique (Lutz and Gutmann, 1995; Connor and Hill, 1995), which provides a simple and consistent way to map the density of volcanic events per unit area in a field within each time interval. This technique provides a basis for comparison of the density and distribution of volcanic events during the development of a volcanic field.
In the kernel estimation technique, spatial variations in the intensity of the volcanic events are estimated from the distance to nearby volcanoes and a smoothing constant, h, using a kernel function. The choice of a kernel function has little impact on the density estimation, but an Epanechnikov kernel is widely used (Silverman, 1986; Cressie, 1991; Lutz and Gutmann, 1995) and is adopted for this analysis. This kernel function is a probability density function that is symmetric about the locations of individual vents. In this case:
(1)where k(p) is the kernel density function at point p, the location where density is estimated, is the distance between the ith vent and point p, which is then normalized by the smoothing constant, h. Given this kernel, the density of volcanic events is:
(2)
where n is the number of vents formed during the time interval and eh is an edge correction (Cressie, 1991). If lh(p) is calculated over a large enough area relative to the total size of the field, then eh = 1, and integrating over the entire area will yield n volcanic events. Estimated values of lh(p) can then be calculated on a grid and contoured.
The shape of the resulting map of vent density depends on the chosen value of the smoothing constant, h. Using a large smoothing constant results in a map that shows little variation in vent density, whereas choosing a small smoothing constant maximizes the variation in vent density. Applications of the kernel method have included exploration of the vent distribution using numerous values of h (Lutz and Gutmann, 1995), basing h on vent spacing and cluster analysis (Connor and Hill, 1995), and optimization of h that minimizes variation in density from an assumed density distribution, such as a bivariate guassian distribution (Silverman, 1986). Silverman (1986) recommends a subjective choice of the smoothing constant when the purpose of the analysis is to explore density variation. Experimentation using h = 3 to 10 km indicates that the spatial patterns in vent density identified in the SVF are not dependent on selection of the smoothing parameter over this range.
The smoothing constant was estimated from vent spacing at 0.25 Ma intervals. Mean vent-vent distance is between 1 km and 2 km for each time interval and vent-vent distances are less than 5 km more than 90% of the time. Therefore, choosing h to be 5 km, maps of vent density show variation in response to changes in the densities of clusters of vents, rather than changes due to the positions of vents within clusters. This smoothing constant is small relative to the area of the field, but is much larger than the average vent spacing and therefore provides a robust measure of density variation.
Density maps are shown for four time intervals (Figures 8a-8d). These maps illustrate the spatial development of the field for 0.25 Ma time intervals during the period in which the SVF was most active, that is, 1.75 to 0.75 Ma. The maps reveal significant spatial variation in the density of volcanic events across the SVF 1.75 to 0.75 Ma.
back to top
back to table of contents
back to top
back to table of contents
The timing of these changes in vent distribution correlate somewhat
with the increased rate of eruptions of mugearites and benmoreites; 50%
of the highly alkaline basalts mapped in the field erupted 1.5 to 1.25
Ma. All of the mugearites and benmoreites erupted at this time are located
in parts of the field where vent density and recurrence rate were highest
(Figure 8b). In contrast, comparatively few
subalkaline basalts (<20%) erupted during this time interval. These
subalkaline basalts consist of one tholeiite and several transitional basalts.
Subalkaline basalts occur in areas of lower vent density.
back to top
back to table of contents
back to top
back to table of contents
The above analyses indicate that models of the recurrence rate of volcano formation in the SVF must take into account several patterns in activity. Models must account for the overall temporal trend of vent formation, including steady-state volcanism prior to 0.75 Ma and waning volcanism since that time. In addition, models must account for the spatial change in the intensity of volcanism within the field because recurrence rate was not uniform throughout the SVF at any particular time. Furthermore, models must be amenable to comparison with observed volumetric and geochemical trends in volcanism.
Connor and Hill (1993, 1995) applied several spatial and spatio-temporal recurrence rate models to volcano formation in the Yucca Mountain region, Nevada. In this paper, one of their models of recurrence rate, a spatio-temporal near-neighbor model, is applied to the recurrence rate of vent formation. In this model, recurrence rate per unit area is estimated by:
(3)
where m near-neighbor volcanoes are determined as the minimum of uiti, ti is the time elapsed since the formation of the ith near-neighbor vent, and ui is the area of a circle, whose radius is the distance between volcano i and point p, with ui < 1 km2.
A near-neighbor approach is used because volcanism occurs in discrete events in space and in time. Recurrence rate at any point in the volcanic field is estimated directly from the distribution and timing of these past volcanic events. This approach is well-suited for application to the SVF because reasonable age estimates exist for most volcanic events. Uncertainty in the use of this spatio-temporal near-neighbor model arises in the selection of the number of m near-neighbor volcanic events that could be used to estimate the recurrence rate at a particular point and time. One approach that can be used to differentiate between various near-neighbor models is to compare the observed recurrence rate for the region with the expected regional recurrence rate calculated using near-neighbor methods, defined by:
(4)
In practice, recurrence rates,ln(p), are calculated on a grid and these values are summed over a region extending slightly beyond the volcanic field.
Calculations were made using m=6,7,8, and 10 near-neighbor vents and equations 3 and 4. Calculations were made at 0.25 Ma intervals, using only vents erupted prior to the time of the calculation in order to compare the near-neighbor estimates with the recurrence rate calculated from age data. The near-neighbor models track the variation in estimated recurrence rate, increasing before 1.25 Ma, and decreasing after 1.0 Ma (Figure 9). The m=7 and 8 near-neighbor models provide the best estimates of the regional recurrence rate before 0.75 Ma. In contrast, the m=10 near-neighbor model underestimates and the m=6 near-neighbor model overestimates the recurrence rate in the SVF.
After 0.75 Ma, all of the near-neighbor models underestimate the decrease in recurrence rate as volcanism wanes, in part due to the nature of the estimation technique. Using equation 3, the recurrence rate estimate can never decrease to zero. Therefore, the near-neighbor estimation technique has a tendency to overestimate recurrence rate when waning magmatism occurs over a relatively short interval.
Overestimation of recurrence rate during the rapidly waning stages of activity in a volcanic field can be addressed by including only those volcanoes formed during some time interval, such as 0.5 m.y., prior to the time for which the calculation is made. For example, making an estimate of recurrence rate for the SVF at 1.0 Ma, only vents formed between 1.5 and 1.0 Ma might be used to determine near-neighbor volcanoes (equation 3), rather than including all vents formed in the field prior to 1.0 Ma. Geographically nearby volcanoes that are too old to be included within the time window are not included in the recurrence-rate estimate. This modification has little impact on recurrence-rate estimates during waxing or steady-state magmatism, but decreases the recurrence-rate estimate during waning magmatism.
Figure 10 shows a comparison of the observed change in recurrence rate and m=7 and 8 near neighbors, using a 0.5-m.y. time window. These two curves better fit the observed recurrence-rate curve after 1.0 Ma than models that do not use 0.5-m.y. time windows (Figure 9). The m=7 near-neighbor model with a 0.5-m.y. time window best matches the overall trend in recurrence rate, although it overestimates the cumulative number of volcanic events slightly. Using m=7 near neighbors and a 0.25 m.y. time window, recurrence rate is underestimated during the last 1.0 Ma (Figure 10). The m=8 near-neighbor model without a time window gives the best fit before 1.0 Ma. However, this model underestimates the rate of change in volcanism after 1.0 Ma, and overestimates the future rate of volcanism (Figure 9).
back to top
back to table of contents
This spatio-temporal technique provides a basis for mapping local recurrence rate of vent formation across the area and identifying of areas of waxing or waning magmatism during a given time interval. The density maps (Figures 8a-8d) indicate that the smooth variation in temporal recurrence rate of vent formation (Figure 5) does not fully capture the pattern of volcanism. Rather, specific areas within the field experience much more intense volcanism than others during a given time interval. This variation is cast in terms of spatio-temporal recurrence rate (v yr-1km-2) using equation 3. Iterative application of equations 3 and 4 using varying numbers of nearest-neighbor vents and time windows, indicates that a m=7 near-neighbor model with a 0.5 m.y. time window provides the best estimate of the change in recurrence rate of vent formation across the SVF.
These maps of recurrence rate of volcanism in the SVF are useful for two reasons. First, they make it possible to identify areas of waxing and waning magmatism within the volcanic field. Second, recurrence rate can be recast probabilistically and probability maps can be developed to show variations in volcanic hazard across a region.
The change in recurrence rate through time is calculated from the difference in recurrence rate (v yr-1km-2) between successive time intervals and is plotted for successive intervals in Figure 11 to identify areas of developing (or waxing) volcanism. Dark areas show where volcanism is waning, light areas show waxing volcanism, and red areas show where it is steady through time, including parts of the field where no volcanism is occurring at all.
Probabilities are calculated from the recurrence-rate values using a Poisson distribution:
(5)
where t is the time interval of the probability estimate, a is the area about point p for which probability is estimated based on recurrence rate at point p, and ln(p) is the recurrence rate estimate at p (equation 3). Use of equation 5 is based on the assumption that ln(p) does not vary significantly within the time interval t or over the area a, and that the probability of more than one volcanic event in any area, a, and time interval, t, is very small.
Probability maps were made from the m=7 near-neighbors and 0.5 m.y. time window to test the utility of the probability model in forecasting subsequent volcanic events in the SVF. The maps were made by contouring the probability (equation 5) of a new volcanic event within t = 50,000 yr and a = 10 km2 for each estimate of ln(p). For example, the probability of volcanic events was calculated and contoured for the SVF at 1.75 Ma using the timing and locations of volcanic events before 1.75 Ma (Figure 12a). Based only upon these mapped volcanic events, two zones of higher probability of future volcanic events were identified: one broad zone in the western portion of the field and a smaller zone in the southeastern portion of the field.
The success of this probability model can be evaluated based on the timing and distribution of subsequent volcanic events that are readily identified by stratigraphic relationships. Although the timing of these events is somewhat uncertain, they are the next volcanic events to occur in the SVF and, of course, were not used in the probability estimate. The mean ages of these subsequent events are 0.05 to 0.1 m.y. younger than the date of the probability calculation. Volcanic events that occurred within 0.05 to 0.1 m.y. after 1.75 Ma, based on stratigraphic relationships and mean ages, correlate well with probability zones estimated from previous eruptions (Figure 12a).
Maps constructed in a similar manner for other time intervals are shown in Figures 12b through Figure 12d and facilitate some observations about the relationship between probability maps and subsequent volcanic activity. Nearly all the next volcanic events to occur are located within zones where P[volcanic event | a=10 km2, t=50,000 yr] > 0.03. During most time intervals after 1.5 Ma (e.g., Figures 12c and 12d) , approximately half the new vents are located in areas where P[volcanic event | a=10 km2, t=50,000 yr] > 0.1.
The utility of the spatio-temporal recurrence rate model can be further evaluated by comparing the estimated recurrence rate at the location of a subsequent volcanic event with average recurrence rate in the field, as might result from a purely temporal model. Average recurrence rate may be determined in several ways (Ho, 1991; Connor and Hill, 1993). One estimate of the average recurrence rate is
(6)
where n is number of volcanic events, based on mean estimated ages, that occurred in the preceding time interval t=0.25 m.y., where A is the area of the volcanic field, the selection of which is somewhat subjective. Here, the area used is the minimum area of a convex hull polygon that encloses all of the mapped vents in the SVF with the exception of three outlying vents in the NW portion of the field (Figure 2). This area is about 3,000 km2. Average recurrence rates may also be calculated from the spatio-temporal model:
(7)
where lt is estimated from equation 4 and A is the area of the volcanic field (3,000 km2). The values of lt (p) and l(p) differ slightly due to variation in the fit of the model (Figure 10).
At 1.75 Ma, the regional recurrence rate was 1.8 x 10-4 v/yr and lt (p) =6.0 x 10-8 v yr-1km-2. Based on the number of volcanic events 2.0-1.75 Ma, l(p)=4.1x 10-8v yr-1km-2. The next 19 vents to form are located in areas withln(p) = 5.8 x 10-8 to 6.6 x 10-7v yr-1km-2, with 11 of the 19 vents formed in locations of ln(p) > 1 x 10-7 v yr-1km-2. At 1.75 Ma, the spatio-temporal model forecasts the locations of subsequent volcanic events significantly better than simply averaging the regional recurrence rate over the entire field (Figure 13a).
A comparison of the variation of ln(p) across the entire volcanic field with the variation inln(p) where subsequent volcanic fields actually occurred is another measure of the success of the spatio-temporal recurrence rate model. More formally, let mtotalbe the mean recurrence rate within the SVF and let msub be the mean recurrence rate where volcanic events subsequently occurred, both estimated from ln(p). If the recurrence rate model is successful, msub > mtotal with a high degree of confidence. Taking the null hypothesis to be mtotal = msub, and the alternative hypothesis to be mtotal < msub, the null hypothesis is rejected for the 1.75 Ma data with greater than 99% confidence (Table 2). The spatio-temporal model estimated high recurrence rates where subsequent volcanic events occurred, compared to the total distribution of ln(p) within the SVF. The spatial-temporal model does equally well at 0.75 Ma (Figure 13d; Table 2), and nearly as well at 1.0 Ma (Figure 13c; Table 2).
The probability model does a poor job of forecasting the location of future volcanic events at 1.5 Ma. Based on the model, the probability of future eruptions was high in the western portion of the field at this time (Figure 12b). However, most volcanism occurred in the central portion of the SVF during the next 50,000 yr, in areas where P[volcanic event | a=10 km2, t=50,000yr] <0.05. The regional recurrence rate at this time was 2.4 x 10-4 v/yr, or =8.0 x 10-8 v yr-1km-2, and =7.4 x 10-8 v yr-1km-2. Approximately 40% of subsequent volcanic events occur in areas where the recurrence rate is estimated to be less than these values (Figure 13b) and the null hypothesis that mtotal = msubcannot be rejected (Table 2). In other words, at 1.5 Ma the spatio-temporal model performed no better than assuming subsequent volcanic events would have a random distribution in the field. This decrease in the effectiveness of the model results from a major change in the locus of volcanism in the field around 1.5 Ma. A change in alkalinity (Figure 7) and increase in the rate of new vent formation (Figure 5) also occurred at this time. Therefore, a major shift in paragenesis is accompanied by a new pattern in the distribution and timing of volcanism.
Even in cases where the spatio-temporal model is effective (e.g., 1.75 Ma, 1.0 Ma, and 0.75 Ma), it is important to properly interpret the probability maps. Numerous maxima occur on many of the probability plots (e.g., Figure 12d) within which P[volcanic event | a=10 km2, t=50,000yr] > 0.3. These areas have been the sites of comparatively intense volcanism during the previous 0.5 m.y. Often, subsequent volcanism did not occur within these maxima, but was instead offset from these maxima by 5 to 10 km. This pattern is clear in the eastern portion of the field at 1.0 Ma (Figure 12c) and the western and central portions of the field at 0.75 Ma (Figure 12d). In general, subsequent volcanic activity does not occur in areas of very high or low recurrence rate in any of the time intervals (Figures 13a-13d).
back to top
back to table of contents
Patterns in volcanic activity in the SVF were identified through detailed mapping and analysis. Although details of the stratigraphy and volcanology of the field are well-known, it is critical to evaluate possible bias in the analysis due to assumptions about the timing and distribution of volcanic events. The effusion of basalts in the field over the last 2 m.y. likely buried or destroyed numerous older vents, and this burial and destruction may have occurred preferentially in some parts of the volcanic field. For example, numerous eruptions occurred in the central portion of the SVF between approximately 1.0 and 0.75 Ma (Figure 8d). These eruptions may have buried numerous older vents accounting, in part, for the pattern of basaltic eruptions observed during earlier time intervals (e.g., Figure 8a). However, the observed tightly clustered pattern in volcanism mitigates the severity of this problem. Inspection of Figure 11 indicates that areas of waxing volcanism occur over limited zones within the SVF at all time intervals. Certainly these intense, clustered episodes of volcanism bury some older vents. It would be quite fortuitous, however, if these relatively few zones of intense volcanism completely overprinted similar, older zones of intense volcanism, given the deduced pattern of activity (Figure 11).
Experimentation with the uncertainty in the ages of the units indicates that some shift in the timing of episodes of volcanism in the SVF is possible, as exemplified by the uncertainty in cumulative rate of volcanic events (Figure 5). However, stratigraphic relationships preclude the possibility that the relative timing of major trends, such as the change from tholeiitic to more alkaline magmatism, are inverted. Similarly, although some variation in the exact timing of cluster formation is permissible, the relative timing of formation of clusters is closely and unambiguously constrained by stratigraphic and radiometric age data.
back to top
back to table of contents
The patterns of volcanic activity in the SVF indicate that hazard models must account for spatial and temporal nonhomogeneity in recurrence rate. Recurrence rate varied by more than two orders of magnitude across the SVF at any given time during its development (Figures 13a-13d). Consequently, averaging the recurrence rate over the entire SVF would significantly overestimate hazard in some regions, and underestimate hazard in others. Application of the near-neighbor spatio-temporal recurrence rate model to the SVF offers an opportunity to evaluate the utility of these models at various times during the development of the field as the locus and intensity of volcanism changed, and through changes in petrogenesis.
Several assumptions are made in the application of equations 3 and 5. Iterative calculation of the local and regional recurrence rates, lt and ln(p), indicates that the model is sensitive to changes in the number of near-neighbor volcanic events used. There are no geologic criteria for choosing among these different numbers of near-neighbor vents, and for much of the early history of the SVF, m= 6 to10 near-neighbors work nearly equally well, given the uncertainty in the age determinations of specific units (Figure 9). However, the use of many near-neighbor events, for example m =10, tends to include volcanic events in the recurrence rate estimate even when they are far away or are old. Use of a large number of near-neighbor vents results in a low recurrence-rate estimate, and results in a cumulative divergence between the model and the true cumulative number of volcanic events through time. Conversely, use of few near-neighbors preferentially weights very recent or nearby volcanic events. This tends to increase recurrence-rate estimates and, ultimately, overestimates the total number of volcanic events. In the SVF, m= 7 to 8 near-neighbors best models recurrence rate throughout most of the <2.1 Ma volcanic activity. In other volcanic fields, with different recurrence rates and vent distributions, different numbers of near-neighbor volcanoes might provide better estimates of the observed recurrence rate.
Empirical observation (Figure 10) indicates that implementation of a 0.5 m.y. time window better models the waning system than longer or shorter time windows. Older events are much less relevant to patterns in volcanic activity in the SVF than younger events, but only up to a point. For example, in the SVF a zone of intense volcanism is no more likely to experience eruptions than another nearby area after 1 m.y. of quiescence. In contrast, 0.25 Ma of quiescence is not sufficient to preclude future activity in the immediate area. The duration of this time window suggests there may be a limit to the duration of melt generation in a particular region of the SVF, despite continued activity in the field as a whole. In a less active volcanic system, or one which is more strongly episodic in time, trends are often not as apparent as they are in the SVF (e.g., Ho and others, 1991; Connor and Hill, 1995) and estimation of an appropriate time window may be difficult.
At most time intervals, the near-neighbor model does a better job of identifying areas of subsequent volcanic activity than simply averaging recurrence rate, or , across the entire field (Figures 13a to 13d). This performance was generally maintained despite shifts in the locus of volcanism and changes in the regional recurrence rate,lt. A large percentage of subsequent events take place in areas with more than twice the average recurrence rate of the SVF at the time. Thus, the spatio-temporal recurrence rate and probability maps have a definite advantage in evaluating long-term hazards over area-averaging techniques.
However, hazards are not significantly greater at local maxima (P[volcanic event | a=10 km2, t=50,000 yr] > 0.5 ) than in nearby areas (Figures 12a to 12d). Subsequent volcanic activity occurs near, but not usually within areas that have experienced intense volcanic activity in the past. Several geological factors may account for this shift in intensity, including a shift in the location of zones of partial melting due to migration in the source of heat or depletion of mantle, or changes in the stress-state of the crust due to multiple dike injections (e.g., Parsons and Thompson, 1991). Based on these considerations, it is best to treat the areas of extreme recurrence rate, either maxima or minima, with caution when estimating the locations of future eruptions and identifying hazard zones.
The model does not perform significantly better than the average recurrence rate at 1.5 Ma. This was a time of rapid change in the SVF, with a shift in the locus of volcanism from west to east, an increase in the recurrence rate of volcanic events, and an increase in the eruption of more highly alkaline basaltic magmas. It makes sense that this major shift in volcanic activity is not well forecast by the method because the recurrence-rate estimate depends on the timing and distribution of past events. With major changes in petrogenesis and possibly other processes governing magma transport, recent patterns in activity are probably less reliable indicators of future activity. Conversely, this implies that hazard models can be improved if petrogenesis and processes governing magma transport can be quantitatively incorporated in probabilistic models.
back to top
back to table of contents
Although additional geochronological information will no doubt improve the resolution of recurrence rate models, there are clear temporal and spatial patterns of volcanism in the SVF. These patterns include: (i) waxing, steady-state, and waning rates of vent formation; (ii) steady-state magma output for more than 1 m.y.; (iii) a change in major element geochemistry accompanying an increase in rate of vent formation, without a change in total magma output; and (iv) formation of vent clusters that are discrete in time and space. These clusters form on timescales of 0.5 Ma or less and in areas that are commonly 10 to 20 km in diameter (Figure 11), during episodes when recurrence rate commonly exceeds 1 x 10-7v yr-1km-2. Episodes of cluster formation took place against a background recurrence rate throughout the SVF that was much lower (e.g., about 2 x 10-8 v yr-1km-2 during a given 0.25 m.y. interval; Figures 8a to 8d). Even during waning magmatism in the SVF as a whole (1.0-0.5 Ma; Figure 11), specific areas of the field still had much higher recurrence rates than average.
Two possible explanations for this localization of vents are: (i) zones of high vent density reflect the areal distribution of zones of melt generation in the mantle, or (ii) melt generation is regional, but crustal structures or the state of stress in the upper crust enhance magma transport and eruption at particular locations and at particular times. Several lines of evidence help differentiate between these two explanations. Generally, stress states are thought to have been uniform, or rotated slightly, during the Quaternary in the southern Colorado Plateau region (Thompson and Zoback, 1979; Zoback and Zoback, 1989) and the region of the SVF contains few and subtle structures (Crumpler and others, 1989). Although only about 20% of vents in the SVF are part of vent alignments, the vent alignments that are present are regional in extent and likely reflect large-scale crustal structures (Figure 2). These vent alignments transect the field, develop over time, and have orientations consistent with regional stress orientation and a verticals1(Connor and others, 1992). Although ascending magmas appear to be influenced by these structures, there is no evidence to indicate that the regional crustal stresses change or that crustal structures develop on the temporal and spatial scales of observed volcanic patterns. This argues that regional structural control is not a major factor in the development of vent clusters.
Alternatively, rapid changes in the local stress state likely resulted from dike intrusion, and this in turn may affect subsequent dike intrusions (Parsons and Thompson, 1991). Such local changes in crustal stress may enhance magma transport in some areas, for example between two intrusions (e.g., Ryan, 1990; Takada, 1994). Thus, dike injection may affect the pattern of vent distribution in and near vent clusters, where dike density is likely to be high. However, changes in stress state due to dike injection cannot account for shifts in activity across the entire SVF or the intensity of volcanism in local areas following periods of relative quiescence (Figure 11).
Instead, given the distinct petrology of some clusters, their timing and distribution, and lack of association with surficially exposed structures, the pattern of vent formation is more likely related to areas of localized melt generation. Patterns of volcanism in other continental basaltic fields (Heming, 1980; Tanaka and others, 1986; Connor, 1990; Connor and Hill, 1995), although often less well constrained, indicate that this nonhomogeneity in timing and distribution of vents, and hence melt generation, is common and may be ubiquitous. Thus, the application of a spatio-temporal recurrence rate model provides a more complete view of the development of the field than is possible through identification of temporal (Condit and others, 1989a) or spatial (Connor and others, 1992) trends alone.
There are significant changes in petrogenesis that occur with changes in the timing and intensity of volcanism in the SVF. The observed change in alkalinity may result from some combination of a decrease in the degree of partial melting, increase in the depth over which partial melting occurred, or increased open-system behavior of the magmas (e.g., Best and Brimhall, 1974; Morse, 1980; Fitton and others, 1988). We do not attempt to differentiate between these mechanisms in this paper. However, the increase in the rate of vent formation with increasing alkalinity and constant volume output for the entire volcanic field does imply that with smaller percentages of partial melting, more numerous magma batches reach the surface. These relatively small batches of magma can only form, or at least reach the surface, where heat flux and magma generation are sufficiently localized to promote transport of these magmas. Ascent of these smaller volume batches may be promoted by higher volatile contents in the more alkalic magmas. Comparing areas of waxing volcanism over time in the SVF (Figure 11) shows that there is little change in the clustered nature of volcanism despite large petrogenetic changes. Persistent vent clustering and constant magma output indicate that a model of early intense heating, resulting in widespread tholeiitic volcanism, followed by waning and increasingly alkalic magmatism (Best and Brimhall, 1974; Fitton and others, 1988; Condit and others, 1989a), does not capture essential details of the development of the SVF. Thus, modeling and field-based constraints provide additional insight into differences between patterns in alkalic and tholeiitic petrogenesis in continental volcanic fields.
back to top
back to table of contents
The SVF developed through episodes of volcanism that occurred at discrete times and locations within the field. These episodes typically are focused in areas 10?20 km in diameter and are less than 0.25 m.y. in duration, possibly representing the area and longevity of magma source regions. Cumulatively, these discrete episodes resulted in waxing rates of vent formation prior to 1.5 Ma, near steady-state rates of vent formation at 1.5 to 1.75 Ma, and waning rates of vent formation since 0.75 Ma. The increase in rate of vent formation at about 1.5 Ma coincide with the time of shift in the locus of magmatism from west to east in the field, and a significant increase in alkalinity of magmas erupted in the most active clusters of vents in the SVF. The volume of erupted magmas, inferred from lava flow areas, was steady-state between 1.75 to 0.75 Ma.
An m=7 near-neighbor spatio-temporal recurrence-rate model with 0.5-m.y. time window most accurately describes a plot of the cumulative rate of volcanic events versus time in the SVF. Application of this spatio-temporal recurrence-rate model reveals that areas of waxing and waning magmatism in the field are much more localized and volcanic activity within these areas much more intense than implied by regional temporal trends. Because volcanic activity is spatially and temporally clustered, the model is more successful at forecasting subsequent activity in specific locations than is possible using forecasts based only on average recurrence rates. These results indicate that spatio-temporal recurrence-rate models are useful tools for quantification of long-term volcanic hazards in continental basaltic volcanic fields.
back to top
back to table of contents
Useful discussions with Brittain E. Hill are gratefully acknowledged. Careful reviews by Bruce Crowe and William Hackett improved the manuscript. This manuscript is the result of work performed in part at the Center for Nuclear Waste Regulatory Analyses (CNWRA) for the U.S. Nuclear Regulatory Commission (NRC), Office of Nuclear Regulatory Research, Division of Regulatory Applications, under Contract No. NRC-02-93-005. This manuscript 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
Aubele, J.C., Crumpler, L.S., and Shafiquallah, M. , 1986, K-Ar ages of late Cenozoic rocks of the central and eastern parts of the Springerville volcanic field, Arizona: Isochron/West, v. 46, p. 3-5.
Aubele, J.C., Crumpler, L.S., and Condit, C.D., 1987, Tectonic deformation of the Late Cenozoic Springerville volcanic field, southern margin of the Colorado Plateau, Arizona: Geological Society of America, Abstracts with Programs, v. 19, p. 576.
Bacon, C.R., 1982, Time-predictable bimodal volcanism in the Coso Range, California: Geology, v. 10, p. 65-69.
Bemis, K.G., and Smith, D.K., 1993, Production of small volcanoes in the Superswell region of the South Pacific: Earth and Planetary Science Letters, v. 118, p. 251-262.
Best, M.G., and Brimhall, W.H., 1974, Late Cenozoic alkalic basaltic magmas in the western Colorado Plateau and the Basin and Range transition zone, U.S.A., and their bearing on mantle dynamics: Geological Society of America Bulletin, v. 85, p. 1,677-1,690.
Bloomfield, K., 1975, A late-Quaternary monogenetic volcanic field in central Mexico: Geologische Rundshau, v. 64, p. 476-497.
CFR, 1994, Title 10 Part 60.122, Code of Federal Regulations, Title 10, Parts 51 to 199: Office of the Federal Register, National Archives and Records Administration, Washington, D.C. 612 pp.
Condit, C. D., 1995, Dynamic Digital Map: The Springerville Volcanic Field: Boulder, Colorado, Geological Society of America, Digital Publication Series DPSM01MC (CD-ROM for the Macintosh).
Condit, C.D., 1991, Lithologic map of the western part of the Springerville volcanic field, east-central Arizona (1:50,000): U.S. Geological. Survey MI Map I-1993, 2 sheets.
Condit, C.D., 1984, The geology of the western part of the Springerville volcanic field, east-central Arizona: (unpublished Ph.D. dissertation), University of New Mexico, Albuquerque, NM, 453 p.
Condit, C.D., and Shafiqullah, M., 1985, K-Ar ages of late Cenozoic rocks of the western part of the Springerville volcanic field, east-central Arizona: Isochron/West No. 44, p. 3-5.
Condit, C.D., Crumpler, L.S., and Aubele, J.C., in press, Lithologic, age-group, magnetopolarity and geochemical maps of the Springerville volcanic field, east-central Arizona, (1:100,000): U.S. Geological. Survey MI Map I-2431, 4 sheets.
Condit, C.D., Crumpler, L.S., Aubele, J.C., and Elston, W.E., 1989a, Patterns of volcanism along the southern margin of the Colorado Plateau: the Springerville Field: Journal of Geophysical Research, v. 94, p. 7,975-7,986.
Condit, C.D., Crumpler, L.S., and Aubele, J.C.,1989b, Field trip road log for the Springerville volcanic field, southern margin of the Colorado Plateau, in Field excursions to volcanic terranes in the western United States, Volume I: Southern Rocky Mountain region, Chapin, C. and Zidek, J., eds., New Mexico Bureau of Mines and Mineral Resources, Mem. 46 , p. 33-38.
Connor, C.B., 1990, Cinder cone clustering in the TransMexican volcanic belt: structural and petrologic implications: Journal of Geophysical Research, v. 95, p. 19,395-19,405.
Connor, C.B., and Hill, B.E., 1995, Three nonhomogeneous Poisson models for the probability of basaltic volcanism: Application to the Yucca Mountain Region, Nevada, USA: Journal of Geophysical Research, v. 100, p. 10,107-10,126.
Connor, C.B., and Hill, B.E., 1993, Estimating the probability of volcanic disruption at the Yucca Mountain site using nonhomogeneous Poisson models: American Nuclear Society, Focus '93, La Grange Park, IL , p. 174-181.
Connor, C.B., Condit, C.D., Crumpler, L.S., and Aubele, J.C., 1992, Evidence of regional structural controls on vent distribution: Springerville volcanic field, Arizona: Journal of Geophysical Research, v. 97, p. 12,349-12,359.
Cooper, J.L., 1991, The Springerville volcanic field: A case study of crust/mantle evolution and magma genesis in a tectonophysical transition zone: Oxford, Ohio, Miami University, Ph.D. dissertation, 298 p.
Cooper, J.L., Aronson, J.L., Condit, C.D., and Hart, W.K., 1990, New K-Ar ages of lavas from the Colorado Plateau-Basin and Range transition zone, east-central Arizona, Isochron/West, v. 55, p. 28-31.
Cressie, N.A.C., 1991, Statistics for Spatial Data: John Wiley and Sons, New York, 900 pp.
Crowe, B.M., Johnson, M.E., and Beckman, R.J., 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, v. 3, p. 167-190.
Crumpler, L.S., Aubele, J.C., and Condit, C.D., 1994, Volcanoes and neotectonic characteristics of the Springerville volcanic field, Arizona, in , eds., Mogollon Slope: New Mexico Geological Society Guidebook, Socorro, p. 147-164.
Duffield, W.A., Bacon, C.R., and Dalrymple, G.B., 1980, Late Cenozoic volcanism, geochronology, and structure of the Coso Range, Inyo County, California: Journal of Geophysical Research, v. 85, p. 2,381-2,404.
Fitton, J.R., James, D., Kempton, P.D., Ormerod, D.S., and Leeman, W.P., 1988, The role of lithospheric mantle in the generation of late Cenozoic basic magmas in the western United States: Journal of Petrology, Special Lithosphere Issue, p. 331-349.
Foland, K.A., and Bergman, S.C., 1992, Temporal and spatial distribution of basaltic volcanism in the Pancake and Reveille ranges north of Yucca Mountain: American Nuclear Society, Third International Conference on High-Level Radioactive Waste Management, LaGrange Park, IL., p. 2,366-2,371.
Griesmeyer, J.M., and Okrent, D., 1981, Risk management and decision rules for light water reactors: Risk Analysis, v. 1, p. 121-136.
Heming, R.F., 1980, Patterns of Quaternary basaltic volcanism in the northern North Island, New Zealand: New Zealand Journal of Geology and Geophysics, v. 23, p. 335-344.
Ho, C.-H., 1992, Risk assessment for the Yucca Mountain high-level nuclear waste repository site: estimation of volcanic disruption: Mathematical Geology, v. 24, p. 347-364.
Ho, C.-H., 1991, Time trend analysis of basaltic volcanism at the Yucca Mountain site: Journal of Volcanology and Geothermal Research, v. 46, p. 61-72.
Ho, C.-H., Smith, E.I. , Feuerbach, D.L., and Naumann, T.R. , 1991, Eruptive probability calculation for the Yucca Mountain site, USA: statistical estimation of recurrence rates: Bulletin of Volcanology, v. 54, p. 50-56.
IAEA, 1991, Earthquakes and Associated Topics in Relation to Nuclear Power Plant Siting, A Safety Guide. Safety Series No. 50-SG-S1. International Atomic Energy Agency, Vienna, 60 pp.
Irvine, T. N., and Baragar, W. R. A., 1971, A guide to the chemical classification of the common volcanic rocks: Canadian Journal of Earth Science, v. 8, p. 523-548.
Kuntz, M.A., D.E. Champion, E.C. Spiker, and R.H. Lefebre, 1986, Contrasting magma types and steady-state, volume-predictable, basaltic volcanism along the Great Rift, Idaho: Geological Society of America Bulletin, v. 97, p. 579-594.
Laughlin, A.W., Brookins, D.G., Damon, P.E., and Shafiqullah, M., 1979, Late Cenozoic volcanism of the central Jemez zone, Arizona-New Mexico: Isochron/West, no. 25, p. 5-8.
Laughlin, A.W., Damon, P.E., and Shafiqullah, M., 1980, New K-Ar dates from the Springerville volcanic field, central Jemez zone, Apache County, Arizona: Isochron/West, no. 29, p. 3-4.
Le Bas, M.J., Le Maitre, R.W., Streckeisen, A., and Zanettin, B., 1986, A chemical classification of volcanic rocks based on the total alkali-silica diagram: Journal of Petrology, v. 27, p. 745-750.
Luedke, R.G., and Smith, R.L., 1978, Map showing distribution, composition, and age of late Cenozoic volcanic centers in Arizona and New Mexico: U.S. Geological Survey Miscellaneous Investigations Series Map I-1091-A, scale 1:100,000 and 1:500:00, 2 sheets.
Lutz, T.M., and Gutmann, J.T., 1995, 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.
Martin Del Pozzo, A.L., 1982, Monogenetic vulcanism in Sierra Chichinautzin, Mexico, Bulletin Volcanologique, v. 45, p. 9-24.
McBirney, A.R., 1992, Volcanology, in, Hunter, R.L. and Mann, J.C., eds., Techniques for Determining Probabilities of Geologic Events and Processes: International Association for Mathematical Geology, Studies in Mathematical Geology No. 4, Oxford University Press, New York, p. 167-184.
Mankinen, E.A., and Dalrymple, G.B., 1979, Revised geomagnetic polarity time scale for 0-5 m.y. B.P.: Journal of Geophysical Research, v. 84, p. 615-626.
McKnight, S.B., Roggensack, K. and Williams, S.N., 1994, Historical eruption dynamics, volumes, and geochemistry of a young volcano, Cerro Negro, Nicaragua: Eos, Transactions of the American Geophysical Union, v. 75, no. 44, p. 731.
Morse, S.A., 1980, Basalts and Phase Diagrams: Springer-Verlag, New York, 493pp.
Nealey, L.D., 1989, Field trip road log for the White Mountains volcanic field, southeastern Colorado Plateau, in Chapin, C. And Zidek, J., eds., Field excursions to volcanic terranes in the western United States, Volume I, Southern Rocky Mountain region: New Mexico Bureau of Mines and Mineral Resources, Memoir 46, p. 221-225.
Parsons, T., and Thompson, G.A., 1991, The role of magma overpressure in suppressing earthquakes and topography: worldwide examples: Science, v. 253, p. 1399-1402.
Peirce, H.W., Damon, P.E., and Shafiqullah, M., 1979, An Oligocene(?) Colorado Plateau edge in Arizona, in McGetchin, T.R., ed., Plateau Uplift; Mode and Mechanism: Tectonophysics, v. 61, no. 1-3, p. 1?24.
Ryan, M.P., 1990, The physical nature of the Icelandic magma transport system, in Ryan, M.P., ed., Magma Transport and Storage: John Wiley and Sons, New York, p. 175-224.
Silverman, B.W., 1986, Density Estimation for Statistics and Data Analysis: Chapman and Hall, London, 175 pp.
Simkin, T., and Seibert, L., 1994, Volcanoes of the World, Second Edition: Geosciences Press, Tuscon, 349 pp.
Smith, E.I., Naumann, T.R., Feuerbach, D.L., and Faulds, J.E., 1990, The area of most recent volcanism near Yucca Mountain, Nevada: implications for volcanic risk assessment: American Nuclear Society, International Meeting on High-level Radioactive Waste Management, LaGrange Park, IL, p. 81-90.
Takada, A., 1994, The influence of regional stress and magmatic input on styles of monogenetic and polygenetic volcanism: Journal of Geophysical Research, v. 99, p. 13,563-13,574.
Tanaka, K.L., Shoemaker, E.M., Ulrich, G.E., and Wolfe, E.W. , 1986, Migration of volcanism in the San Francisco volcanic field, Arizona: Geological Society of America Bulletin, v. 97, p. 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 Fedotov, S.A. and Markhnin, Ye. K., eds., The Great Tolbachik Fissure Eruption, July 1975, in The Great Tolbachik Fissure Eruption, Geological and Geophysical data, 1975-1976: Cambridge University Press, Cambridge, p. 27-35.
Thompson, G.A., and Zoback, M.A., 1979, Regional geophysics of the Colorado Plateau: Tectonophysics, v. 61, p. 149-181.
Ulrich, G.E., Condit, C.D., Wenrich, K.J., Wolfe, E.W., Holm. R.F., Nealey, L.D., Conway, M., Aubele, J.C., and Crumpler, L.S., 1989, Miocene to Holocene volcanism and tectonism of the southern Colorado Plateau, in Chapin, C. and Zidek, J., eds., Field Excursions to Volcanic Terranes in the Western United States, Volume I: Southern Rocky Mountain region: New Mexico Bureau of Mines and Mineral Resources, Mem. 46, p. 1-2.
Wadge, G., Young, P.A.V., and McKendrick, I.J. ,1994, Mapping lava flow hazards using computer simulation, Journal of Geophysical Research, v. 99, p. 489-504.
Walker, G.P.L., 1993, Basaltic-volcano systems, in Prichard, H.M., Alabaster, T., Harris, N.B.W., and Neary, C.R., eds., Magmatic Processes and Plate Tectonics: Geological Society Special Publication No. 76, p. 3-38.
Wilcox, R.E., 1954, Petrology of Parícutin Volcano: U.S. Geological Survey Bulletin 965C, p. 281-353.
Zoback, M.L., and Zoback, M.D.,1989, Tectonic stress field of the continental United States, in Pakiser, L.C. and Mooney, W.D., eds.,Geophysical Framework of the continental United States: Memoir of the Geological Society of America, v. 172, p. 523-539.
back to top
back to table of contents