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New criteria for systematic mapping and reliability assessment of monogeneticvolcanic vent alignments and elongate volcanic vents for crustal stress analyses
Timothy S. Paulsen a,, Terry J. Wilson b
a Department of Geology, University of Wisconsin, Oshkosh, WI 54901, USAb Byrd Polar Research Center and School of Earth Sciences, The Ohio State University, Columbus, OH, 43210, USA
a b s t r a c ta r t i c l e i n f o
Article history:
Received 13 September 2008
Received in revised form 25 July 2009
Accepted 19 August 2009
Available online 6 September 2009
Keywords:
Monogenetic cinder cones
Vent alignments
Vent elongation
Stress indicators
San Francisco volcanic field
Mount Morning volcano
Linear arrays of monogenetic volcanic vent alignments represent an important source of stress/strain data
from volcanic regions of the Earth and other planets. Currently, however, there is no standard methodology
for mapping vent alignments or for assessing alignment reliability, which are essential to defining a robust
stress datum from vent alignments. Here we define a systematic method for defining monogenetic vent
alignments by mapping the locations and shapes of vents. Elongation of vents into elliptical shapes is directly
related to the trend of subsurface fissures that control alignments. Elongated vents therefore are critical for
defining reliable regional vent alignments, and also provide an independent means for assessing stress
directions. Our reliability assessment system (A>B>C>D) for vent alignments is based on the number of
vents, the standard deviation of vent center points from a best-fit line, the numbers and types of elongate
vents, the standard deviation of long axes of elliptical vents from a best-fit line, and, in cases where
alignments lack elongate vents, by vent spacing distances. We quantified morphometric parameters of well-
defined fissure-fed vent alignments from polygenetic volcanoes and platform volcanic fields to establish
appropriate threshold values for reliability assessments. In this new method, the combined analysis of vent
locations and shapes optimizes the process of alignment mapping and the assessment of the reliability of
alignments to be incorporated in stress analyses. We provide quality-ranking schemes for stress data derived
from reliability-assessed vent alignments and from elongate vents. We demonstrate the utility of this new
mapping and assessment methodology by analyzing monogenetic cinder cone fields within a platform
volcanic field (the San Francisco volcanic field in Arizona) and within a volcanic field on the flank of a
polygenetic volcano (Mount Morning in Antarctica).
2009 Elsevier B.V. All rights reserved.
1. Introduction
Linear arrays of monogenetic volcanic vents (e.g., cindercones) form
ontheflanksof polygenetic volcanoesand in platform volcanicfieldsdue
to spacederuptions alongfissures fed by subsurface feeder dikes (Fig. 1)
(MacDonald, 1972; Settle, 1979; Delaney and Pollard, 1982; Vergniolleand Mangan, 2000). Vent alignments and their subsurface feeder dikes
form parallel to the maximum horizontal stress (SH) in the crust
(Anderson,1951; Nakamura,1977, Nakamuraet al.,1977;Zoback,1992)
due to intrusions creating magmatically-induced hydrofractures and/or
exploiting preexisting fracturesoriented at a high angle to the minimum
horizontal stress (Sh) (Haimson, 1975; Nakamura, 1977; Delaney et al.,
1986). Vent alignments therefore yield reliable contemporary tectonic
stress directions in cases where they are demonstrably young
(Quaternary) in age, do not show radial patterns around a polygenetic
volcano as is typical for isotropic stress fields, and are not controlled by
local factors, such as volcano topography, magma chamber shape and
pressures, and/or surface loading (Simkin, 1972; Nakamura, 1977;
Nakamura et al., 1977; Chadwick and Howard, 1991; Chadwick and
Dieterich, 1995). Although vent alignments represent an important
source of the world's contemporary stress data (e.g., the World Stress
Map Project at www.world-stress-map.org) (Heidbach et al., 2008) andof paleostress data (Bosworth et al., 1992, Bosworth et al., 2003), there
are few studies that have described the methodologies used to define
alignments when determining stress directions. It appears that the
common approach used to map alignments is to visually select
alignments by connecting the center points of vents (e.g. Nakamura,
1977; Nakamura et al., 1977) which,in practice,is fraught with potential
ambiguities (Fig. 1a), especially in localities where vent densities are
high (Lutz, 1986). Statistical methods have been developed to
objectively define vent alignments using the locations of vent center
points (e.g., Wadge and Cross, 1988; Connor et al., 1992), but these
techniques are seldom utilized for stress studies and neglect key
information provided, for example, by the elongated shapes of the
rims of cindercones(Fig.1b). Likeslip-sense determination for fault-slip
analyses (Sperner et al., 2003), vent alignment studies are sensitive to
Tectonophysics 482 (2010) 1628
Corresponding author. Tel.: +1 920 424 7002; fax: +1 424 0240.
E-mail address: [email protected] (T.S. Paulsen).
0040-1951/$ see front matter 2009 Elsevier B.V. All rights reserved.
doi:10.1016/j.tecto.2009.08.025
Contents lists available at ScienceDirect
Tectonophysics
j o u r n a l h o m e p a g e : w w w . e l s e v i e r. c o m / l o c a t e / t e c t o
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the reliability of the data used to derive a stress datum. Data reliability
shouldbe assessed when defining thequality ranking of a volcanic stress
datum, as is done with fault inversion data (Sperner et al., 2003). The
convention forranking the quality of astress datum
incorporated in the2008 World Stress Map Project is based on the numbers of vent
alignments and/or dikes and their degreeof parallelism (Heidbach et al.,
2008), but this ranking system does not consider the actual reliability of
each alignment used to produce a particular stress datum.
The purpose of this paper is to present a systematic approach for
defining monogenetic vent alignments and for assessing their
reliability based on quantifiable parameters of alignments. The steps
involved in mapping monogenetic vents, defining alignments, and
assessing alignment reliability are reviewed and the utility of the
methodology is demonstrated by applying the approach to map and
assess alignments in monogenetic cinder conefields withina platform
volcanic field (the San Francisco volcanic field in Arizona) and within
a volcanic field on the flank of a polygenetic volcano (Mount Morning
in Antarctica). We demonstrate the importance of elongate vents
when identifying and assessing vent alignments. Our results, buildingon prior work, show that elongate vents (e.g., Figs. 1b, 2, and 3) are
common in monogenetic vent fields, that elongate vents represent
reliable proxies for subsurface dike trends, and that elongate vent
shapes provide a higher confidence that an alignment marks the
presence of a subsurface dike. Elongate volcanic vents can therefore
be used to determine stress directions in the same way that dikes and
alignments are used in the 2008 World Stress Map Project. Elongate
vents also guide alignment mapping and we present a new approach
for defining vent alignments that relies on this concept, specifically by
systematically mapping the locations and elongated shapes of
volcanic vents.
Fig. 1. Schematicdiagramillustrating(a) theproblem ofambiguity when mapping alignments using vent centerpoints in a scatter fieldof vents without consideration of vent shapes
or spacings and(b) theutility ofusing vent shapesand spacings to guidealignmentselection. Elongate volcaniclandformstrendparallel to thesubsurface trace ofthe feederdikeand
can therefore be used to guide mapping of vent alignments on a regional scale. Volcanic landforms after Breed (1964).
Fig. 2. (a) Location of the Mount Morning polygenetic shield volcano in Antarctica, (b) the locations offi
gures on Hurricane Ridge on the northernfl
ank of the Mount Morningvolcano, (c) oblique aerial photograph and (d) LIDAR-derived digital elevation model (4 m resolution) showing basaltic NE-trending cleft cone (~1.3 km long) on the Mount
Morning volcano. The highly elongate, cleft shape of the crater of this cinder cone reflects the orientation of subsurface feeder dike. Note the circular craters aligned within the
NE-trending cleft crater.
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2. Observations of volcanic vent alignments
Vent alignments produced by fissure eruptions commonly initiate
as fairly continuous curtains of fire, with differential cooling
typically causing eruptions to become localized at several points
(MacDonald, 1972; Delaney and Pollard, 1982; Vergniolle and
Mangan, 2000), producing alignments of circular or elongate vents
(i.e., cinder cones, domes, volcanic necks) depending on whether the
eruptive conduits are pipe or planar shaped (MacDonald, 1972).
Alignments of circular and elongate vents can also be produced by
isolated effusive eruptions from pipe or planar shaped conduits
sourced along a subsurface dike that never completely reached the
surface. Vent alignments therefore need not display any eruptive
volcanic material between adjacent vents within an alignment.
Elongate vents produced by effusive eruptions from subsurface
dikes may include the following landforms: (1) linear ridges (i.e.,
fissure ridges) comprised of lava and agglutinate (e.g., Fig. 1b), (2)
cleft cones, which have parallel, elongate ridges of pyroclastic rocksrimming craters (Figs. 1b, 2, and 3), (3) elongate cones (Figs. 1b and
3), and (4) elongate domes. The elongation direction of these vents
will parallel the strike of the elongate eruptive conduit and the overall
trace of the fissure and subsurface dike (Breed, 1964; Nakamura,
1977; Tibaldi, 1995; Chorowicz et al., 1997; Korme et al., 1997;
Adiyaman et al., 1998; Dhont et al., 1998; Toprak, 1998). On a regional
scale, vent alignments and exposed feeder dikes typically form
relatively straight lines that can range from tens of meters to tens of
kilometers in length (Table 1) (Knopf, 1936; Od, 1957; MacDonald,
1972; Nakamura, 1977; Nakamura et al., 1977; Delaney and Pollard,
1982; Sigurdsson, 1987; Connor et al., 1992; Thordarson and Self,
1993; Delaney and Gartner, 1997; Walker, 1999). The main excep-
tions to straight fissures are seen on the summits of polygenetic
volcanoeswherevent alignments anddikesmay curve dueto radialorconcentric fracturing about the central magma chamber (Od, 1957;
Nakamura, 1977).
Despite the importance of understanding morphometric attri-
butes, particularly the dimensional characteristics, of vents and vent
alignments for stress analyses and magmatic processes, there has
been surprisingly little work published on the subject. To better
understand the typical attributes of a good vent alignment beyond a
qualitative level, and to set the foundation for effective alignment
mapping and assessing their reliability, we compiled morphometric
data for vent alignments from existing literature and used previously
published maps to characterize classic alignments in different tectonic
settings, including platform volcanicfields and polygenetic volcanoes.
The alignments we studied in platform volcanic fields include nine
individual vent alignments erupted along the Laki fissure from 1783
to 1785 in Iceland (Fig. 4a; Thordarson and Self, 1993) and eleven
individual Pliocene to Pleistocene alignments erupted along the Lunar
Craters volcanic field within the Basin and Range rift in Nevada
(Fig. 4b; Scott and Trask, 1971). The alignments we studied on
polygenetic volcanoes include a Quaternary flank alignment on the
Makushin stratovolcano in Alaska (Fig. 5a; Drewes et al., 1961), andtwo Quaternary alignments along the Kohala rift on the Kohala shield
volcano in Hawaii (Fig. 5b; Wolfe and Morris, 1996). For the Laki
fissure and the Makushin volcano, we quantified parameters of vent
alignments defined by previous authors (Thordarson and Self, 1993;
Drewes et al., 1961). For the Lunar Craters volcanic field and the
Kohala rift, we found no published information specifically on align-
ments, so we defined alignments by drawing a line through the long
axes of a series of elongate vents, including any circular vents along
the same trend, and then measured their morphometric parameters.
For alignments in each of these volcanic areas, we analyzed the
following six parameters to define the morphometric attributes of
reliable vent alignments: (1) numbers of vents,(2) alignmentlengths,
(3) standard deviations of vent centers from a best-fit line (Fig. 6a),
(4) numbers of elongate vents (>1.2 ratio between the lengths of themaximum and minimum axes; Fig. 6b), (5) standard deviations of the
trend of elongate vent long axes from the best-fit line trend (Fig. 6a),
Fig. 3. Oblique (a) LIDAR digital elevation model (4 m resolution; Csatho et al., 2005) and (b) aerial photograph of a basaltic vent alignment mapped on the Mount Morning shield
volcano by using cleft and elongate cones as a guide. The long axes of the cleft cones (CC), elongate cones (EC), and slightly elongate cones (SEC) mark the trend of the subsurface
feederdike,and their alignmentalongthe long axis trend ofeach other suggests that they collectively erupted from thesame feederdike.The alignmentis ~6 kmlong. Thecleftcone
in the foreground is .8 km long.
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and (6) average vent spacing distances (Fig. 6a). Map resolutions did
not permit us to assess vent shapes along the vent alignment on the
Makushin volcano or for the majority of the smaller vents that
comprise the vent alignments along the Laki fissure. The results of our
analyses are provided in Table 1.
Our morphometric analyses show three important results about
vent alignments. First, best-fit lines determined by Deming regression
analyses (i.e., orthogonal linear regression; Deming, 1943) of vent
center points indicate that all of the vent alignments studied have low
standard deviation distance, with the majority (20 of 23 alignments)
Fig. 4. Volcanic vent alignments along the (a) the Laki fissure, Iceland, and (b) the Lunar Craters vent field, Nevada, that were used to characterize the morphometric parameters of
alignments in platform vent fields. All vents shown along the Laki fissure are included within the nine alignments. Only black vents are included in the vent alignments in the Lunar
Craters vent field. Gray vents in the Lunar Craters vent field are excluded from the vent alignments because they do not lie close to and along trend of fissure ridges, cleft cones, or
elongate vent long axes. Individualfi
ssures along the Lakifi
ssure alignment progressively propagated and formed from southwest to northeast from 1783 to 1785. We utilized ventalignments that had been defined by previous authors along the Laki fissure (Thordarson and Self, 1993). Thordarson and Self (1993) outline 10 separate fissures. Fissures 4 and 5 of
Thordarson and Self (1993) spatially overlap and are treated as one alignment (4 on the map) in this study. Maps modi fied from Thordarson and Self (1993) and Scott and Trask
(1971).
Table 1
Morphometric parameters of monogenetic vent alignments.
Location age Setting Alignment
ID
Rock
type
Length
(km)
# vents # elongate
vents
Standard deviation
best-fit line
distance (m)
Standard angular
deviation vent
long axes ()
Average vent
spacing distance
(m)
Alignment
azimuth
()
Average vent
long axis
azimuth ()
Laki Fissure,
IS Quaternary(17831785)
Platform
field
1 B 1.1 13 1 31 1 93/84b 042 041
2 B 1.6 6 1 139 7 318/238b
034 0413 B 4.4 28 8 37 10 162/146b 038 041
4a B 4.8 62 4 31 20 85/74b 054 041
5 B 4.3 53 5 35 11 82/77b 038 033
6 B 3.5 40 4 60 13 89/82b 038 032
7 B 3.0 29 4 36 11 106/78b 039 035
8 B 1.2 8 1 49 1 172/124b 040 041
9 B 1.5 8 1 37 4 154/134b 037 041
Overall B 27.0 247 29 100 18 107/104b 041 038
Lunar Craters, NV
PliocenePleistocene
Platform
field
1 B 7.7 4 3 32 3 2138/579b 040 039
2 B 11.9 4 4 32 10 4000/649b 027 032
3 B 10.9 6 5 94 27 1278/851b 033 019
4 B 10.0 12 9 86 10 513/432b 027 023
5 B 8.2 4 4 74 10 2104/1811b 029 034
6 B 8.7 7 7 125 22 1364/1175b 027 048
7 B 12.6 9 5 49 9 1344/527b 031 029
8 B 8.3 8 7 86 18 2490/880b 027 043
9 B 11.0 14 12 62 21 846/708b 033 032
10 B 3.5 4 4 143 19 990/859b 045 025
11 B 14.2 14 8 181 19 1043/865b 031 025
Kohala Rift, HI
Quaternary
Polygenetic
field
1 B 4.8 15 10 52 13 729/488b 323 332
2 B 2.1 6 5 65 14 684/492b 336 329
Makushin, AK
Quaternary
Polygenetic
field
1 B, A 6.6 12 ?c 85 NA 558/474b 290 NA
A: andesite; B: basalt; NA: not available.a Alignment 4 is comprised of vents created during fissure eruptions 4 and 5 ofThordarson and Self (1993).b Average distance when largest vent spacing distance not included in calculation.c Number of elongate vents unknown.
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having a standard deviation distance125m. This holds regardless of
alignment length, which ranges from 1.1 to 14.2 km and averages
6 km. The low standard deviation distance of vents from their
alignment's best-fit line is consistent with the relatively narrow
widths of feeder dikes (typically a few meters and rarely in excess of
tens of meters) (MacDonald, 1972; Delaney and Pollard, 1982;Opheim and Gudmundsson, 1989; Rubin, 1995). This shows that
monogenetic vents should tightly conform to straight lines if an
alignment has been produced by a single feeding fissure.
Second, elongate vents are common along vent alignments,
typically have average long axis trends that are subparallel (10)
to an alignment's best-fit line and the long axis trends of individual
elongate vents show
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average vent spacing distances in platformfields are caused, in several
instances, by one anomalously distant vent along an alignment, which
produces a relatively high average even though most vents along the
alignment have closer spacing distances. For example, in the Lunar
Craters platform field (e.g., alignments 1, 2, and 8), eliminating the
largest vent spacing alongthe alignments produces a marked decrease
in vent spacing distance (from ~2100
4000 m to
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in the Mount Morning vent field (Fig. 8d). The dominant SE and NE
trend of the long axes offissure ridges, cleft cones, and elongate cones
(Figs. 7e and 8c) substantiates the SE and NE alignment trends in the
San Francisco and Mount Morning vent fields, respectively. Alignment
A2 in the San Francisco vent field is further substantiated by a NWSEline of fumarolesand redoxidized ashthat occursalongthe northwest
portion of the alignment (Colton, 1937).
As an example of the utility of the method, we show a traditional
alignment analysis based on visually selecting alignments from the
center points of vents mapped from the DEM and previous geologic
mapping (Moore and Wolfe, 1987) (Figs. 7b and c). This visual
alignment analysis yields eight vent alignments forming NWSE, NSand EW alignment sets (Fig. 7c). The quality of each of these
alignments could be assessed by considering the numbers of vents
Fig. 7. (a)Digitalelevationmodelof volcanicvents(mainlybasalticcinder cones)within a portion ofthe platformSan Franciscoventfieldin Arizona (from http://seamless.usgs.gov/).
(b) Map of the center point location of 39 vents in a portion of the San Francisco volcanic field, after mapping by Moore and Wolfe (1987). (c) Eight volcanic alignments visually
selected by examination of vent center point locations shown in (b). (d) Map of cone rims and traces offissure ridges based in part on the previous mapping by Moore and Wolfe
(1987). Note theSE elongate shapeof many ofthe cinderconesandfissureridgesin thearea. (e)Map ofbest-fit ellipses drawnto matchthe cinderconerims.Rosediagramof thelong
axes offissure ridges (n =7), cleft cones (n =3), and elongate cones (n =16). (f) Vent alignments mapped using vent location and shape data. F = fissure ridge; CC = cleft cone.
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and the standard deviation of a best-fit line (e.g., Suter, 1991; Suter
et al., 1992) or by statistical methods (e.g. Wadge and Cross, 1988;
Connoret al., 1992), but this would not revealwhichtrendmore likely
represents the trace of a subsurface feeder dike. The visual method
ignores the key information provided by the elongated shapes of the
vents (Fig. 7d). By using the elongate vents to define alignments, the
apparent NS and EW alignments are ruled out, and a consistent SE
alignment trend is mapped (Fig. 7f), more compatible with a singlegeodynamic model.
4. Assessing the reliability of vent alignments
Assessing the reliability of vent alignment data is desirable because
it indicates the confidence level that an alignment marks a subsurface
dike. It also permits the comparison of stress data derived from
alignments of similar reliability. We are aware of only two previous
stress studies in which the quality of vent alignment data is
considered. Suter (1991) and Suter et al. (1992) assessed vent
alignment quality (A>B>C>D) based on the number of vents that
comprised a given alignment and the standard deviation of the vent
centers from a best-fit line. In Suter's assessment system, alignments
with A and B quality grades were required to have 5 and 4 vents,respectively. Alignments with standard deviations of vent centers
from best-fit lines >750 m and 2250 m were given a penalty of three grades. Our character-
ization of vent alignments indicates that these standard deviation
thresholds from best-fit lines are too large for meaningful classifica-
tion of individual fissure-controlled vent alignments. Instead, Suter's
system applies to regional alignments that must be formed by
separate feeders. We therefore developed a new assessment system
that classifies individual volcanic alignments in four reliability grades(A>B>C>D) based on the results of our morphometric analysis
of alignments (Table 2). This assessment system considers the fol-
lowing alignment characteristics: (1) numbers of vents, (2) standard
deviations of vent centers from a best-fit line, (3) elongate vent
evaluation, including numbers of elongate vents, their degree of
elongation (index of elongation), and standard deviations of the trend
of elongate vent long axes from the trend of the best-fit line, and (4)
average vent spacing distances. Although we established the
morphometric attributes of very well-defined vent alignments, we
cannot use actual measurements from possible or unreliable
alignments, which by definition have a low confidence of marking a
feeder dike. Therefore, the lower reliability thresholds that define
grades B, C, and D are defined as progressively lower steps from the
thresholds that define A-grade alignments. Higher gradings representa higher confidence that an alignment marks the subsurface trace of a
feeder dike.
Fig. 8. (a)Digital elevationmodelof basalticcinderconefieldon thepolygenetic Mount Morningvolcano in Antarctica (Csathoet al., 2005).(b)Mapof conerims and tracesoffissure
ridges. Note the NE elongate shape of many of the cinder cones and fissure ridges in the area. (c) Map of best-fit ellipses drawn to match the cinder cone rims mapped in the area.
Rose diagram of the long axes offissure ridges (n =4), cleft cones (n =9), and elongate cones (n =17). (d) Vent alignments mapped using vent location and shape data. F = fissure
ridge; CC = cleft cone.
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4.1. Number of vents
Vent alignments with higher numbers of vents are most clearly
defined and are assigned a high reliability grade (Table 2). All vents,
including those that are considered as possible or unreliable in
confidence for vent certainty or shape certainty, are included in the
total number of vents for each alignment. Alignments with elongate
vents have threshold vent number requirements of A4, B3, and C
and D2, whereas alignments with only circular vents have more
stringent requirements of A5, B4, and C and D3.
4.2. Standard deviations of vent centers from a best-fit line
Vent alignments with low standard deviations in vent position
from a best-fit line achieve a high reliability grade because they better
conform to straight lines (Fig. 6a; Table 2). We have therefore defined
threshold values for best-fit line standard deviations of A125 m,
B150 m, C175 m, and D>175 m for alignments with elongate
vents. All vents, including those that are considered as possible or
unreliable in confidence for vent certainty or shape certainty, are
included in the calculation for a best-fit line using the vent center
points (determined from the best-fit ellipses). The best-fit line and its
standard deviation are calculated by conducting a Deming regression
analysis (i.e., orthogonal linear regression) (Fig. 6a) (Deming, 1943).
4.3. Elongate vents
Vent alignments with high numbers of elongate vents, especially
highly elongate vents (Table 2; index of vent elongation criteria)
achieve a high reliability grade because elongate vents representindependent indicators of subsurface dike orientation. Only fissure
ridges, cleft cones, and elongate cones with definite and probable
confidence for vent and shape certainty are considered in the
elongation index criteria for reliability assessment. Using vents with
possible or unreliable confidences could lead to higher reliability
grades than justified given the uncertainties. A particular reliability
grade can be achieved by a few vents that are more elongate or higher
numbers of vents that are less elongate. For example, A-grade align-
ments with elongate vents are required to have an elongation index of
at least one cleft cone, one fissure ridge, or two clearly elongate vents.
Lower reliability grades have progressively less stringent elongation
index requirements.
Vent alignments with low angular standard deviations of vent long
axesfromthe trend of the best-fit line (Fig. 6a; Table 2) achieve a highreliability grade. A-grade alignments are therefore required to have
standard deviations 30, whereas alignments with lower grades
have progressively greater threshold values (B
35, C
40, andD> 40). As with theelongation index criteria, onlyfissure ridges, cleft
cones, and elongate vents with a definite or probable confidence for
vent and shape certainties are used for reliability grading. At this
stage, vent elongation directions should also be inspected to
determine whether differences in the vent elongation directions
with respect to the alignment direction are random or systematic. A
systematic deviation may provide useful tectonic data, since dikes can
be intruded in en echelon patterns (Delaney et al., 1986; Rubin, 1995),
potentially forming vent alignments with en echelon elongate vent
long axes.
4.4. Vent spacing distances
Although elongate vents are common within volcanicfields, not all
alignments will have elongate vents. Alignments without elongate
vents require separate reliability assessment criteria (Table 2). To be
graded equally with alignments that contain elongate vents, they
must meet a more stringent best-fit line standard deviation distance
criteria (A100 m, B125 m, C150 m, and D>150 m), and an
additional vent spacing distance criterion. For reasons outlined earlier,
cinder cones have modal average vent spacing distances on
polygenetic volcanoes that range from 600 m to 800 m, and on
platform fields that range from 1000 m to 1200 m (Settle, 1979). We
have therefore defined threshold average vent spacing distances of A
and B600 m, C800 m, and D800 m for vent alignments on the
flanks of polygenetic volcanoes, and A and B800 m, C1000 m, and
D1000 m for vent alignments in platform fields.
4.5. Application of alignment reliability assessment system
Applying our alignment reliability assessment system to the vent
alignments we mapped in the San Francisco and Mount Morning
vent fields identifies: (1) three A-grade alignments (A1A3), and one
C-grade alignment (C1) in the San Francisco vent field, and (2) four
A-grade alignments (A4A7), one B-grade alignment (B1), and two
C-grade alignments (C2 and C3) in the Mount Morning vent field
(Figs. 7f and 8d; Table 3).
Defining reliability grades during an iterative process of alignment
definition allows alignments with realistic characteristics, and higher
quality alignments, to be selected for the final analysis and derivation
of a stress datum. For example, at first glance, it might be tempting to
extrapolate alignment A2 in the San Francisco vent field such that it
includes the two vents that comprise alignment C1, rather than thenorthwest fissure ridge and cone that lie along the southeast portion
of alignment A2 as shown in Fig. 7f. Statistical analysis of such an
Table 2
Reliability assessment system for vent alignments.
Reliability
grade
# vents Sta nda rd deviat ion best-fit
line distance (m)
Index of vent
elongation
Standard angular deviation
vent long axes ()
Average vent spacing
distance (m)
A 4 125 1 cleft cone -or- 30 No limit
1 fissure ridge -or-
21.6 -or-11.6 and 11.4
5 100 No shape data No shape data 600a or 800b
B 3 150 11.6 -or- 35 No limit
21.4 -or-
11.5 and 21.2
4 125 No shape data No shape data 600a or 800b
C 2 175 11.4 -or- 40 No limit
21.2
3 150 No shape data No shape data 800a or 1000b
D 2 >175 11.2 >40 No limit
3 >150 No shape data No shape data >800a or >1000b
See Fig. 6 for definition of parameters.a For vents on the flanks of polygenetic volcanoes.b For vents within platform fields.
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alignment results in an increased standard deviation of a best-fi
t linefrom 108 m to 268 m and, consequently, a D quality grade. Although
relatively high standard deviationscould occur in cases where fissures
have curved traces, the lower standard deviation of alignment A2 as
shown in Fig. 7f substantiates our mapping, which is based on the
shapes of the fissure ridges and elongate cones in the alignment. Two,
separate alignments (A2 and C1, Fig. 7f) are therefore indicated in this
example.
5. Reliability-assessed volcanic alignments as stress data
The 2008 World Stress Map quality-ranking system for a stress
datum derived from volcanic vent alignment data is based on the
numbers of alignments and their degree of parallelism (evaluated by
their standard deviation), but this ranking system does not consider
the actual reliability of each alignment used to produce a particular
stress datum (Heidbach et al., 2008). For example, according to the
2008 World Stress Map quality-ranking system, an A-ranked stress
datum could be derived from5 alignments, just as long as they have
a standard deviation 12, without knowledge of the reliability of
each alignment used (i.e.,they could all achieve a D reliability grade in
our assessment system). It goes without saying that knowledge of
data quality lends higher or lower confidence to stress interpretations
based on vent alignment data. We therefore propose a simple and
effective method for synthesizing our new vent alignment reliability
assessment system with the 2008 World Stress Map quality-ranking
system for a stress datum. To incorporate alignment reliability in the
quality-ranking system for a stress direction derived from volcanic
alignment data, each stressdatum quality rank must have a minimumof one alignmentwith an equivalent reliability grade. For example, for
a stress datum to achieve an A quality rank, it must have 5
alignments (standard deviation12) with 1 alignment with an A
reliability grade. Although an A-ranked stress datum could include
four other alignments with C reliability grades, the parallelism of
these four alignments with at least one alignment of a high A
reliability grade, as measured by the low standard deviation (12)
requirement for an A-ranked stress datum, lends higher confidence in
the stress datum. Similarly, a B-ranked stress datum is required to
have 3 alignments (standard deviation20) with 1 alignment
with a B reliability grade, a C-ranked stress datum is required to
have1 alignment with a C reliability grade, and a D-ranked stress
datum is required to have 1 alignment with a D reliability grade.
Unlike the current World Stress Map C quality rank, a minimum of 5vents are not required if elongate vents are present in the alignment
(see Table 2 for reliability grading parameters).
In the Mount Morning ventfi
eld, the NNE to NE vent alignments,fissure ridges, cleft cones, and elongate cones trend at a high angle to
contours on the volcano flanks, which suggests that the effects of the
topographic slope of the volcano on the orientations of fissure
eruptions were limited (Paulsen and Wilson, 2009). Considering all of
the vent alignments on Mount Morning, Paulsen and Wilson (2009)
determined that the alignments do not show a radial pattern around
the central edifice, indicating their orientations are likely primarily
controlled a regional stress field, rather than an isotropic stress field
due, for example, to the hydrostatic effects of the central magma
chamber (Nakamura, 1977; Nakamura et al., 1977). An average of the
azimuths of the six NE alignments of A, B, and C alignment reliability
grades yields a 039 average direction (15 standard deviation), which
is similar to the 031 SH direction (A quality rank) determined from a
greater number of vent alignments from a larger area around the
Mount Morning volcano (Paulsen and Wilson, 2009). If the 039
average direction determined herein were to be treated as a stress
datum, it would achieve a B-quality rank according to both our
quality-ranking scheme and that of the 2008 World Stress Map
Project (Heidbach et al., 2008) because the azimuth standard
deviation exceeds 12.
Our proposed system produces quality ranked stress data for the
San Francisco and Lunar Craters vent fields with improved reliability
compared with stress data listed for these areas in the 2008 World
StressMap database. In the San Francisco vent field shown in Fig. 7, an
average of the azimuths of the four SE alignments, with three A and
one C reliability grades, yields a 115 maximum horizontal stress (SH)
direction (11 standard deviation), which is similar to the contem-
porary 120 SH direction interpreted by Zoback and Zoback (1980) for
the same region. Our San Francisco stress datum achieves a B-qualityrank according to our new system. In the 2008 World Stress Map
database, the stress datum from this same region is assigned an B
quality rank (Heidbach et al., 2008),however, there is no record of the
number of alignments or standard deviation of their azimuths in the
source reference (Zoback and Zoback, 1980), making the reliability of
this ranking questionable. All eleven of the alignments that we
analyzed in the Lunar Craters vent field (Fig. 4b) achieved an A
alignment reliability grade and their average 032 trend (6 standard
deviation) achieves an A quality stress datum rank according to our
scheme and the World Stress Map quality-ranking system (Heidbach
et al., 2008). Again, this is the same quality rank given to the 030 SHdirection reported for the Lunar Craters area in the 2008 World Stress
Map database (Heidbach et al., 2008), yet no supporting alignment
number or azimuth data are provided to substantiate this ranking.Adopting our new hybrid stress ranking system would lend higher
confidence to stress data derived from vent alignments.
Table 3
Mount Morning and San Francisco volcanic field vent alignments.
Alignment
grade/ID#
Rock
type
Length
(km)
# vents FR, CC, and EV
axial ratios
Standard deviation best-fit
line distance (m)
Standard angular deviation
vent long axes ()
Average vent spacing
distance (m)
Alignment
azimuth ()
Sunset Peak Cinder Cone Field, San Francisco Volcanic Field, Arizona (Quaternary)
A1 B 9.4 6 3 FR, 1.6, 1.3 71 3 1587 106
A2 B 11.4 8 3 FR, 1.7, 1.5, 1.4 108 7 1493 113A3 B 10.2 8 1 FR, 2 CC, 1.7, 1.2, 1.2 94 3 1547 131
C1 B 1.7 2 1.5, 1.5 NA 3 991 108
Hurricane Ridge Cinder Cone Field, Mount Morning Polygenetic Volcano, Antarctica (Quaternary)
A4 B 5.2 9 3 CC, 1.5, 1.4, 1.3 111 5 827 047
A5 B 2.7 9 FR a, CC, 1.3, 1.3 61 3 322 058
A6 B 5.1 5 CC, 1.7, 1.6, 1.4 66 20 833 047
A7 B 0.6 6 FR, 1.2 10 28 122 161
B1 B 2.8 4 CCa 56 9b 366 034
C2 B 3.7 4 FR a, 1.5 21 8 1233 033
C3 B 3.3 4 1.7, 1.5 62 45 645 016
See Fig. 6 for definition of parameters. B: basalt; CC: cleft cone; FR: fissure ridge; EV: elongate vent; NA: not applicable.a Fissure ridge, cleft cone, or elongate vent not included because of possible or unreliable vent or shape certainty.b Angular deviation vent long axis calculated with vent of possible shape certainty.
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6. Elongate vents as stress data
Volcanic alignments and dikes are the only two volcanic indicators
of contemporary stress directions used by the 2008 World Stress Map
Project (see www.world-stress-map.org) (Heidbach et al., 2008).
Volcanic alignments are used as stress indicators in the World Stress
Map Project in lieu of direct measurements of dike trend because theyprovide an indirect means to assess the trend of subsurface dikes.
Elongate volcanic vents also provide an indication of local subsurface
dike trends (Breed, 1964; Nakamura, 1977; Tibaldi, 1995; Korme
et al., 1997), but are underutilized as stress direction indicators, even
though they have lengths on the order of hundreds of meters and in
some cases up to several kilometers, and thus record subsurface dike
orientation over considerable distances of the crust. The utility of vent
elongation for stress direction is well illustrated by comparing SHdirections derived from vent long axes and alignments in the San
Francisco, Mount Morning, and Lunar Craters vent fields. The average
orientations of all the long axes of elongate vents in the San Francisco
vent field yields a 110 SH direction (18 standard deviation), whereas
fissure ridges and cleft cones show an average 120 direction (13
standard deviation); both results are strikingly similar to the 115 SHdirection indicated by all of the vent alignments that we mapped
(Fig. 9). Likewise,the average of the orientationsof all of the long axes
of elongate vents with a definite to probable vent and shape certainty
in the Mount Morning vent field suggests a 025 SH direction (39
standard deviation) and fissure ridges and cleft cones show an
average 030 SH direction (24 standard deviation). Again, both
results are similar to the 039 SH direction indicated by vent
alignments on Hurricane Ridge (Fig. 9) and are similar to the 031
SH direction (A quality rank) determined by Paulsen and Wilson
(2009) for the Mount Morning volcano. Finally, the average of the
orientations of all of the long axes of elongate vents in the Lunar
Craters vent field indicates a 027 SH direction (25 standard
deviation) and fissure ridges and cleft cones show an average 035SH direction (14 standard deviation). Both results are also strikingly
similar to the 032 SH direction indicated by the vent alignments that
we mapped in the Lunar Craters vent field (Fig. 9).
Our results indicate that elongate vents should also be used to
calculate stressdirections. Using elongate vents is particularlyattractive
because they do not require the definition of alignments and yet
potentially offer a quick and efficient means of obtaining stress data
from volcanic fields that have been mapped or imaged at appropriate
topographic or geologic resolution. Our results from the San Francisco,
Mount Morning, and Lunar Craters ventfields indicate that the average
orientation of all elongate vents with a definite to probable vent and
shape certainty in a field (numbers of vents range from 26 to 75) will
have standard deviations that are higher than standard deviations for
alignments in the same region, but are typically 1.4 and 20% of vents with the largest
magnitude deviations removed) requires the same standard deviation
thresholds. Using these criteria, cleft cones and fissure ridges in the
Mount Morning (9 vents), Lunar Craters (30 vents), and San Francisco
(8 vents) ventfields yield a 038 SH direction (9 standard deviation), a
034 SH direction (8 standard deviation), and a 115 SH direction (9
standard deviation) respectively. All of these directions are 2 from
the SH directions indicated by vent alignments and achieve an A quality
stress datum ranking. Applying these criteria to the elongate vents with
definite and probable confidence for vent and shape certainty, the
Mount Morning (16 vents), Lunar Craters (48 vents), and San Francisco(16 vents) vent fields yield a 027 SH direction (21 standard deviation),
a 030 SH direction (10 standard deviation), and a 112 SH direction
(10 standard deviation) respectively. The directions for the Lunar
Craters and San Francisco vent fields achieve an A quality ranking and
are 3 from the SH directions indicated by vent alignments in these
areas. The direction for the Mount Morning volcano achieves a C quality
ranking because of the relatively high standard deviation. This direction
is 12 from the SH direction indicated by vent alignments on Hurricane
Ridge, but is only 4 from the SH direction indicated by a greater
number of vent alignments from a larger area around the Mount
Morning volcano (Paulsen and Wilson, 2009).
7. Conclusion
Elongate vents are common in volcanic fields and should be
considered when defining vent alignments because they represent
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Fig. 9. Effect of removing 5%, 10%, 15%, and 20% of the vent long axis directions with the largest magnitude deviation (LDR) from the average vent long axis direction. This noise
reduction technique results in an average vent long axis direction that approaches the average vent alignment direction (SH direction), while also decreasing the standard deviation
of vent long axes.
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independent indicators of subsurface dike trends. We propose a
system for defining and assessing the reliability of volcanic vent
alignments based on quantifiable parameters such as the number,
shape,and spacing distanceof vents,and theirdegree of alignmentand
uniformity in elongation direction. We propose a modified quality-
ranking scheme for vent alignments that incorporates the reliability of
each alignmentused to define a stress datum.We provide quantitativeevidence that elongate ventsare also reliablestress indicators, without
the need to define vent alignments, and propose a quality-ranking
scheme that can be incorporated in the World Stress Map system.
Utilization of our proposed methods lends higher confidence to
interpretations based on vent alignment data and, if adopted by a
wider community, would permit a more meaningful comparison of
vent alignment data within and amongst volcanic fields.
Acknowledgments
This work was funded by NSF grant OPP-990970 to T. Wilson and
NSF grant OPP-9910879 and University of Wisconsin Oshkosh Faculty
Development Program sabbatical grants to T. Paulsen. We thank
William Bosworth and John Reinecker for the helpful critiques thatimproved this manuscript. We also thank Bea Csatho for providing the
LIDAR dataof theMountMorning area, Paul Morin (Antarctic Geospatial
Information Center) for helping produce Fig. 2d, Yaron Felus for support
in the field and lab aspects of this research, Peter Braddock for thefield
assistance, PHI Helicopters for providing us with excellent support
during our vent mapping, and Rick Allmendinger for providing his
stereonet program. Yaron Felus wrote the best-fit ellipse program for
Arcview. Christie Demosthenous provided reviews that clarified drafts
of this manuscript.
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