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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.

17T.S. Paulsen, T.J. Wilson / Tectonophysics 482 (2010) 1628


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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.

18 T.S. Paulsen, T.J. Wilson / Tectonophysics 482 (2010) 1628


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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


C 2 175 11.4 -or- 40 No limit

21.2


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.



14/14


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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