GSA Bulletin: Physical Processes of Shallow Mafic Dike Emplacement

Physical processes of shallow mafic dike emplacement near the San Rafael Swell, Utah

Paul T. Delaney* U.S. Geological Survey, 2255 North Gemini Drive, Flagstaff, Arizona 86001

Anne E. Gartner† U.S. Geological Survey, 345 Middlefield Road, Menlo Park, California 94025

ABSTRACT crustal extension during the magmatic interval relieved compressive stresses localized by intrusion. Some 200 shonkinite dikes, sills, and breccia bodies on the western Colorado Plateau of south-central Utah were intruded from ap- INTRODUCTION proximately 3.7 to 4.6 Ma, contemporaneous with mafic volcanism along the nearby plateau margin. Thicknesses of dikes range to about A Pliocene dike swarm, almost 60 km long and nowhere more than 30 6 m; the log-normal mean thickness is 85 cm. Despite the excellent ex- km wide, is exceptionally well exposed on the western Colorado Plateau posures of essentially all dikes in strata of the Jurassic San Rafael (Figs. 1 and 2). The dikes are mostly less than 1 m thick and have almost Group, their number is indeterminate from their outcrop and spac- 300 km of outcrop within nearly flat-lying clastic and fine-grained strata. ing because they are everywhere greatly segmented. By our grouping Plug-like bodies, or necks, formed along many dikes and usually contain of almost 2000 dike segments, most dikes are less than 2 km in out- breccias that reflect their mode of development. Together, they fed some crop length; the longest is 9 km. Because the San Rafael magmas were sills and, probably, some eruptive rocks now removed by no more than primitive and probably ascended directly from the mantle, dike about 2 km of erosion. The intrusions likely exemplify the shallow subsur- lengths in outcrop are much less than their heights. The present ex- face beneath volcanic fields of mafic maars, cinder cones, and small-vol- posures probably lie along the irregular upper peripheries of dikes ume lava flows, such as are common throughout western North America. that lengthen and merge with depth. Orientations of steps on dike This paper summarizes observations and measurements collected to contacts record local directions of dike-fracture propagation; about constrain some physical processes of mafic dike emplacement in a setting half of the measurements plunge less than 30°, showing that lateral of relatively simple igneous and host-rock geology. We report on length, propagation at dike peripheries is as important as the vertical propa- thickness, strike, and dip of dikes and on the character and strikes of joints gation ultimately responsible for ascent. The San Rafael dikes, now in adjacent strata of the San Rafael Group and the Navajo Sandstone of exposed after erosion of about 0.5–1.5 km, appear to thicken and the underlying Glen Canyon Group. We also report on directions of dike- shorten upward, probably because near-surface vesiculation en- fracture propagation. These measurements characterize the means of hanced magmatic driving pressures. Propagation likely ceased soon magma ascent and the state of regional stress and ongoing crustal exten- after the first dike segments began to feed nearby sills or vented to ini- sion during the magmatic interval, which lasted about 1 m.y. tiate small-volume eruptions. Among the modes of igneous intrusion, dikes are perhaps the best un- Most of the dikes are exposed in clastic strata of the Jurassic San derstood from a theoretical perspective. Many aspects of the San Rafael Rafael Group. They probably acquired their strikes, however, while dikes seem to confound theory, however, primarily by displaying attrib- ascending along well-developed joints in massive sandstones of the utes seemingly obtained from underlying units and by revealing only underlying Glen Canyon Group. Rotation of far-field stresses during hints of their complex three-dimensional forms and propagation paths. the emplacement interval cannot account for disparate strikes of the The dikes are also of interest for the volcanic processes recorded by the dikes, which vary through 110°, most lying between north and breccia bodies, and the sills for in situ differentiation of shonkinite as re- N25°W. Rather, the two regional horizontal principal stresses were vealed by the syenites localized within; both are of interest for pervasive probably nearly equal, and so the dominant N75°E direction of dike hydrothermal alteration of the host and wall rocks. opening was not strongly favored. Across the center of the swarm, about 10 to 15 dikes overlap and produce 15–20 m of dilation. Many GEOLOGY are in sufficient proximity that later dikes should be thinner than earlier ones if neither the magma pressures nor regional stresses were Tectonics changing during the emplacement interval. However, dike thicknesses vary systematically neither along the length of the swarm nor The form of the San Rafael dike swarm is irregular but trends slightly in proportion to the number of neighboring dikes. It appears that east of north, roughly parallel with the nearby boundary of the Colorado Plateau and the Basin and Range provinces about 20–50 km to the west (Fig. 1). The swarm lies between the Waterpocket monocline and the an- *e-mail: [email protected] ticlinal San Rafael Swell, although it parallels neither of these Laramide †e-mail: [email protected] folds nor other nearby flexures and faults (Fig. 2). The mean N14°W

GSA Bulletin; September 1997; v. 109; no. 9; p. 1177–1192; 16 figures; 2 tables

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strike of the dikes approximately parallels an inferred N20°W direction of fractures in Precambrian basement of the Colorado Plateau (Davis, 1978); the trend of the northern laccolithic intrusions of the Henry Moun- tains and of the Henry basin to the south-southeast, for example, are aligned along this direction with the younger San Rafael swarm (Fig. 1). The San Rafael intrusions resemble other Tertiary alkaline mafic rocks that crop out in sparse, widely spaced groups along the western margin of the North American craton. Such rocks are locally exposed along the transition zone between the Colorado Plateau and Basin and Range provinces (Thompson and Zoback, 1979; Kempton et al., 1991) and were discussed by Tingey et al. (1991); the nearest, the minettes and melanephelinites of the Wasatch Plateau, are about 40–80 km north of the San Rafael swarm (Fig. 1). The Colorado Plateau margin has been a locus of volcanism since the Tertiary Period. The San Rafael swarm is at the eastern limit of a broad zone of basaltic volcanism that crosses to the plateau from the Basin and Range Province of southern Utah (Fig. 1). Although this volcanism dates back to middle Miocene time, most is of Pliocene and Qua- ternary age, including the alkalic and tholeiitic basaltic rocks of the adjacent high plateaus (Nelson, 1989; Mattox, 1991, 1994). Judging from the primitive nature of the shonkinites, they probably ascended directly from a source region in the mantle. No geophysical anomaly suggestive of a crustal magma reservoir has been identified near the San Rafael swarm. The swarm lies on the flanks of an elongate re- Figure 1. San Rafael shonkinite dike swarm shown in relation to gional aeromagnetic high and a positive Bouger-gravity anomaly identi- other melanocratic rocks of the western Colorado Plateau margin; fied from locally sparse data (Zietz et al., 1976; Cook et al., 1989). The the Wasatch Plateau swarm is the closest. Also shown are the Henry nearby aeromagnetic high extends northeasterly from the Waterpocket Mountains and the zone of Tertiary and Quaternary volcanism along monocline to the San Rafael anticline; the gravity anomaly is centered the margin of the Colorado Plateau (after Kempton et al., 1991; over the San Rafael anticline. Tingey et al., 1991; S. Nelson, 1996, personal commun.). Plateau uplift was waning during dike emplacement at about 4 Ma (Thompson and Zoback, 1979) and much of the post-Mesozoic strata was already stripped by erosion. Dikes at 2200–2600 m elevations on the west inites is typically chloritic, and calcite and zeolites, mostly thomsonite, side of the San Rafael swarm are within 6 km of trachybasalt flows of occur as veins, fillings of abundant vesicular and amygdaloidal cavities, similar age and composition at elevations above 3000 m (Nelson, 1989). and replacements of phenocrysts. From intergrowths and textural rela- Dikes occur as much as 30 km east of the these lavas, at elevations as low tions of analcite, which generally composes 3%–4% of modal abun- as 1500 m. Although no paleotopographic reconstruction is available, dances, Gilluly (1927) concluded that it is a primary mineral. Contact modern exposures probably correspond to no more than about 2 km of metamorphism and alteration of wall rocks occurs locally along many emplacement depth, consistent with the probable stratigraphic thick- dikes and is pervasive around the sills. nesses of overlying units (Smith et al., 1963). About 45 dikes contain abundant breccias of admixed shonkinite and comminuted host rock (Gartner and Delaney, 1988). In most instances, Igneous Rocks brecciation was accompanied by wall-rock erosion, leading to local widening of dikes during magma flow. Although the breccia bodies prob- The dike rocks are dark gray, locally porphyritic, microshonkinites and ably merged upward to volcanic necks, now removed by erosion, no un- alkali diabases containing clinopyroxene, biotite, sanidine, olivine, am- ambiguous scoria, tephra, agglutinate, or tuffaceous facies of the shonk- phibole, plagioclase, and magnetite (Gilluly, 1927; Williams, 1983). SiO2 inites were identified. ranges from 44 to 48 wt%, total alkalies range from 5.2 to 7.2 wt%, and magnesium numbers range from 0.72 to 0.75. In the total alkali-silica Age of Intrusion classification for volcanic rocks of the International Union of Geological Sciences (Le Bas et al., 1986), they correspond to trachybasalts and We used K-Ar methods to determine the 4 Ma age of the swarm (Ta- basanites. Like other primitive alkaline rocks along the western margin of bles 1 and 2). Seven samples collected from four dikes, a breccia body, the North American craton, the San Rafael magmas probably originated and a sill yielded ages ranging from 3.4 ± 0.2 to 4.7 ± 0.3 Ma. Ages rang- in a mantle region of low partial melt and did not fractionate much during ing from 3.8 ± 0.2 to 6.4 ± 0.4 Ma were determined from four trachy- ascent (Tingey et al., 1991). basalt and basaltic andesite flows at higher elevations west of the swarm Because of the field relations and similar compositions of the San (Fig. 2). Dike emplacement was thus contemporaneous with some nearby Rafael dikes and sills, Gilluly (1927) concluded that they were contem- volcanism. poraneous and comagmatic. Syenites in the sills are present as lenses, Ages of the intrusive rocks fall into two groups; three samples range globules, and veins formed from residual magma during fractional crys- from 3.4 ± 0.2 to 3.8 ± 0.2 Ma, and four samples range from 4.6 ± 0.2 to tallization of the shonkinitic liquid, perhaps by development of silicate- 4.7 ± 0.3 Ma. The youngest radiometric age, 3.4 ± 0.2 Ma, was obtained liquid immiscibility (Williams, 1983). There are about 12 sills, none of from a sample (SAL-2) collected from the same dike as another sample which is thicker than 30 m. (SAL-1A) with an age of 3.8 ± 0.2 Ma. Within the analytic uncertainty of Hydrothermal alteration is pervasive. The groundmass of the shonk- our modest sampling, magmatism may have been confined to only two

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TABLE 1. K-AR RADIOMETRIC AGES OF SHONKINITE DIKES TABLE 2. K-AR AND 40Ar/39Ar RADIOMETRIC AGES 40 40 40 tot OF INTRUSIVES AND LAVAS Sample Latitude N Material K2O Ar* Ar*/ Ar Apparent Longitude W dated (o/o) (mole/g) age (Ma) Sample Latitude N Material Method Apparent Reference FRY-4 111¡05¢07¢¢ Biotite 8.73 5.880 ´ 10Ð11 27.3 4.62 ± 0.15 Longitude W dated age (Ma) 38¡36¢32¢¢ Basalt breccia body 111¡19¢02¢¢ Whole rock K-Ar 3.8 ± 0.2 Delaney et al. (1986) near Cathedral 38¡31¢06¢¢ SAL-4¤ 111¡07¢45¢¢ Biotite 7.93 5.243 ´ 10Ð11 29.3 4.59 ± 0.15 Junction 38¡34¢30¢¢ Basalt flow 111¡28¢06¢¢ Whole rock K-Ar 3.8 ± 0.2 Delaney et al. (1986) SOL-1¤ 111¡15¢14¢¢ Whole rock 2.96 1.995 ´ 10Ð11 29.2 4.68 ± 0.26 near Hogan Pass 38¡35¢57¢¢ 38¡30¢45¢¢ Less olivine 2.97 1.978 ´ 10Ð11 42.5 4.62 ± 0.25 Syenite sill 111¡05¢47¢¢ Biotite K-Ar 4.6 ± 0.2 Delaney et al. (1986) at Table Mountain 38¡32¢38¢¢ SAL-1A¤#111¡14¢12¢¢ Whole rock 3.02 1.652 ´ 10Ð11 25.6 3.80 ± 0.25 38¡30¢25¢¢ Basaltic andesite 111¡28¢42¢¢ Whole rock K-Ar 6.4 ± 0.4 Delaney et al. (1986) from vent on 38¡25¢00¢¢ SAL-2¤# 111¡13¢10¢¢ Whole rock 2.71 1.332 ´ 10Ð11 25.2 3.42 ± 0.23 Thousand Lake 38¡32¢18¢¢ Mountain Note: K-Ar constants: lb = 4.962 ´ 10Ð10 yr Ð1; le + le¢ = 0.581 ´ 10Ð10 yr Ð1; Basalt Dike, IRE-2 111¡06 54 Whole rock 40Ar/39Ar 6.60 ± 0.68 Tingey et al. (1991) 40K/K = 1.167 ´ 10Ð4 mole/mole. ¢ ¢¢ Age analysis by U.S Geological Survey, Menlo Park, California. 38¡37¢58¢¢ ¤ Age analysis by U.S. Geological Survey, Denver, Colorado. 40 39 #Samples collected from the same dike, see intersection h in Figure 9. Basalt Dike, SOL-3 111¡15¢05¢¢ Whole rock Ar/ Ar 5.17 ± 0.38 Tingey et al. (1991) 38¡30¢39¢¢

periods, a little more than a million years apart. Two other samples Thickness yielded 40Ar/39Ar ages of 5.2 ± 0.4 and 6.6 ± 0.7 Ma (Tingey et al., 1991). These determinations, however, lack plateaus in their age spectrums and Thickness generally varies along most dike segments so that they are are not isochronous on inverse-correlation plots (S. Nelson, 1995, per- thickest near their centers and thinnest near their tips. We obtained 287 sonal commun.). measurements from the outcrops of greatest thickness at localities distributed evenly across the swarm. Some segments are locally anomalous Host Strata owing to brecciation and erosive removal of wall rocks (Delaney and Pol- lard, 1981), a nondilational component of intrusive form, or to overlap- The great majority of intrusions are exposed in Middle Jurassic strata ping of adjacent segments (Pollard et al., 1975, 1982). We do not include of the San Rafael Group, consisting of the Carmel Formation, Entrada these among our data. Sandstone, and Curtis and Summerville Formations (Gilluly, 1929; Smith Median dike thickness is 110 cm and ranges from 10 to 650 cm in a et al., 1963). These rocks are mostly nearshore clastic marine deposits, fashion that is not Gaussian, or normally distributed. Some dikes are a dominantly fine-grained sandstones and siltstones commonly cemented few meters thicker than the median, but none can be a few meters thinner. with interstitial calcite. The thickness of this group averages about 550 m. Log-normal distributions seem to fit the thickness measurements reason- A few dikes are exposed in the lowermost strata of the Late Jurassic Mor- ably well (Fig. 3). The log-normal mean of all thickness measurements of rison Formation, which unconformably overlies the San Rafael Group. dikes in the San Rafael Group is 85 cm. The log-normal mean thickness Exposures of intrusions in the San Rafael Group and Morrison Formation of dikes in the Carmel Formation is 104 cm; dikes there are the thickest in are generally good or excellent; we are confident that virtually all dike the swarm and the thickest among these are near its base. Log-normal segments cutting these units were identified in the course of our work. A mean thicknesses of dikes in the Entrada Sandstone and Curtis and Sum- few other dikes, at higher elevations west of the swarm, are exposed in merville Formations are 77 and 70 cm, respectively. the Cretaceous Mancos Shale (Fig. 2; Nelson, 1989); others are undoubtedly hidden beneath the volcanic rocks and young deposits that drape the Length Colorado Plateau margin there. Some dikes are traceable down to the underlying Triassic(?) and Juras- Virtually all dikes consist of numerous segments (Pollard et al., 1975, sic Navajo Sandstone of the Glen Canyon Group. This sandstone uncon- 1982), each separated by host rocks from its neighbors. A total of about formably underlies the Carmel Formation, consists of massive beds of eo- 1950 dike segments, ranging in length from about 25 to 2140 m, can be lian origin, and is about 250 m thick. The Glen Canyon Group is distinguished on the 1:48 000 scale map of the San Rafael swarm (Gart- composed dominantly of massive sandstones and is about 450 m thick. ner and Delaney, 1988), which includes all dikes exposed in the San Difficult access to the Navajo Sandstone and accumulations of sand in the Rafael Group and Morrison Formation and excludes those exposed in the slot canyons left by rapid weathering of the dikes made them difficult to underlying Navajo Sandstone and overlying Mancos Shale. The median examine. Our observations suggest that far fewer dikes are exposed there dike-segment length is 80 m; the log-normal mean is 29 m (Fig. 4a). Al- than in the overlying strata. though we are confident of having found virtually all dike outcrops in the strata of the San Rafael Group, more segments would be distinguished at DIKE FORM larger map scales. Dike segments are not everywhere arranged en echelon. Their arrange- Thicknesses and lengths of the San Rafael dikes scale roughly as ment is so irregular that the number of dikes in the San Rafael swarm is 1:1000, in accordance with the simplest theoretical expressions for dila- indeterminate, both in the number of dikes formed of groupings of seg- tion of pressurized cracks in stressed solids with the elastic moduli for ments and of temporally discrete magma-intrusion events. One of the rocks. More refined expressions that take into account the varied strikes, areas of greatest intrusive density shows more than 250 segments after thickness, and lengths do not improve upon this scaling. compilation at a scale of 1:48 000 (Fig. 5). We grouped these segments

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into 13 dikes. By a similar grouping of segments, the entire San Rafael thicker than short dikes, this relation is not particularly well supported by swarm comprises 174 dikes; the median dike-outcrop length is 1090 m these data. and the log-normal mean is 390 m (Fig. 4b). One dike has 50 segments and several have only one. In spite of—or because of—the excellent ex- Relations Among Thickness, Length, and Strike posures, other workers would likely group the segments somewhat dif- ferently. Dike dilation might display another dependency on regional stresses if there are preexisting planes of weakness, such as joints, to guide dikes Orientation into orientations other than that perpendicular to the direction of least compressive stress and if the differences between the two horizontal prin- Dips of dikes were measured where exposures permitted. The 79 mea- ciple stresses are small, as expected in a province such as the Colorado surements reveal dips typically steeper than 80° (Fig. 6a). Although there Plateau (Thompson and Zoback, 1979). Delaney et al. (1986) presented is no marked preference for easterly or westerly dip directions, those less an expression that must be satisfied, relating the magma pressure to the

than 80° are more commonly directed eastward than westward. The mean minimum and maximum compressive regional stresses Sh and SH, re- dip is 89° westward. spectively, and the clockwise angle a between the normal to the strike of

Strikes of the San Rafael dike segments were measured by their aver- the dike and direction of Sh (Fig. 7b). Under these circumstances, rela- age azimuth and most strike from about N25°W to N0°E (Fig. 6b); the tions among maximum crack thickness, crack length, crack orientation, full range spans 120° of azimuth from N85°W to N35°E. The mean strike and driving pressures are is N14°W, oblique to the trend of the swarm. Taken as a whole, strikes of

the dikes do not differ from those of the segments; there is no preference, Pm > Sa (4) for example, for the segments to be arranged in left- or right-stepping echelon patterns. 1 P - S T = m a L (5) max 2 m (1 - n) Relation Between Thickness and Length

Sa = S – (DS/2)cos 2a, (6) Dikes emplaced in similar settings with similar host rocks and magmas

should, using the simplest principles of two-dimensional linear elastic where S = (SH + Sh)/2 is the mean horizontal stress and DS = SH – Sh is the fracture mechanics, possess a relation between maximum thickness and maximum horizontal stress difference (Delaney et al., 1986). Pm – Sa is length. Dilatant cracks propagate when the fracture toughness Kcrit/I of the difference between magma pressure and mean horizontal regional

the surrounding solid is exceeded by the stress intensity KI at the crack stress. A dike oriented with a = 0° would have a lesser driving pressure, tip (Broek, 1978). A uniformly pressurized crack growing quasistatically Pm – Sh, than one at a = 90°, which would require Pm – SH. If the magma- in an elastic medium (Fig. 7a) maintains a relation among maximum driving pressure is large in comparison to the horizontal stress difference,

thickness Tmax , half-length L, driving pressure Pm – Sh, the difference be- then a dike is able to dilate joints of any strike; if the magma-driving pres- tween magma pressure Pm and the far-field compressive stress acting nor- sure is small in comparison to the stress difference, then only joints of a mal to the crack Sh, and the shear modulus and Poisson’s ratio, m and n, narrow range of strikes would be suitable. respectively. We have The driving pressure Pm – Sa in equations 4–6 varies linearly and symmetrically about the crack midplane such that the driving pressure at the

Pm > Sh (1) crack tip is zero. The horizontal regional stress Sa is resolved from the stresses Sh and SH and the angle a (Fig. 7b). The stress intensity at the Pm - Sh crack tip is zero, K = 0, because the magma flows along a preexisting T = L (2) I max m (1 - n) fracture. Accordingly, the half-length L of the crack is not constrained by the fracture toughness of the host rock (Delaney and Pollard, 1981). K crit K P S L (3) We plot dike strikes as a function of maximum thickness (Fig. 8b) and I = I = ( m - h ) found no significant relation between the two. There do not appear to be (Broek, 1978, chapter 1; Pollard and Segall, 1987). As cracks grow significant relations among thickness, length, and strike to suggest, for crit longer, maintaining KI = KI, they propagate at lower driving pressures, example, that thicker dikes are systematically either longer than others or which is why dike propagation is energetically favorable. It is also favor- more optimally oriented with respect to the regional stresses. able that a crack be oriented perpendicular to the direction of least compressive stress. Log-normal means of dike thicknesses and lengths are RELATIVE AGES OF INTERSECTED DIKES about 1 m and 1 km (Figs. 3 and 4b), respectively. Equations 1–3 predict

driving pressures of Pm – Sh » 5 MPa for dike-aspect ratios of Tmax / L » Dikes of northwesterly and northeasterly strikes cut or deflect each 10–3 and in situ stiffnesses of m/(1 – n) » 5 GPa appropriate for intact sed- other at eight localities (Fig. 9). At two of them (c and h), three intersec- imentary rocks. These estimates, in turn, yield fracture toughnesses of tions exist among four dikes. Rotation of the least compressive stress di- crit –– KI » 150 MPaÖm, far exceeding values measured in the laboratory, as rection during magmatism could cause rotation of strikes of dikes. We discussed by Rubin (1993, 1995), among others. show, however, that their relative ages are not consistent with rotation. Attempting to constrain parameters relating dike thickness and length Mechanical interactions of a later dike intruding near an earlier dike in equations 1–3, we plot lengths of the 85 San Rafael dikes with thick- permit their relative ages to be determined. The simplest interaction re- ness measurements (Fig. 8a). Assuming that , , and Kcrit vary negligi- sults when one dike cuts across the other. This relation is not observed at n m I –– bly among the host rocks, equations 1–3 predict that Tmax µ ÖL for dikes all intersections, however, because of the dikes’ segmented forms. A less emplaced with the dike-tip stress intensity maintained at the critical value simple but equally persuasive interaction is the deflection of a later crack necessary for continued propagation. Although long dikes tend to be caused by the presence of an earlier one (Olson and Pollard, 1989). The

1180 Geological Society of America Bulletin, September 1997

Downloaded from http://pubs.geoscienceworld.org/gsa/gsabulletin/article-pdf/109/9/1177/3382791/i0016-7606-109-9-1177.pdf by guest on 03 October 2021 San EXPLANATION Rafael Swell fault, bar and ball on downthrown side Figure anticline monocline syncline 11b

38û 45' dike sill

6.4 K-Ar age not mapped

0 10 km Figure 11a JTR

Jm Jt Js

Cedar Mtn

not mapped JTR

4.6 Jm

Tvs 4.6

3.9 Figure 12b Tla Js 3.8 3.4 Jm 3.8 4.7 QTb 3.8

38û 30'

JTR Tba Jm Jm

Js Tba

QTb Figure 12a

n 6.4 i Jm l c

n JTR o M

e l Waterpocket Monocline l i

111û 30' 111û 00' Figure 2. Generalized geologic map of the San Rafael area. Host rocks of the San Rafael swarm are the San Rafael Group (Js), the underlying Navajo Sandstone (JTrn) of the Glen Canyon Group, and the overlying Morrison Formation (Jm). Tertiary and Quaternary volcanic rock units of the high plateaus of Utah include Tertiary latite and trachybasalt flows (Tla); Tertiary volcanic sediments (Tvs); Tertiary basaltic andesite (Tba); and Quaternary trachybasalt (QTb). Dikes and sills are shown in red. Axes of the Waterpocket and Caineville monoclines are shown as solid lines. Black circles show sample locations of radiometric ages (after Williams and Hackman, 1972; Gartner and Delaney, 1988; Nelson, 1989).

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deflection is caused both by the presence of a structural inhomogeneity, of 4.6 ± 0.2 Ma (SOL-1 and FRY-4, respectively, Table 1). Thus, dike in- the dike, and by the stresses produced in the host rocks by its intrusion. tersections cannot reflect changes of emplacement conditions during the On the basis of field evidence, intersections at five of the eight locali- million year interval between the two episodes of magmatism. These K- ties (a, b, e, f, and h in Fig. 9) indicate that dikes with northeasterly strikes Ar ages are nowhere inconsistent with determinations of relative ages of are younger than those with northwesterly strikes. The two intersections the intersecting dikes; however, they require that some of the intersections at locality c reveal the opposite sense of relative age. Relative ages of were produced during the 4.6 Ma episode. dikes were indeterminate at the remaining two localities (d and g). At locality c, the relatively older dike has an age of 4.6 ± 0.2 Ma (sample SAL- HOST-ROCK JOINTS AS MAGMA PATHWAYS 4, Table 1), suggesting the younger dike may have been emplaced during the 3.6 Ma magmatic episode. One of the younger, northeasterly striking No simple relations exist among dike thickness, length, and strike (Figs. dikes of locality h has ages of 3.4 ± 0.2 and 3.8 ± 0.2 Ma (SAL-2 and 3, 4, 6, and 8). Moreover, it does not appear that the disparate strikes of the SAL-1A, Table 1), consistent with the northwesterly striking dikes being San Rafael dikes can be explained by rotation of the regional stress field emplaced in the 4.6 Ma episode. Another northeasterly striking dike at lo- during the magmatic interval (Fig. 9). We show that dikes exposed in strata cality h and the relatively younger dike at locality e, however, have an age of the San Rafael Group probably acquired their strikes when magma ascended along joints of the underlying rocks of the Glen Canyon Group.

Dikes and Joints in the San Rafael Group

Strikes of near-vertical host-rock joints in each unit of the San Rafael Group were compared with those of the dikes to test whether magma may have ascended along them. We measured only systematic joints, those vertically continuous across outcrops and part of a set that is horizontally continuous along much of an outcrop. We took measurements throughout

Figure 4. Histograms of lengths of dikes and dike segments in Carmel Formation, Entrada Sandstone, and Curtis and Summerville Formations. Data were compiled at a scale of 1:48 000. (a) Segment- Figure 3. Histograms of dike thicknesses in Carmel Formation, En- outcrop lengths. Also shown is the best-fit relation between length and trada Sandstone, and Curtis and Summerville Formations. Also frequency of occurrence for lengths up to 1.5 km. (b) Dike-outcrop shown are best-fit log-normal distributions. lengths. The best-fit log-normal distribution is also shown.

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the area of the dike swarm to avoid bias toward areas of exceptional ex- lated particular joints of this set. The westernmost dike is different from posure. We also avoided taking measurements within about 50 m of dikes the others, however. From north to south, it rotates from a strike of because joints there can be caused by stresses associated with intrusion N25°W in an area with nearby parallel joints to a strike of N8°W in an of the dike itself (Delaney et al., 1986). area with no such joints. Delaney et al. (1986) suggested that the northern The distribution of strikes of dike segments does not conform to that of section of the westernmost dike probably created its own fracture during the host-rock joints (Fig. 6, b and c). In general, no unit of the San Rafael propagation. Therefore, its strike is probably an excellent indicator of the Group has a distinctly different distribution of joint strikes than the others. normal to the direction of least compressive stress acting there at the time Furthermore, there exists no dominant direction of host-rock jointing; his- of intrusion. tograms of number versus strike show that many joints cluster among di- Rock surfaces in the San Rafael Group are not generally exposed over rections of about N80°–65°W, N40°–20°W, and N25°–55°E. Many of the areas large enough to determine the spatial continuity of joint sets. At one dikes parallel the N40°–20°W cluster of joints, but the distribution of dike strikes is distinctly different than any part of the distribution of host-rock joint strikes. The N14°W mean and N15°W median strike of the dike segments lie within a minimum in the strike distribution of host-rock joints. We studied a well-exposed locality near Willow Wash (Fig. 10a, location shown in Fig. 2) to test whether magma could locally have found a path along particular joints, suitably positioned and oriented. The dikes near Willow Wash are exposed in a 2 km2 area where joints of two general orientations, N55°–20°W and N25°–75°E, strike across longitudinally semicontinuous outcrops of the Summerville Formation. All dike segments, with the exception of those along the northern outcrops of the westernmost dike, parallel the more northerly striking joints of the N55°–20°W set. We suggest that magma entered, flowed along, and di-

Figure 5. Outcrop pattern of dike segments near Cedar Mountain, compiled at a scale of 1:48 000. The number of dikes or magma-intrusion events that produced the more than 250 dike segments is difficult to determine. Js—Jurassic San Rafael Group.

Figure 6. Histograms of dips of dike segments (a), strikes of dike segments (b), and strikes of systematic joints in the Carmel Forma- tion, Entrada Sandstone, and Curtis and Summerville Formations (c).

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locality, near South Salt Wash, we were able to map dike segments and terpocket monocline (Figs. 2 and 11a), joint sets are continuous across host-rock joints in well exposed strata of the Entrada Sandstone (Fig. 10b, distances comparable to dike lengths. Although the joints exhibit a wide location shown in Fig. 2). There, strikes of joints vary considerably across range of strikes (Fig. 12a), a dominant set, striking between N10°W and distances that are small in comparison to the lengths of most dikes. More- N25°E, is approximately parallel to strikes between N8°W and N12°E of over, individual joints are generally not nearly so long as dikes, and some dikes in the nearby Navajo Sandstone and overlying Carmel Formation. areas of the Entrada Sandstone lack systematic joints. In areas of such dis- Elsewhere, near the southwestern margin of the San Rafael Swell (Figs. 2 continuous and irregular jointing, intruding magma must have created its and 11b), dikes also cut the Navajo Sandstone parallel to prominent own fractures as it formed the dikes. nearby joints. Strikes of these joint sets range from N80°W to N25°E We conclude that some of the San Rafael dikes dilated preexisting (Fig. 12b); 80% strike through 60° of azimuth from about N80°W to joints, at least along part of their length. Apparently, however, most ob- N20°W. The parallelism between some of the joints and the nearby dikes, tained their strikes by some other mechanism. which strike between N65°W and N15°W, suggests that they also served as pathways for the magma. Dikes and Joints in the Navajo Sandstone No dike of the San Rafael swarm is exposed more than about 600 m stratigraphically above the Navajo Sandstone, a distance that is less than Along much of the eastern and southwestern margins of the San Rafael the outcrop lengths of most dikes. Wherever dikes are exposed in the swarm, prominent, extensive joint sets of the Navajo Sandstone parallel Navajo Sandstone or in nearby Carmel Formation, they strike parallel to nearby dikes. To document these relations, we used aerial photographs to joint sets of the Navajo Sandstone (Figs. 11 and 12). We suggest that make maps and to measure strikes of joints. Along the westernmost Wa- strikes of the San Rafael dikes may everywhere parallel those of certain joint sets in the massive sandstones of the underlying Glen Canyon Group. If so, magma ascended along these joint sets and strikes of dikes now exposed in overlying units reflect structural features of units beneath them.

DIRECTIONS OF DIKE PROPAGATION

As dikes dilate, adjacent segments coalesce, leaving offsets, steps, or ridges along the dike contact (e.g., Fig. 13a; Pollard et al., 1975, 1982; Nicholson and Pollard, 1985; Baer and Reches, 1987; Rickwood, 1990;

Figure 7. Definition sketches of the relations between minimum

and maximum regional compressive stresses Sh and SH, dike thickness T(x) as a function of coordinate x, maximum dike thickness Tmax, and dike half-length L. (a) Dilation of a dike in unjointed host rock in

response to uniform magma pressure Pm. (b) Dilation of a dike along a joint oriented at angle a to the direction of least compressive regional stress Sh in response to an axisymmetric linear distribution of Figure 8. Dike length (a) and strike (b) as a function of maximum magma pressure Pm(x). thickness. Error bars are 1s.

1184 Geological Society of America Bulletin, September 1997

Baer, 1991). These features are mechanically equivalent to hackle and dike propagation apparently made use of all surfaces of host-rock weak- plumose structures observed on joint surfaces (Pollard and Aydin, 1989) ness, including bedding. These results point toward the importance of lat- or cleavage steps observed in crystals (Broek, 1978, p. 34). Dike-segment eral spreading of the fractures even as they grew upward. The horizontal offsets parallel the local direction of fracture propagation. For a dike seg- propagation of the San Rafael dikes differed substantially from the lateral ment to dilate, the direction of magma flow initially parallels this direc- propagation of dikes along volcanic rift zones (Rubin and Pollard, 1987; tion. The overall or eventual direction of flow, however, need not every- Walker, 1987). Whereas rift-zone dikes propagate from high-level magma where correspond to fracture-propagation directions. reservoirs, the San Rafael dikes ascended from great depth. Most of the San Rafael dikes have plunges of offsets that vary along their length (a range of about 20° is apparent in Fig. 13a). Some dikes dis- VERTICAL CHANGE IN DIKE THICKNESS AND LENGTH play two directions at a single outcrop (e.g., Fig. 13, b and c). Where this is so, one direction invariably parallels bedding. We interpret these two As the San Rafael dikes approached the Earth’s surface they encoun- directions to correspond to the local upper and lower edges of segments tered rocks of generally decreasing densities. Near the Earth’s surface, before coalescence. The bottom of the segment propagated on top of a volatile phases separated to form vesicles present at most localities. Be- bedding plane while the top continued to propagate upward. We envision cause lithostatic loads generally far exceed tectonic loads and have large that where a dike segment ascends above a suitable bedding plane, vertical gradients, dike form may be expected to vary significantly with magma flows laterally on that bed even as it continues to ascend. As depth. Moreover, we might expect that the San Rafael dikes, which are nearby dike segments rise to the bedding plane, the fracture coalesces only about 1 km long, lengthen with depth. Although there are no precise across it, leaving an offset or step. estimates of emplacement depth, elevation serves as an approximation of Where possible, we studied the structures exposed on dike contacts, relative depths among the dikes. Strata of the San Rafael Group vary eventually collecting 107 measurements of propagation direction (Fig. through about 700 m of elevation, as do the dikes; any elevation-depen- 14). The directions range from vertical to horizontal, and approximately dent changes in dike thickness or length, therefore, are unlikely to stem half of the measurements plunge less than about 30°. The magma during from changing host-rock lithologies.

Figure 9. Sketch maps of eight dike-intersection localities labeled a-i, identifying relative ages where they are well determined by field relations.

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For each unit of the San Rafael Group, dike thicknesses and outcrop lengths were fitted to elevation (Fig. 15) assuming that their variations are log-normally distributed (Figs. 3 and 4). For the Carmel Formation, En- trada Sandstone, and Curtis and Summerville Formations, thickness tends to increase upward with gradients of 105 cm/km, 60 cm/km, and 129 cm/km, respectively; the best fit to all 236 data is 102 cm/km. Dike- outcrop length tends to decrease upward with gradients of –2.4 km/km, –0.02 km/km, and –5.3 km/km for these same units; the best fit to all 174 data is –2.0 km/km. Although none of these fits are statistically superior to the model that thickness and outcrop length are independent of elevation, the senses of these best-fit gradients are the same for all units. This lends support for the presence of such an elevation dependence. The estimated gradients in thickness are unsustainable through more than several kilometers of dike height. However, present outcrops are probably less than several kilometers from the paleosurface and are greatly influenced by it; at greater depth, near-surface effects are presumably unimportant. One expects that dike-outcrop lengths should increase downward, as it seems they do.

Figure 10. Relations of host-rock joints to nearby dikes. (a) Map of dikes and systematic joints exposed in the Summerville Formation, Wil- low Wash. (b) Map of dikes and systematic joints exposed in the Summerville Formation, South Salt Wash. Localities are shown in Figure 2. Qal—Quaternary alluvium.

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DILATION OF THE SWARM variant and there was regional crustal extension during swarm emplacement, then later dikes emplaced near the center of the swarm would re- Extension quire greater magma pressures to attain the same thicknesses as earlier dikes. If magma pressure, on the other hand, remained relatively invariant Thicknesses of dikes show no regular variation as a function of dis- from one intrusion to the next, then later dikes would be narrower where tance along the swarm (Fig. 15a). This result is somewhat unexpected be- they invaded nearby earlier dikes. cause there are more dikes, 8 to 16, across the center of the swarm than Invasion of the San Rafael swarm probably accompanied regional ex- near the ends (Fig. 15b). Dikes cause compression of adjacent rocks and tension across the Colorado Plateau margin; host-rock stresses produced this compression decays to ambient values across distances that are com- by earlier dikes were apparently relieved before emplacement of later parable to, but greater than, dike length. If regional stresses remained in- ones. If so, the maximum dilation is 15–20 m, or 500–600 m strain across the center of the swarm, perpendicular to the average N14°W strike; if emplaced during a million-year interval, then the average extension rate was small, about 15–20 mm/yr.

Dilation Profile

Because thicknesses of the San Rafael dikes do not vary in a regular fashion along the swarm, by multiplying the number of dikes in trans- verse sections by the 85 cm log-normal mean thickness, we obtain the ap- proximate dilation profile of the swarm (Fig. 16b). To examine the manner in which the dikes successively intruded to produce this profile, we return to the two-dimensional solution for a pressurized crack in an infinite elastic plate (Fig. 7a). If the driving pressure is constant along the crack surface, then the thickness profile T(x) is elliptical

Figure 12. Strikes of host-rock joints visible in aerial photographs Figure 11. Relations of dikes to joints in Navajo Sandstone. (a) Map of the Navajo Sandstone of the Glen Canyon Group. Histograms from of dikes and joints along the Waterpocket monocline. (b) Map of data collected along the Waterpocket monocline (a) and along the dikes and joints near the southwestern margin of the San Rafael western and southwestern margin of the San Rafael Swell (b). Also Swell. Localities are shown in Figure 2. JTrn—Triassic (?) and Juras- shown are strikes of dikes exposed in the Navajo Sandstone or in the sic Navajo Sandstone; Js—Jurassic San Rafael Group. adjacent overlying Carmel Formation.

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Figure 13. Offsets and steps along walls of dike segments. (a) Oblique side view showing the steps plunging steeply to north; plunges vary through about 20° along the outcrop. (b) Oblique side view eastward showing segments offset along bedding planes; lower segment is closer. Top segment shows steeply dipping offsets as well. (c) Dike-plane view northward of same dike as b, showing tops and bottoms of dike segments offset on bedding planes.

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P - S probably induced local stresses, which were subsequently relaxed by re- T(x) = m h L2 - 4x2 (7) m /(1 - n) gional crustal extension. Nonetheless, the San Rafael swarm appears to have attained a dilation profile (Fig. 16b) consistent with driving pres- (from equation 8.34, Pollard and Segall, 1987). We fit this equation to the sures that are greatest across the center of swarm, decaying to zero at the dilation profile of the swarm (dashed line, Fig. 16b). Near the ends of the ends. This could, in principle, be produced by a gradient in the regional swarm, thicknesses predicted by the model exceed those observed; along stresses symmetrically disposed about the center of the swarm. The ta- the center of the swarm, observed thicknesses exceed those predicted by pered tips of the swarm-dilation profile could also be produced by inelas- the model. tic deformation. Magma pressures were probably greatest near the center We now examine a dilation profile for magma dilating preexisting frac- of the swarm and lessened toward the periphery. tures. The loading varies linearly so that the crack-tip tapers in such a fashion that the dT(x)/dx = 0 there (Fig. 7b). In this instance, we have DISCUSSION

2 ö Dike Form Pm - Sh 1 æ 2 2 4x 2x T(x) = ç L - 4x - ln ÷ (8) m / 1 - n 2 è L L - L2 - 4x2 ÷ ( ) ø Observed dike lengths, maximum thicknesses, and strikes are not well related by theoretical relations obtained from the two-dimensional theory We fit this equation (equation 22, Delaney and Pollard, 1981) to the ap- of elasticity (equations 1–6; Fig. 8). Outcrop lengths of the San Rafael proximate dilation profile of the swarm (solid line, Fig. 15b) and find dikes are short in comparison to their presumed heights and their present good agreement with the observed dilation profile. exposures lie near their upper, discontinuous peripheries. Physical attrib- –2 The latter model requires that (Pm – Sa)(1 – n)/m » 10 . For a m/(1 – n) utes of dikes probably exhibit their greatest variability near this complex = 5 GPa elastic stiffness, we obtain an average driving pressure of about and intrinsically three-dimensional dike-tip region, and simple two-di- 50 MPa. This estimate is almost certainly high because the model as- mensional approximations fail to account for their form. sumes that the swarm dilated in a perfectly elastic and otherwise unde- The best estimates of gradients in both thickness and outcrop length are forming crust. During the million years of swarm emplacement, each dike large; dikes seem to thicken upward and lengthen downward (Fig. 15).

Figure 14. Equal-area lower hemisphere projection of dike- propagation directions.

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These gradients may arise from the proximity of the Earth’s surface, Fracture Propagation and Magma Transport which remains free of tractions. Traction-free surfaces interact with cracks in a manner that enhances propagation toward them. This effect Because some of the San Rafael magmas flowed along and dilated pre- may have been enhanced by vesiculation of the shonkinite magma, which existing host-rock joints, fracture-propagation directions exposed along would serve to maintain magma pressure even as lithostatic stresses less- dike contacts may bear little relation to the direction of magma advance. ened toward the Earth’s surface. However, the measured directions of propagation are typically consistent over distances of hundreds of meters (e.g., Fig. 13a), much greater than Size Distributions the dimensions of most joints. Many or most of the measurements of sub- horizontal propagation (Fig. 14), therefore, probably reflect spreading of The log-normal distributions used here to characterize thicknesses and the dikes even as they propagated upward. lengths of the San Rafael dikes lack a physical justification. A negative- A well-known result for the dilation of an ellipsoidal crack (Broek, exponential relation between segment lengths and their frequency of oc- 1978, p. 80) in an infinite three-dimensional elastic material suggests why, currence accounts for those data equally well and a power-law relation in a general way, dikes must grow laterally as they ascend. The opening- a b only somewhat less so (solid and dotted lines, respectively, Fig. 6a). How- mode stress intensities KI and KI at the major and minor axes along the ever, these distributions do not account well for the dike-thickness data. crack plane, a and b, respectively, exhibit the proportionality Where the latter data are obtained from field measurements, and are therefore representative of the entire population of thicknesses, the for- K a b I (9) b = mer depend upon map-compilation scale; the particular relations por- KI a trayed in Figure 6a would not be reproduced from data compiled at other scales. As discussed by Clark et al. (1995) and Jolly and Sanderson These stress intensities must exceed the tensile host-rock fracture (1995), among others, negative-exponential and power-law distributions toughness during crack propagation. As a crack extends along the direc- are indicative of certain random and scale-invariant, or fractal, processes, tion of one axis, the stress intensity increases along the crack tip near per- respectively. We doubt that these properties can be assigned to the San pendicular axis. In the absence of pressure gradients from the relative Rafael dikes and speculate that a log-normal distribution of dike-segment lengths would result from a scale-independent sampling of them.

Figure 16. Dike thickness (a) and number of dikes (b) along the San Rafael swarm. Data are projected onto azimuth of N14°W. Solid line in (a) is log-normal mean thickness and dashed lines are ±2 log-normal standard deviations. Because dike thickness does not vary along the swarm, the number of dikes across the swarm is proportional to the total swarm dilation. Solid line in (b) is best-fit theoretical shape Figure 15. Dike thickness (a) and outcrop length (b) as a function of dilation along an existing fracture (equation 8 in text). Dashed of elevation. Also shown are the best-fit lines, assuming that thick- equation line in (b) is best-fit theoretical shape of dilation along a nesses and lengths are log-normally distributed. dike-created fracture (equation 7 in text).

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weights of magma and host rocks, dikes have a strong tendency to attain feed a sill or vented to initiate an eruption. The difficulty of determining circular shapes if the host-rock fracture toughnesses were everywhere the number of dikes is not one of poor exposure; it is more likely a re- similar. In that case, about as many horizontal as vertical propagation di- flection of the apparently random configuration of dike-segment length rections would be expected around the crack periphery. (Figs. 2, 4a, and 5). Whereas the San Rafael dike-segment geometry al- Judging from the primitive nature of the San Rafael magmas, the dikes lows for as many as several hundred discrete intrusions of magma, radio- must have heights that far exceed their <10 km lengths, presumably re- metric ages (Tables 1 and 2) allow for as few as two pulses, at about 3.7 sulting from magma buoyancy. The horizontal propagation directions Ma and 4.6 Ma. If breccia bodies along dikes are characteristic of the sub- may reflect spreading in response to the difficulties of ascent through in- surface beneath eruptive vents and if dikes exposed so near their paleo- creasingly less dense host rocks. Lister and Kerr (1991) pointed out that surface must have either vented or fed sills, then we estimate that swarm magma can rise above its so-called level of neutral buoyancy if the inte- emplacement consisted of about 40–50 episodes. gration of body forces along the magma and adjacent rock columns per- Strikes of dikes exposed in strata of the San Rafael Group (Fig. 6) were mits; it is the relative weight of this “elevated” magma that promotes lat- probably acquired as magma flowed along and dilated systematic joints eral propagation. of the underlying massive sandstones of the Glen Canyon Group (Figs. Breccia bodies and pipes along the San Rafael dikes have vertical con- 11 and 12). Variation in strikes of the dikes is consistent with differences tacts, indicating that magma transport in these bodies must also have been in the magnitudes of the horizontal principal stresses that were small in vertical. These pipes undoubtedly served as the primary conduits of comparison to the magma-driving pressure, consistent with the Colorado magma transport upward along the dikes (Delaney and Pollard, 1981). Plateau setting of low deviatoric horizontal stress (Thompson and Elsewhere, magmas probably stagnated along much of the surfaces of the Zoback, 1979). Nevertheless, the dominant west-of-north strikes of the dikes soon after dilation. dikes provide a robust estimate of the direction of least compressive principal stress, about N75°E, acting at the time of emplacement. Poor agree- State of Stress ment between theoretical relations for crack thickness, length, and strike (Fig. 8) are attributed both to the irregular three-dimensional form of the The northward strikes of the San Rafael dikes, although variable, are San Rafael dikes and the complex emplacement, where magma dilated consistent with the east-of-north strikes of the 7 to 8 Ma dikes on the along preexisting joints in some places and formed its own in others. Wasatch Plateau (Fig. 1; Tingey et al., 1991); both give an easterly direc- Maximum dilation of the San Rafael swarm (Fig. 16) amounted to tion of least compressive regional stress consistent with crustal extension about 17 m and was probably accommodated by crustal extension during in that direction (Thompson and Zoback, 1979). Our examination of the the million-year magmatic interval. The form of the dilation profile along San Rafael swarm offers two estimates of direction of least compressive the present exposure of the swarm is consistent with a distribution of regional stress. The normal to the mean strike of the dikes is N75°E (Fig. magma pressure and regional stresses interacting with host rocks of neg- 6). The normal to the one section of a dike that propagated in unjointed ligible tensile strength. Many of the local fracture-propagation directions host rock strikes N82°E (Fig. 6a). of the dikes are nearly horizontal (Fig. 14). As the dikes attained greater We estimate from Figure 6 that the inequality of equation 4 for dilation heights during propagation, they also spread laterally to maintain dike-top

of preexisting fractures is satisfied for –35° < a < 35°, giving (Pm – Sa) / stress intensities sufficient to assure continued ascent. DS > 0.2. For a driving pressure Pm – Sa » 1 MPa, we obtain DS > 5 MPa. Many, if not most, of the results reported could not have been easily At 2 km depth, the mean horizontal stress S might be about 30 MPa, cor- anticipated; they may be unique to the San Rafael swarm. In the end, de- responding to 15 MPa/km (McGarr and Gay, 1978), and assuming that termination of emplacement processes is best worked out primarily by horizontal stresses at the Earth’s surface were zero on the Colorado field examination and only secondarily by derivation and application of Plateau. We then estimate that the horizontal stress difference could have theoretical relations. been as much as about 15% of the mean horizontal stress. A broader estimate of a is obtained for the entire 110° range of strikes. If dikes strike ACKNOWLEDGMENTS

through a range in excess of 90°, then (Pm – Sa)/DS > 0.5 and Pm – Sa DS < 2 MPa, or 5% of the mean stress at 2 km depth. This study was instigated in great part by David Pollard and Herbert The San Rafael swarm caused about 17 m of dilation (Fig. 16b) during Shaw. Discussions with Myron Best, Jonathon Fink, Gordon Haxel, an interval of about a million years, implying a deformation rate modest Marie Jackson, Stephen Nelson, Kim Sullivan, Dave Tingey, and Danny in comparison to those associated with plate motions. The lack of corre- Williams improved our perspective and understanding of the regional and lation between the number of dikes across the swarm and their thickness igneous geology. Notable advances followed initial reviews by Herb strongly suggests that stresses imposed upon the host rocks by successive Shaw, Donald Peterson, and Mary Lou Zoback. We thank Stephen Nel- dike intrusions were either accommodated by crustal extension or other- son, Karen Carter-Krogh, and Frank Perry for commenting on the penul- wise relaxed before emplacement of successive dikes. timate revision, and Sue Priest, who drafted the figures.

CONCLUSIONS REFERENCES CITED

We grouped into 174 dikes the 1950 dike segments of the San Rafael Baer, G., 1991, Mechanisms of dike propagation in layered rocks and in massive, porous sedi- mentary rocks: Journal of Geophysical Research, v. 96, p. 11911–11929. swarm discernible at 1:48 000 scale on the basis of alignment and prox- Baer, G., and Reches, Z., 1987, Flow patterns of magma in dikes, Makhtesh Ramon, Israel: Ge- imity along strike (Fig. 4b). Many of these dikes, now exposed as separate ology, v. 15, p. 569–572. intrusions, almost certainly coalesce at depth to form laterally continuous Broek, D., 1978, Elementary engineering fracture mechanics: Netherlands, Sijthoff and No- ordhoff, 437 p. “parent” dikes. Conversely, upper peripheries of these parent dikes, of Clark, M. B., Brantley, S. L., and Fisher, D. M., 1995, Power-law vein-thickness distributions which the present exposure is a representative sample, are discontinuous and positive feedback in vein growth: Geology, v. 23, p. 975–978. Cook, K. L., Bankey, V., Mabey, D. R., and DePangher, M., 1989, Complete Bouger gravity and irregular in form. This form was probably preserved when propaga- anomaly map of Utah: Utah Geological and Mineralogical Survey Map 122, scale tion ceased after some segment at the uppermost periphery either began to 1:500 000.

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1192 Geological Society of America Bulletin, September 1997

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