Some lava flows may not have been as thick as they appear

manuscript submitted to

Geophysical Research Letters

Some lava flows may not have been as thick as they

1

appear

2

Jonas Katona

, Xiaojing Fu

, Tushar Mittal

, Michael Manga

, and

3

Stephen Self

4

1

University of California Berkeley, Berkeley, CA, United States

5

2

Yale University, New Haven, CT, United States

6

3

California Institute of Technology, Pasadena, CA, United States

7

4

Massachusetts Institute of Technology, Cambridge, MA, United States

8

Key Points:

9

•

Lava lobes can heat and melt underlying lobes if erupted in close enough succes-

10

sion;

11

•

Based on the time between successive eruptions, there are three regimes for lava

12

lobe cooling: fused, in parallel, and in sequence;

13

•

Macroscopic structures may not reflect the original lobe thicknesses.

14

Corresponding author: Jonas Katona,

jonas.katona@yale.edu

Corresponding author: Xiaojing Fu,

rubyfu@caltech.edu

Corresponding author: Tushar Mittal,

tmittal2@mit.edu

–1–

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Article

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Geophysical Research Letters

Abstract

15

Individual lava flows in flood basalt provinces are composed of sheet p ̄ahoehoe lobes and

16

the 10-100 m thick lobes are thought to form by inflation. Quantifying the emplacement

17

history of these lobes can help infer the magnitude and temporal dynamics of prehistoric

18

eruptions. Here we use a phase-field model to describe solidification and remelting of se-

19

quentially emplaced lava lobes to explore additional processes that may lead to thick flows

20

and lobes. We calibrate parameters using field measurements at Makaopuhi lava lake.

21

We vary the lobe thicknesses and the time interval between eruptions to study the in-

22

terplay between these factors and their impact on the thermal evolution of flows. Our

23

analysis shows that if the time between emplacements is sufficiently short, remelting may

24

merge sequentially emplaced lobes — making lava flows appear thicker than they actu-

25

ally were — which suggests that fused lobes could be another mechanism that creates

26

apparently thick lava flows.

27

Plain Language Summary

28

The observation of thick basaltic lava flows has long been explained by vertical in-

29

flation. Here we explore an additional mechanism that could also create thick lava flows,

30

where a sequence of thinner lobes that are emplaced on top of each other could fuse into

31

one larger flow. Our analysis suggests the formation of thick lobes and flows by merg-

32

ing can occur if the lobes are emplaced relatively close to each other in time.

33

1 Introduction

34

Continental flood basalt (CFB) province eruptions contain the largest (

1,000 km

35

Bryan and Ernst (2008); Self et al. (2014)) and longest (

∼

1000 km; Self et al. (2008))

36

lava flows. Since CFBs are frequently coeval with severe environmental perturbations

37

including mass extinctions, ocean anoxic events, and hyperthermal events (Clapham &

38

Renne, 2019), understanding the physical process and time-scale of flow field emplace-

39

ment would help quantify the release of volcanic gases that have environmental impacts

40

(e.g., CO

, SO

). However, despite decades of work, the tempo and style of CFB erup-

41

tions remain poorly quantified.

42

CFB lava flow fields are composed of 5-100 m thick dominantly p ̄ahoehoe lobes (Self

43

et al., 1998, 2021). Given the general lack of large lava tubes in CFBs (Kale et al., 2020;

44

Self et al., 1998), the primary process hypothesized for creating thick flows is the for-

45

mation of p ̄ahoehoe lobes by inflation (Hon et al., 1994). If the quasi-continuous magma

46

flux into individual lava lobes is sufficient, the solidifying surface crust can continuously

47

rise due to increasing pressure (Hoblitt et al., 2012; Hon et al., 1994). If the lateral magma

48

pressure is large enough, the lobe can propagate laterally by sporadic breakouts (Hamilton

49

et al., 2020; Hon et al., 1994; Kauahikaua et al., 1998). This process has been observed

50

in modern meter-scale Icelandic and Hawaiian lobes (Self et al., 1998). In addition, the

51

lobe structures in CFB flows have similar internal characteristics as Hawaiian inflated

52

lobes (Vye-Brown et al., 2013). The maximal final inflated lobe thickness in Hawaiian

53

flows, however, is only 10-15 m (Kauahikaua et al., 1998), which is smaller than many

54

CFB flows (up to 80-100 m; Puffer et al. (2018); Self et al. (2021)). This suggests that,

55

for typical basaltic magmas, the yield strength of the crust is insufficient to support the

56

large lateral pressure gradients that would arise from much thicker flow lobes. Further-

57

more, lava flow inflation has been shown to potentially require pulsating eruptive con-

58

ditions that may not always be possible (Rader et al., 2017). Thus, a fundamental ques-

59

tion remains: How do CFB flows become so thick? This question underlies a broader ques-

60

tion: What are the eruptive conditions and fluxes associated with common

∼

1000 km

61

scale CFB flows?

62

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Article

manuscript submitted to

Geophysical Research Letters

In this study, we quantitatively analyze a physical process that can, in addition to

63

flow inflation, also lead to apparently thick lobes and flows: The final flow is an amal-

64

gamation of smaller lobes, piled on top of each other quickly enough to remelt the in-

65

tervening solidified crust (Basu et al., 2012, 2013). We study this process for a wide range

66

of flow thicknesses. While our model could still be applicable to shallow flows undergo-

67

ing predominantly unidirectional solidification and moving at low velocities, the model

68

simulated in this paper cannot capture the inherently 3D, meandering nature of phoe-

69

hoe flows, especially those present during the amalgamation of small (

1 m), predom-

70

inantly non-inflated phoehoe lobes, e.g., in lava piles where hummocky phoehoe or com-

71

pound lavas are forming (e.g., Baloga et al., 2001; Hamilton et al., 2020). Thus, we fo-

72

cus most of our discussion on large CFB flow lobes where our model is best suited, since

73

for such flows, the dynamics in the non-vertical directions are dominated by those in the

74

vertical (Hon et al., 1994; Wright & Okamura, 1977).

75

We use simplified magma solidification models to constrain how quickly two sub-

76

sequent flow lobes must be emplaced to fully merge, thereby providing constraints on

77

CFB eruption tempo. In section 2, we describe a new phase-field model for lava lobe cool-

78

ing, and then simulate the solidification of a single flow lobe and two sequentially em-

79

placed flow lobes using our model in 1D. In section 3, we use these results to outline three

80

distinct regimes (fused, in parallel, in sequence) for inter-lobe cooling. Finally, in sec-

81

tion 4, we compare our results with observations to assess whether remelting can help

82

explain thick CFB flows and analogous thick flows in other planetary settings. Our re-

83

sults are used to put lower bounds on how quickly CFB flow fields were emplaced in or-

84

der to preserve multiple lobes within a single flow.

85

2 A phase-field model of lava solidification

86

2.1 Model equations

87

The phase-field framework is a mathematical approach to describe systems out of

88

thermodynamic equilibrium (Anderson et al., 1998), first introduced in the context of

89

solidification processes and phase transitions of pure or multi-component materials (Boettinger

90

et al., 2002; Cahn & Hilliard, 1958). The framework evolves the solidification front via

91

a system of partial differential equations, avoiding the need for explicit tracking of the

92

moving interface as traditionally done in the Stefan problem (Anderson et al., 1998). Here,

93

we consider a simplified model of lava solidification where we track the binary solidifi-

94

cation of lava through a phase variable, denoted

(

= 1 for the melt and

= 0 for

95

the solid phase), with corresponding temperature,

. The evolution of

and

can be

96

described by the following system of partial differential equations:

97

∂φ

∂t

∇·

(

−

∇

)

−

dφ

−

(

−

)

dφ

(1)

∂T

∂t

∇·

(

−

∇

) =

dφ

∂φ

∂t

(2)

where

is the melting temperature of the lava,

is the thermal diffusivity,

is the

98

interfacial width coefficient,

is the characteristic time of solidification (

not

the solid-

99

ification time of a lobe),

is the latent heat of fusion for lava, and

is the energy bar-

100

rier; see Table S1 for the values of these parameters used in this work, which are adopted

101

from the typical thermal properties of basaltic melt (Audunsson & Levi, 1988; Cooper

102

& Kohlstedt, 1982; Patrick et al., 2004; Peck et al., 1977; Worster et al., 1993; Wright

103

& Marsh, 2016).

∇

is a partial differential operator defined in text S2. Γ = Γ (

) and

104

Ψ = Ψ (

) are auxiliary functions of the phase-field model (see text S1). Because we

105

are working with a binary phase-field model, we do not model the so-called “mush zone”

106

that exists in actual lavas (e.g., Wright & Marsh, 2016). Consequently, we combine the

107

solidus and liquidus temperatures as

= 1070

◦

C, which is within the range of rea-

108

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Geophysical Research Letters

sonable values reported in literature for the liquidus of typical basaltic magmas (e.g., Cash-

109

man & Marsh, 1988; Wright & Marsh, 2016).

110

We impose convective and radiative boundary conditions at the surface while fix-

111

ing the temperature at the bottom of the domain. Moreover, we integrate our phase-field

112

equations over a sufficiently large domain such that the lower boundary does not influ-

113

ence the temperature and phase during solidification (see text S2). Because the horizon-

114

tal dimensions (kilometers) are much larger than the vertical scale (meters) for the flows

115

of interest here, we perform our simulations in a 1D vertical dimension. Consequently,

116

the conductive heat transfer will be primarily in the vertical direction. We provide ad-

117

ditional details regarding the numerical scheme we used in text S3.

118

2.2 Model validation and limitations

119

The phase-field modeling parameters

and

are derived in terms of measurable

120

quantities in text S1 using the approach in Kim and Kim (2005), and then calibrated

121

based on field data collected from Makaopuhi lava lake (Wright & Marsh, 2016; Wright

122

& Okamura, 1977; Wright et al., 1976). The calibration results show that the model agrees

123

with the lava lake data for a range of parameters (see Figure S1 and Table S1); we ul-

124

timately choose

= 3

−

m and

= 2

s in our simulations, both of

125

which are well within these ranges.

126

As an additional test, we use the calibrated parameters from Makaopuhi lava lake

127

to simulate measurements of inflating phoehoe lava flows on the Klauea volcano in Hawaii,

128

taken from Hon et al. (1994). The results (Figures S2-S3) show decent agreement at depths

129

deeper than

∼

10 cm below the cooling surface, although there is noticeable disagreement

130

near the surface. These validation efforts demonstrate that, while our model robustly

131

captures macroscopic cooling of lava across multiple data sets, it lacks accuracy in de-

132

scribing the temperature evolution in the uppermost section of cooling lava (

∼

10 cm).

133

One explanation is that the bubbles and vesicles that accumulate near the lava’s surface

134

(Audunsson & Levi, 1988; Cashman & Kauahikaua, 1997; Self et al., 1998) tend to de-

135

crease

near the surface (Keszthelyi, 1994). We also neglect the temperature dependence

136

(Jaupart & Mareschal, 2010). While it is possible to include these effects in the model,

137

it would also introduce additional parameters that are challenging to calibrate, and would

138

also require resolving multiphase physics and chemistry at the sub-centimeter spatial scale

139

and sub-second time scale. The fact that we neglected to include such effects adds an

140

increasingly non-negligible degree of uncertainty to our results as the lobe size decreases,

141

the degree of which should be explored in future studies.

142

Nevertheless, the model presented here, although simplified, still captures the first-

143

order effects of latent heat and thermal diffusion that dominate lava cooling while allow-

144

ing us to simulate cooling processes spanning from seconds to years. From our valida-

145

tion tests above, we see that any surface effects appear to be negligible for depths be-

146

low

∼

10 cm. This is especially true for larger lava lobes, where the influences of latent

147

heat release and diffusion on the velocity of the solidification front and evolution of tem-

148

perature profiles are especially greater in both spatial and temporal extent than those

149

which are due to the surface and near-crust phenomena aforementioned (Patrick et al.,

150

2004; Wright & Marsh, 2016; Wright & Okamura, 1977; Wright et al., 1976).

151

2.3 Setup for lava cooling simulations

152

We use the model to perform two types of simulations. We first simulate solidifi-

153

cation of a single lava lobe of thickness

to obtain the total time

it takes to reach com-

154

plete solidification for a single lobe of thickness

. The results are used to design the sec-

155

ond set of simulations, where we simulate sequential emplacement of two lava lobes of

156

equal thickness

, separated by a time period of

emp

. We consider 17 different lobe thick-

157

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ness

, from 0.1 m to 20 m, to explore the behaviors of both thin p ̄ahoehoe lobes (

158

m), as seen in recent Klauea eruptions (Lundgren et al., 2019; USGS, 2019), and thick

159

lobes (

1 m), as seen in Columbia River Basalt Group and other CFBs (Self et al.,

160

2021). For the sequential emplacement simulations, we scale

emp

relative to

and ex-

161

plore nine different emplacement intervals for each thickness:

emp

= 2

−

,...,

162

Here,

emp

is sampled along multiple orders of magnitude in order to capture a wide range

163

of cooling times. The lower bound for the emplacement intervals is based on typical phoehoe-

164

type flows (Anderson et al., 1999; Hon et al., 1994) while the upper bound is provided

165

by examples from flood basalt provinces (Self et al., 1996; Thordarson & Self, 1998).

166

3 Results

167

We perform a total of 153 simulations of the sequential emplacement of two lava

168

lobes and identify three distinct qualitative regimes of inter-lobe solidification. These regimes

169

can be delineated based on the ratio between

emp

and the conductive time scale, the lat-

170

ter of which is more precisely described by

, but approximated here by

/α

to be more

171

physically interpretable (see Figure S4 for how well the approximation

∼

/α

holds).

172

Below, we describe each regime in detail with examples in Figure 1 for the case of

173

10 m lava lobes.

174

In sequence (

emp

/α

The first lava lobe completely solidifies before the sec-

175

ond lobe is emplaced (Figure 1, left). The cooling times of both lobes are simi-

176

lar and the bottom lobes does not remelt.

177

In parallel (

/α < t

emp

/α

As indicated by the narrowing of both black

178

contours in the top plot and the decreasing melt thickness in the lower plot with

179

time, both lava lobes solidify for overlapping time, but the interface between them

180

does not remelt (Figure 1, middle). Because the bottom lobe is hot, the collec-

181

tive cooling of both lobes is slower than for

in sequence

flows, as indicated by the

182

decrease in slope in Figure 1 (bottom middle).

183

Fused flow (

< t

emp

/α

After emplacement, the solidified portion of the

184

lower lava lobe remelts completely, after which both lobes combine to form a sin-

185

gle, larger lobe. For early times, there are four solid-melt interfaces that correspond

186

to the simultaneous solidification of two independent lobes. However, the two in-

187

terior interfaces eventually disappear, which marks the merging of the two lobes.

188

The remelting event is also evident when we track the total melt thickness over

189

time (Figure 1, right). After the arrival of the second lobe (indicated by the red

190

dot), the total melt thickness increases slightly at some point, corresponding to

191

the remelting that caused a reduction in the solid fraction. Despite a monotonic

192

loss of entropy over time after the second flow arrives, remelting can still occur,

193

since some sensible heat is converted into latent heat. In the other two regimes,

194

the melt thickness never increases after the arrival of the second lobe.

195

We compile the results from all the simulations into a regime diagram in Figure

196

2, which shows the combined control of individual lobe thickness and emplacement in-

197

tervals on the inter-lobe solidification during sequential emplacement. We map the three

198

regions of inter-lobe solidification, separated by two boundaries extrapolated from our

199

results:

emp

= 0

/α

and

emp

= 0

/α

. These regimes and the boundaries that

200

define them are universal for both thin and thick lobes.

201

The bottom four panels in Figure 2 also illustrate examples of lava flows that ap-

202

pear to have been emplaced

in parallel

in sequence

, as suggested by their distinct inter-

203

lobe boundaries. These examples are also marked in the regime diagrams, where the ver-

204

tical position of the marker corresponds to the minimum emplacement interval predicted

205

by our model (e.g.,

emp

= 0

/α

). The hexagonal marker corresponds to

∼

10 cm

206

thin lobes seen in the Kupaianaha flow field (Self et al., 1998) that are predicted to have

207

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Geophysical Research Letters

been emplaced at least

∼

4 minutes apart. The square marker corresponds to

∼

0.5 m thin

208

lobes seen in Elephanta Caves (Deccan Traps) (Patel et al., 2020), and are predicted to

209

have been emplaced at least

∼

2 hours apart. The circular marker corresponds to

∼

8 m

210

thick lobes — part of a single flow and seen in Rajahmundry Traps (Fendley et al., 2020a)

211

— that are predicted to have been emplaced at least

∼

20 days apart. The star-shaped

212

marker corresponds to

∼

20 m thick lobes seen in Columbia River Basalts (Self et al., 2021)

213

that are predicted to have been emplaced at least

∼

4 months apart.

214

4 Discussion

215

There is a body of literature that commonly assumes that even the thickest (

216

m) CFB flows were formed by flow inflation (e.g., Anderson et al., 1999; Rader et al.,

217

2017; Self et al., 1996, 1998), inspired by observations of Hawaiian lava flows (Hon et al.,

218

1994). However, our analysis suggests that even thick (30-40 m total height) flows could

219

have arisen by fusing lobes together if eruption intervals are shorter than a month or two.

220

One practical challenge in testing our proposed mechanism is the ability to identify fused

221

flow boundaries in the field, since fusing would remove structures corresponding to the

222

crusts of the two lobes. However, some relics of the originally distinct flows may remain,

223

such as compositional differences (Reidel, 2005; Vye-Brown et al., 2013) and possibly struc-

224

tures indicative of fused flow crusts, such as multiple differential cooling zones and vesicle-

225

rich horizons (see text S6 and Figure 3). Moreover, vesicle-rich horizons are commonly

226

interpreted as remnants of inflation (Self et al., 1998; Thordarson & Self, 1998), and so

227

the presence of these alone may not be sufficient to distinguish between lobe inflation

228

and fusion, or at least with our current understanding of how the observable character-

229

istics of said horizons reflect their formation.

230

4.1 Potential example of a fused CFB flow

231

One potential example of a fused CFB flow is the

∼

70 m thick Cohassett Flow from

232

the Columbia River Flood Basalts. The flow is part of the Grande Ronde Basalt Group

233

and is a member of the Sentinel Bluffs Member lava flows in Pascoe Basin (e.g., McMil-

234

lan et al., 1989; Reidel, 2005, see Figure 3A for a map of outcrops and drill core data).

235

As shown by the annotated picture in Figure 3B, the Cohassett has a multi-tiered struc-

236

ture with alternating entablatures and colonnades (see text S6 for a description), as well

237

as a 6.5 m thick internal vesicular zone (IVZ;

∼

20 m from the flow top, Figure 3B,C,D)

238

with many

∼

1 cm diameter vesicles (McMillan et al., 1989; Tomkeieff, 1940). To first

239

order, the Cohassett flow in the outcrops (Figure 3) appears to be a single thick sheet

240

lobe. The Cohassett flow also exhibits one of the most striking geochemical variations

241

amongst the Grande Ronde flows. The flow has an approximate vertical bilateral sym-

242

metry geochemically centered just under the IVZ, as seen from data across sections more

243

than 50 km apart (Figure 3). Using characteristic patterns in TiO

, P

(and other

244

major and trace elements), Reidel (2005) defined four distinct compositional types within

245

the flow: California Creek, Airway Heights, Stember Creek, and Spokane Falls. Typi-

246

cally, these compositional types are separated by a vesicular horizon. For example, a hori-

247

zon

∼

13-15 m from flow top separates massive basalt of the California Creek composi-

248

tion from the Airway Heights composition. Similarly, the Airway Heights and Stember

249

Creek transition is characterized physically by a series of large vugs. The IVZ acts as

250

the contact between the Spokane Falls and the Stember Creek compositional types (Fig-

251

ure 3B,C,D). Finally, a vesicular horizon

∼

40 m from flow top defines the transition from

252

the Spokane Falls back to the Stember Creek compositional types. Interestingly, the sub-

253

sequent compositional type changes from Stember Creek to California Creek/Airway Heights

254

lack clear vesicular horizons (Figure 3).

255

Corresponding spatially with these geochemical changes, the Cohassett flow also

256

exhibits systematic changes in plagioclase abundance and fine-grained fraction (groundmass,

257

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Figure 3C based on data from Reidel, 2006). In particular, the flow part comprising the

258

IVZ and the Spokane Falls composition member has a fine fraction significantly more

259

indicative of a flow top rather than the flow interior. Thus, this flow interior was poten-

260

tially emplaced rapidly and cooled faster than a continuously inflating flow lobe interior

261

(McMillan et al., 1989; Philpotts & Philpotts, 2005). The IVZ-entablature-colonnade se-

262

quence in the Spokane Falls lava further supports the conclusion that the cooling rates

263

in this part of the flow were more akin to a flow top (DeGraff et al., 1989; Forbes et al.,

264

2014). Even on an overall flow scale, the textural data for the Cohassett flow are incon-

265

sistent with the slow cooling expected for a

∼

70 m flow; the plagioclase crystal size does

266

not significantly change throughout the flow, unlike the case for a slowly cooling ponded

267

lava lake (Cashman & Marsh, 1988; Philpotts & Philpotts, 2005).

268

Previously, Reidel (2005) proposed that the Cohassett flow formed via the com-

269

bination of different sheet flows (for each compositional type), each sourced from a dif-

270

ferent magma reservoir and eruptive vent. These individual flows sequentially intruded

271

into the Cohassett flow as flow lobes and inflated it to its final height. However, the Reidel

272

(2005) model does not explain the abrupt shift to distinct compositional types along with

273

sharp vesicle horizons (Figure 3B, B1-B2) without any signs of magma mixing or shear

274

instabilities, despite intrusion and transport within the Cohassett flow for 10s of km. Al-

275

ternatively, Thor Thordarson (personal communication; see also Vye-Brown et al. (2013))

276

proposed that the Cohassett flow was formed by semi-continuous inflation with chang-

277

ing magma compositions in the magmatic system feeding the eruption. As evidenced by

278

observations from some modern long-lived basaltic eruptions, e.g., Pu u

O ̄o eruption at

279

Klauea, Hawai’i from 1983 to 2018 (Garcia et al., 2021), these changes can be relatively

280

abrupt and could correspond with the presence of a vesicle horizon. Philpotts and Philpotts

281

(2005) proposed that crystal-mush compaction in an inflated sheet lobe can also partially

282

explain the observed geochemical variation and bubble segregation.

283

Here, we put forward a third alternative, building upon the original idea proposed

284

by Reidel (2005): We posit that the Cohassett flow is an example of a

fused

flow with

285

multiple flow lobes. Suppose the Cohassett was close to the boundary between the fused

286

and in-parallel flow types (Figure 2). In that case, the presence of separating vesicle hori-

287

zons as well as high fine-grained size fraction, especially for the Spokane Falls type, can

288

be explained. Within this scenario, each constituent

∼

10-20 m lobe would have to be

289

emplaced within a few months of the previous lobe. However, more detailed modeling

290

work specifically focused on the Cohassett as well as textural analysis, e.g., stratigraphic

291

crystal size distributions to estimate cooling rates (Cashman & Marsh, 1988; Giuliani

292

et al., 2020), would be needed to ascertain which of the proposed models is correct and

293

if Cohassett is indeed a

fused

flow.

294

It is similarly challenging to distinguish between

in parallel

and

in sequence

flows

295

based on field volcanological observations alone without detailed textural analysis. One

296

potential distinguishing feature may be the 2D shape of the bottom flow lobe in a

in par-

297

allel

flow since it will be visco-elastically deformed by the load from the overlying flow

298

lobe (Abbott & Richards, 2020). One consequence of this would be the formation of squeeze-

299

up structures at flow lobe edges seen in some CFB flow edges, e.g., for the Western Ghats

300

and the Rajahmundry Trap flows in the Deccan CFB (Dole et al., 2020; Fendley et al.,

301

2020b).

302

4.2 Relevance of fused flows for planetary geology

303

Our results also have implications for inferring eruption conditions on other plan-

304

etary bodies (Venus, Mars, Mercury, the Moon) where we can only observe the final lava

305

flow thickness from remote sensing observations. Below, we briefly summarize observa-

306

tions of thick lava flows on each of these bodies:

307

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•

Venus

: With a surface area (

∼

60,000 km

) comparable to many CFB flows (Moore

308

et al., 1992; Wroblewski et al., 2019), the most striking example of a thick lava

309

flow (

∼

100-200 m) on Venus is the Ovda Flactus flow. Although initially classi-

310

fied as a potentially high silica or rhyolitic flow, morphological analysis by Wroblewski

311

et al. (2019) shows that Ovda Flactus has an emplacement rheology most consis-

312

tent with basalt. Several other basaltic flows mapped across Venus have thicknesses

313

ranging between 30-100 m (Guest et al., 1992; Lancaster et al., 1995; MacLellan

314

et al., 2021; Moore et al., 1992; Zimbelman, 2003). We envision that our proposed

315

process of fused flows can help explain these large flow thicknesses, especially since

316

cooling rate during solidification on Venus will be smaller (

∼

30-40% compared to

317

Earth) due to higher surface temperatures (Snyder, 2002). Correspondingly, in-

318

dividual flow lobes can be separated by longer times and still fuse together.

319

•

Mars

: There is a wide range of estimated flow thickness for Martian lava flows

320

with values ranging from a few meters to

∼

100-125 m (Hiesinger et al., 2007; Mouginis-

321

Mark & Rowland, 2008; Mouginis-Mark & Yoshioka, 1998; Peters, 2020; Zimbel-

322

man, 1998). In particular, both the Tharsis volcanic province and the Elysium Plani-

323

tia region on Mars have a number of flows with typical thickness greater than 40

324

m (Peters, 2020). These flow thicknesses are challenging to explain with inflation,

325

but may be explained by lobe fusion. Since the mean Martian surface tempera-

326

ture (-60

◦

C) is colder than Earth’s, the lava solidification time is about 5% shorter

327

than on Earth (based on results from a model with Martian surface temperature).

328

Since Martian surface gravity is

∼

38% of Earth’s, flow lobes may inflate to greater

329

thickness before overcoming basalt yield strength to form new breakouts.

330

•

Mercury

: J. Du et al. (2020) used observations of partially and completely buried

331

impact craters on Mercury to estimate lava flow thicknesses and found values be-

332

tween 23-536 m with a median of 228 m (with potentially even thicker flows), con-

333

sistent with some other estimates, e.g., 180 m (Wilson & Head, 2008). Even if we

334

account for the difference in surface gravity (38% of Earth’s), the median thick-

335

ness of 228 m translates to 86 m of Earth’s equivalent (in terms of flow dynam-

336

ics; the cooling times are independent of gravity).

337

•

Moon

: Lunar mare basalts have a range of flow thicknesses, from thin (

1 m)

338

to thick (

100 m). These estimates come from a combination of in situ observa-

339

tions by Apollo Astronauts, remote sensing, and lunar penetrating radar on rovers

340

(Chen et al., 2018; Gifford & El-Baz, 1981; Hiesinger et al., 2011; Rumpf et al.,

341

2020; Spudis & Guest, 1988). Since lunar gravity is only about 16 % of the ter-

342

restrial gravity, lobe inflation could form much thicker flows (a 15 m flow lobe on

343

Earth will be equivalent to a 91 m lobe on Moon with respect to lateral pressure

344

gradients). Thus, except for the thickest flows (

100 m), flow fusion may not be

345

required to explain the observed lunar flow thicknesses.

346

In aggregate, there are a number of very thick planetary basaltic flows. We posit that

347

these could be potentially emplaced by the same process as we are proposing for thick

348

terrestrial CFB flows (fused flow lobes). However, more data and careful analysis is nec-

349

essary to rule out the possibility that these were primarily formed via flow lobe inflation.

350

4.3 Implications for eruption rates

351

In combination with viscous flow models for channelized lava flows (e.g., Jeffrey’s

352

equation), measurements of lava flow thickness have been used to estimate the mean flow

353

velocity and viscosity (e.g., Baloga et al., 2001, 2003; Chevrel et al., 2018; Glaze et al.,

354

2003; Harris & Rowland, 2001). Frequently, estimated flow velocities are used in com-

355

bination with constraints on total flow volume to calculate an eruption duration. How-

356

ever, these calculations are predicated on the assumption that the final flow thickness

357

is representative of the molten channelized flow thickness at the time of eruption. Since

358

the velocity depends strongly on the lava flow thickness (velocity

∼

thickness

for a New-

359

–8–

Accepted

Article

manuscript submitted to

Geophysical Research Letters

tonian fluid), an incorrect estimate could strongly impact the estimates of eruption rate

360

(

∼

flow rate

thickness) (Baloga et al., 2003). Suppose that the observed lava flow re-

361

sults from the merging of two (or more) equally thick flow lobes. Then, the models will

362

overestimate instantaneous effusion rates by about a factor of 2

= 8 (or larger for three

363

or more fused lobes) if the final flow thickness is used as the characteristic open chan-

364

nel lava flow thickness, i.e., with an error that grows

∼

cubically. This issue is further

365

exacerbated by how, during the emplacement of phoehoe flows by inflation, the “active”

366

molten part of the flow is smaller than the thickness of each lobe.

367

In the other end-member, wherein the total observed flow thickness is assumed to

368

be only a consequence of lava flow inflation, most models require a relatively continu-

369

ous, long-lived effusion rate that gradually thickens the flow lobe (Hamilton et al., 2020;

370

Hon et al., 1994; Kauahikaua et al., 1998; Self et al., 1998). However, if the CFB flow

371

is a fused flow, each constituent flow lobe must inflate to a smaller thickness. Consequently,

372

since the two lobes can be sequentially emplaced days to months apart, the total erup-

373

tive duration can be smaller and/or allow for more effusion rate variations but will still

374

form a single fused flow in the end. In conclusion, the possibility that different flow lobes

375

merged into a single flow has important implications for inferences of effusion rate, es-

376

pecially its steadiness.

377

5 Conclusion

378

We provide a theoretical lower bound on emplacement interval that distinguishes

379

fused flow

from non-merged flows. For instance, a distinct boundary between two lobes

380

of 10 cm each suggests that they were emplaced at least 4 minutes apart (

emp

/α

≈

381

4 minutes). The same calculation for two 20 m thick lobes suggests that the emplace-

382

ment interval is at least 4 months if a distinct boundary exists between the two lobes.

383

Furthermore, while it is often assumed that the 10

−

100 m thick lobes found in flood

384

basalt provinces are primarily formed from inflation, our results suggest that these large

385

lobes also could have been formed by smaller lobes emplaced in quick succession. Re-

386

latedly, some volcanological studies could be overestimating eruption rates and flow ve-

387

locities by assuming that solidified flows belong to one flow rather than a series of smaller

388

flows that merged with little to no trace of their original separation. While more work

389

is necessary (especially empirically) to distinguish conclusively between a large, solid-

390

ified flow that formed primarily via multiple-lobe emplacement vs. the usually assumed

391

mechanism of inflation, we still propose that the emplacement and subsequent fusion of

392

multiple lobes is a plausible, additional process for forming CFB flows.

393

Noting some limitations, we also demonstrate the effectiveness of using phase-field

394

models in simulating observed lava solidification over a range of timescales faithfully (Hon

395

et al., 1994; Wright & Marsh, 2016; Wright & Okamura, 1977; Wright et al., 1976), with

396

some local deviation

∼

10cm near the top surface. The phase-field model can be gen-

397

eralized to arbitrary domains in higher dimensions and account for additional complex-

398

ities in thermal diffusivity, flow, and nonlinear rheology.

399

–9–