Hydrothermal Cooling as a Requirement for Short Storage of Silicic Magmas

Kelly, Liam J.; Gualda, Guilherme A. R.; Gravley, Darren M.; Dempsey, David E.

doi:10.1029/2021gc009794

Magma for large eruptions in New Zealand's Taupō Volcanic Zone appears to have crystallised within decades to centuries. In our calculations, conduction through rock took over 1,000 years to remove the heat. Circulating groundwater above the magma, with a heat output of about 1,000 MW, could remove it within decades.

The problem

Caldera-forming eruptions are among the most explosive on Earth (Bryan et al., 2010; Gravley et al., 2016). In New Zealand's Taupō Volcanic Zone (TVZ), the magma bodies that fed them were larger than 50 km³. Titanium in quartz crystals from their pumice suggests that the magma was stored for only decades to a few centuries before it erupted (Gualda et al., 2018). Magma crystallises as it loses heat. So how did such a large body lose its heat so quickly? In this study, we argue that it needed groundwater circulating above the magma.

If stored magma raises the heat output of the hydrothermal system above it, then heat measurements at a restless caldera may indicate whether eruptible magma lies below.

What we did

Our case study is the Mamaku ignimbrite, erupted from the Rotorua caldera about 240,000 years ago (Gravley et al., 2007). The caldera hosts a geothermal system today. We treated the magma as a single body of 150 km³, about 14 km across and 1 km thick.

Using rhyolite-MELTS, we calculated how much heat the magma must lose to reach 10% crystals by weight, the highest crystal content observed in Mamaku pumice. To lose that heat in 100 years, heat must leave the top of the body at 11 to 17 W/m². That is 8 to 12 times the average heat flux through a TVZ geothermal field today, about 1.4 W/m² (Dempsey, 2012; Weir, 2009).

We compared this requirement with the heat flux from three models. The first is conduction through the rock between the magma and the surface. In the second and third, heat conducts through a thin layer of rock above the magma, and circulating groundwater above that layer takes it to the surface. In the second model, rainfall entering the ground sets the heat flux (Weir, 2009; Dempsey et al., 2018). In the third, it depends on how fast groundwater flows through the crust. We drew its uncertain inputs at random 10,000 times.

What we found

In our calculations, conduction took more than 1,000 years at every storage depth we tested. This is because conduction through several kilometres of rock gives a heat flux of 0.3 to 1.1 W/m². To crystallise in decades or centuries by conduction, the magma would have to be stored 13 to 130 m below the surface. The Mamaku magma was stored about 1.8 to 5.5 km deep (Bégué et al., 2014; Gualda et al., 2018).

The rainfall model removed the heat in 200 to 300 years, measured from the onset of quartz crystallisation to compare with the quartz timescales. This is longer than most of the quartz timescales. If 20 to 25% of rainfall entered the groundwater, instead of the 10% we assumed, cooling would take decades. However, present estimates are 5 to 10% (Kissling & Weir, 2005; O'Sullivan et al., 2009).

In the groundwater flow model, half the trials lost the heat within 100 years, and 90% within 280 years. These times are consistent with the quartz evidence. Trials that cooled the magma within 100 years had a mean heat output of about 1,000 MW, ranging from 400 to 1,600 MW. That mean is about a quarter of the 4,200 MW from all TVZ geothermal systems today (Bibby et al., 1995; Rowland & Simmons, 2012).

Rotorua releases about 470 MW today (Bibby et al., 1995). Most trials that cooled the magma within 100 years needed two to three times this. We therefore argue that it is unlikely that a magma body of Mamaku size is cooling over decades beneath Rotorua now. Spread over the 420 km² caldera, today's 470 MW would remove the heat in about 500 years from the onset of quartz crystallisation. By our calculation, a body cooling over decades to centuries beneath Rotorua today would be 30 km³ or smaller.

A single, well-mixed body of 150 km³ probably could not lose its heat in the time required. At 1.4 W/m², only a body about 100 m thick could lose its heat in 100 years, against the 1 km we assumed. One possibility is that the Mamaku magma was stored as several smaller bodies within the caldera (Bégué et al., 2014). Smaller bodies need less heat output to cool on these timescales.

Limitations

The short storage times depend on how fast titanium diffuses in quartz. Slower rates have recently been proposed (Jollands et al., 2020a), although other evidence supports the short timescales (Gualda & Pamukçu, 2020). Even if those timescales prove inaccurate, our calculations still show the heat loss needed to cool magma this fast. We did not model convection inside the magma. Including it would only shorten the cooling times, by about 15% in one estimate (Andersen & Weis, 2020).

Our groundwater speeds and rainfall infiltration come from the present-day TVZ. A period of faster rifting before the Mamaku eruption may have raised crustal permeability and rainfall infiltration (Gravley et al., 2016; Rowland & Sibson, 2004). This would shorten the cooling times in the rainfall model.

High heat output alone does not indicate shallow magma. The Waimangu, Waiotapu, and Reporoa systems together release about 1,000 MW, but they are thought to be driven by a hot zone in the middle to lower crust, where basalt magma intrudes (Rowland & Simmons, 2012). Storing 150 km³ of magma would probably also cause seismicity, ground deformation, or unusual gas chemistry. Measuring these alongside heat output may help detect a large body of stored magma.

Glossary

A caldera is a large depression formed when the ground collapses during or after a large eruption.

An ignimbrite is a deposit of pumice and ash from an explosive eruption.

Pumice is light, gas-rich volcanic rock formed from erupted magma.

Rhyolite is a silica-rich magma, and the volcanic rock formed from it.

Titanium-in-quartz dating estimates how long a quartz crystal grew from how far titanium has diffused within it.

A well-mixed magma body is assumed to have the same properties throughout, so that it loses heat as a single unit.

Heat flux is the heat passing through a unit area per second, in watts per square metre (W/m²).

Heat output is the total heat released over an area, in megawatts (MW), where one megawatt is a million watts.

Conduction is the transfer of heat through rock without the movement of fluid.

A hydrothermal system is groundwater that is heated at depth, rises and removes heat from the crust.

Permeability is a measure of how easily fluid flows through rock.

Rifting is the stretching and thinning of the crust.

Infiltration is the fraction of rainfall that soaks into the ground and joins the groundwater.

Rhyolite-MELTS is a thermodynamic computer model that calculates which crystals form in a silica-rich magma as it cools, and how much heat it loses.

Abstract

Large (>50 km 3 ) magma bodies that contribute to caldera‐forming eruptions in the Taupō Volcanic Zone (TVZ), New Zealand have shown evidence for crystallization and storage on the order of decades to centuries prior to eruption. We compare various conductive and convective heat extraction models to determine which is more likely to enable the heat loss required for short magma storage. We conclude that purely conductive models only account for heat loss on millennial or longer timescales. We also show that convective hydrothermal systems with heat output of 1,000 MW in magnitude are required for decadal heat extraction from a large, contiguous magma body; yet, heat output similar to present‐day conditions would be suitable for cooling magma distributed as a patchwork of smaller magma bodies. This study shows the potential connection with heat flow at the surface and the presence of a magma body, providing future directions for monitoring restless calderas in environments with a wealth of hydrothermal activity like the TVZ.