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Incipient magma chamber formation as a result of repetitive intrusions

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Abstract

An analytical solution for periodic magma intrusions in conduits was developed to study the onset of shallow magma chamber formation. The solution is based on determining when a repetitive series of intrusions can cause the wall rock of a conduit to reach its melt temperature. The results show that magma chamber formation in conduits is a strong function of the volume rate of intrusion and that magma chamber formation is likely when the intrusion rate exceeds 10−3 km3/ yr. which agrees with observations by other investigators. Once this critical value of intrusion rate is reached, magma chambers are likely to begin forming after only a few intrusive pulses (less than ten). Results for both cylindrical conduits and dikes show cylindrical conduits are more favourable for the formation of shallow magma chambers.

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Abbreviations

A :

Area, constant

B :

Constant

C :

Specific Heat

F :

General Function

f :

General Function

I 0 :

Modified Bessel Function of First Kind

J 0,J 1 :

Bessel Function of First Kind

K 0,K 1 :

Modified Bessel Function of Second Kind

k :

Thermal Conductivity

L :

Length of Conduit

£:

Latent Heat of Magma

£−1 :

Inverse Laplace Transform

m :

Total Number of Intrusive Pulses

n :

Specific Number of an Individual Intrusive Pulse

Q :

Heat Lost by Magma to Conduit

R :

Radius of Conduit

r :

Radial Coordinate

s :

Laplace Transform Variable

S :

Unit Step Function

T :

Temperature

T a :

Ambient Temperature of Wall Rock

T 1 :

Temperature of Magma Entering Conduit

T 2 :

Temperature of Magma Exiting Conduit

u :

Dummy Variable

V :

Volume of Ejected Magma

X :

Position Coordinate

Y 0,Y 1 :

Bessel Function of Second Kind

α :

Thermal Diffusivity

γ :

Euler’s Constant (0.57722…)

σ:

Unit Impulse Function (Delta Function)

ρ:

Density

τ:

Time

τ 0 :

Time Between Intrusive Pulses

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Authors and Affiliations

  1. Geothermal Research Division, Sandia National Laboratories, 87185, Albuquerque, NM

    H. C. Hardee

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  1. H. C. Hardee
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Hardee, H.C. Incipient magma chamber formation as a result of repetitive intrusions. Bull Volcanol 45, 41–49 (1982). https://doi.org/10.1007/BF02600388

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  • DOI: https://doi.org/10.1007/BF02600388

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