46th Lunar and Planetary Science Conference (2015)
MODELING APPROACH. P. J. McGovern1, 1Lunar and Planetary Institute, USRA, 3600 Bay Area Blvd., Houston, TX 77058 ([email protected]).
Introduction: Jupiter’s moon Io is the most volcanically active body in the solar system. Io also exhibits enormous mountains with relief up to 18 km and
widths of up to hundreds of km [1]. Yet, such mountains appear to be dominantly tectonic in origin, rather
than being edifices built up by magmatic activity. This
apparent paradox can be explained by an unusual state
of stress in Io’s crust/lithosphere, the result of continual burial of the surface by new flows and the resulting
subsidence of older materials [2-4]. Stresses from this
“crustal conveyor belt” have mechanical and thermal
components, combining to produce a state with compression increasing with depth in the lithosphere. Here,
I construct mechanical models reflecting this configuration of stress using the Distinct (alternatively, “Discrete”) Element Method, or DEM. Enforcing the specified stress gradient produces tall mountains with jagged morphologies that resemble Io’s largest mountains.
Further, the stresses break apart the crust into moderate-sized cohesive blocks separated by incoherent,
disrupted zones that may provide magma pathways to
the surface.
Models: The Distinct Element Method, or DEM
[5] is a particle-based numerical approach that employs
a time-stepping, finite-difference approach to solve
Newtonian equations of motion for every particle in
the system. In a typical calculation cycle, known particle velocities are used to compute relative velocities at
interparticle contacts, which are then integrated to obtain the relative displacements at the contacts. Employing suitable contact laws, the current values of
interparticle contact forces are determined from the
displacements. Particle motions are induced by gravitational forces, external forces prescribed by stress or
strain rate boundary conditions, and by forces resolved
at interparticle contacts. The disequilibrium of forces
drives particle displacements, which are unrestricted;
thus, the system can accumulate large strains. Interparticle bonds transmit tensile and shear forces, imparting cohesion to the model and allowing more complex brittle deformation (e.g., rock fracture and communition) to be studied in detail. Previous applications
of this method include analysis of the growth and evolution of large volcanic edifices on Earth and Mars [6,
7]. I use the PFC2D code from Itasca Corp. to carry
out the 2-dimensional models discussed here.
Results and Discussion: Now I present a new application of DEM to the study of mountain building on
Io, using PFC2D’s ability to move wall boundaries by
rotation. By rotating the left retaining wall counterclockwise about the top left corner of the model assemblage, I create a state of downward-increasing
compression, as inferred for Io [3, 4]. After a rotation
of about 28 degrees (Fig. 5c-d), several fault-like discontinuities in the uppermost layers that result in tiltedblock exposures at the surface are revealed. These exposures are superposed on a broad rise of modest
height, also consistent with characteristic topographic
variations on Io [1]. The steep margin of the rise itself
is also interpretable as an Io mountain.
I also calculated a model in which the left wall
translates uniformly rightward without rotation (a
“bulldozer”-type model). After ~ 45 km of convergence, a broad fold system has developed, with a peak
height of about 20 km and an arch-like shape of the
uppermost crustal layer. There is a discontinuity in the
upper surface near the top of the arch that could be
interpreted as the face of a mountain, but overall there
is little that strongly resembles the tilted block morphology of mountains on Io, and in any event the
amount of convergence required to reach this state
produces a topographic arch of height well in excess of
any thought to exist at Io. The broad arch morphology
and lack of significant short-scale topography is likely
the result of pervasive breaking of bonds resulting
from the uniformly large strains in the model. Thus, I
conclude that the rotating wall model captures much
more of the characteristic signature of Io’s mountain
terrain than a simple “bulldozer” model of convergence.
An examination of bond strengths in the rotatingwall model (Fig. 1) reveals several zones where the red
and black bond strength markers are absent, indicating
bond breakage that accommodates fault-like motion of
the model crust. Zones with broken bonds separate
triangular blocks with intact bonds that may constitute
stable Io “cratons” (a somewhat similar “rockberg”
idea was proposed by [8]). The broken bonds zones
extend all the way down to the base of the crust, indicating potential favored pathways for the ascent of
magma from sub-crustal melt source to the surface.
Further, these pathways of broken material occur at the
margins of the mountain-like structures, consistent
with the often-observed occurrence of volcanic paterae
at the periphery of Io mountains [e.g., 9].
To summarize: I have recreated several primary aspects of Io’s mountains and offered new insights into
46th Lunar and Planetary Science Conference (2015)
their structure with a very simple model of mountain
formation via relief of lithospheric stresses.
References: [1] O. L. White et al. (2014) JGR,
119, doi:10.1002/2013JE004591. [2] T. C. O’Reilly
and G. F. Davies (1981) GRL, 8, 313. [3] Schenk and
Bulmer (1998) Science, 279, 1514. [4] M. R. Kirchoff
and W. B. McKinnon (2009) Icarus, 201, 598. [5] P.
A. Cundall and O. D. L. Strack (1979) Geotechnique,
29, 47. [6] J. K. Morgan and P. J. McGovern (2005)
JGR, doi: 10.1029/2004JB003252. [7] P. J. McGovern
and J. K. Morgan (2009) Geology, 37, 139. [8] W. B.
McKinnon et al. (2001) Geology, 29, 103. [9] E. P.
Turtle et al. (2001) JGR, 106, 33,175.
Figure 1. Visualization of PFC-2D DEM model for formation of mountains on Io, demonstrating effects of
compressional stress. Colors (10 km height increments) represent original undeformed stratigraphy of model assemblage. Model is 50 km in height and extends 400 km in length; the leftmost 150 km of the model is shown. Coordinate axes show the origin at the pre-deformation upper left corner. The model has a rotating left wall that enforces
increasing compression with depth. Note exposed tilted scarps with heights of several km, superimposed on a broader high (itself bounded by a several-km scarp at its margin). The red and black symbols in the left-side figure show
locations of inter-particle bonds and forces accommodated by them (black for compression, red for tension); the
right-side figure hides the symbols to reveal details of the structure. Note that bonding comes after gravitational
compaction, so that the bond forces in the left-side figure represent “deviatoric” rather than absolute force components. Note triangular or keystone-shaped cores of bonded particles separated by fault zones lacking bonds (broken).
The configurations of bonded cores and fault zones would tend to send magma to margins of blocks/scarps, as observed on Io.