Summary

Robotic missions to destinations throughout our solar system have illuminated in increasing detail evidence of past and present tectonics combined with manifestations of internal dynamics. Interpretation of observations, such as sustenance of high mountains on Venus for potentially hundreds of millions of years, formation of the grooved terrain on the surface of Ganymede, and tidally driven tectonics and volcanism on Io, requires the application of realistic constitutive equations describing the rheological properties for the materials that constitute the crusts and interiors of these planetary bodies. Appropriate flow laws can only be derived from careful experimental studies under conditions that may be reliably extrapolated to those believed to exist on and in the planetary body under consideration. In addition, knowledge of the appropriate rheological behavior may, coupled with measurements made from orbiting satellites, enable the determination of geophysical properties, such as heat flow, that are otherwise not quantifiable without an expensive surface mission. In this chapter, we review the current state of knowledge of the rheological properties of materials appropriate to understanding tectonic behavior and interior dynamics for the terrestrial planets as well as the major Jovian satellites. We then discuss the utility of experimentally constrained constitutive equations in understanding large-scale processes on Venus, Mars, Europa, Ganymede and Io.

Introduction

Historically, much of our understanding of the deformation behavior of planetary materials derives from experimental investigations undertaken to explore the mechanical properties of minerals and rocks as related to tectonic processes on our own planet, Earth.

There are few periods in the history of science that compare to the explosion of knowledge from robotic and manned exploration of the bodies of our solar system over the last 50 years. In this golden age of planetary exploration, hundreds of thousands of detailed images of the terrestrial planets, the outer planets and their icy satellites, and many asteroids and comets have been obtained by manned and unmanned spacecraft. In the near future, spacecraft already in flight will complete surveys of our innermost planet, Mercury, and provide the first high-resolution images of outermost Pluto.

In the pursuit of understanding the origins and geologic evolution of the solid bodies in the solar system, many similarities and differences have emerged in the processes that shaped their landscapes. One of the most fundamental of these processes is tectonics. The number and diversity of tectonic landforms is truly remarkable. The investigation of these tectonic landforms has stimulated an equally diverse range of studies, from the characterization and modeling of individual classes of tectonic landforms to the assessment of regional and global tectonic systems. These investigations expose the complex interplay between the forces that act on planetary crusts, both internal and external, and the mechanical properties of crustal material.

Over the past several decades, planetary tectonics has become an important component at geoscience and planetary science meetings, conferences, and workshops worldwide.

Summary

Tectonic landforms on the Moon predominantly occur on the nearside, associated directly with the lunar maria. Basin-localized lunar tectonics is expressed by two landforms: wrinkle ridges, and linear and arcuate rilles or troughs. Wrinkle ridges are complex morphologic landforms found in mare basalts, interpreted to be contractional tectonic landforms formed by thrust faulting and folding. Linear and arcuate rilles are long, narrow troughs, interpreted to be graben formed by extension, deforming both mare basalts at basin margins and the highlands adjacent to the basins. In contrast to basin-localized tectonics, landforms of the nearside are the more broadly distributed lobate scarps. Lobate scarps on the Moon are relatively small-scale asymmetric landforms that are often segmented with lobate margins. These landforms are the surface expression of thrust faults and are the dominant tectonic feature on the lunar farside. Crater density ages indicate that crustal extension associated with lunar maria ceased at ~3.6 Ga. Crustal shortening in the maria, however, continued to as recently as ~1.2 Ga. The cessation of extension may have resulted from the superposition of compressional stresses from global contraction on flexural extensional stress due to loading from the mare basalts. The lobate scarps formed less than 1 Ga and appear to be among the youngest endogenic features on the Moon. The presence of young lobate scarp thrust faults supports late-stage compression of the lunar crust.

Summary

Solar system bodies smaller than ~200 km mean radius have little internal heat energy to drive tectonics typical of the terrestrial environment. Short-lived high stresses from impacts or long-term, low stresses are the primary shapers of these bodies. This chapter provides an overview of the basic features and processes that can be regarded as small-body tectonics.

Introduction: types of small bodies, their properties, and environments

Small bodies of the solar system are here taken to be those too small for gravitationally driven viscous relaxation to have determined their shapes. This definition restricts consideration to objects less than about 150 km radius (Johnson and McGetchin, 1973; Thomas, 1989). Within this definition are some dozens of satellites of planets, and thousands of asteroids, cometary nuclei, and Centaur and Kuiper-Edgeworth belt objects (Binzel et al., 2003). As of early 2006, spacecraft have visited small satellites, asteroids, and four cometary nuclei (Figure 6.1). Resolved information on these objects is dominated by the NEAR mission that orbited and then landed on 433 Eros, by images of the Martian satellites, Phobos and Deimos, and by images of comet Tempel 1 (A'Hearn et al., 2005). Radar images of near-Earth objects are beginning to show some details of asteroid shapes and surface features (Hudson et al., 2003). Meteorites provide small samples of asteroids, though only in the case of asteroid Vesta (larger than the size range considered here) are there positive connections of meteorite samples to a specific object (Binzel et al., 1993; Keil, 2002).

Summary

Tectonic features on the satellites of the outer planets range from the familiar, such as clearly recognizable graben on many satellites, to the bizarre, such as the ubiquitous double ridges on Europa, the twisting sets of ridges on Triton, or the isolated giant mountains rising from Io's surface. All of the large and middle-sized outer planet satellites except Io are dominated by water ice near their surfaces. Though ice is a brittle material at the cold temperatures found in the outer solar system, the amount of energy it takes to bring it close to its melting point is lower than for a rocky body. Therefore, some unique features of icy satellite tectonics may be influenced by a near-surface ductile layer beneath the brittle surface material, and several of the icy satellites may possess subsurface oceans. Sources of stress to drive tectonism are commonly dominated by the tides that deform these satellites as they orbit their primary giant planets. On several satellites, the observed tectonic features may be the result of changes in their tidal figures, or motions of their solid surfaces with respect to their tidal figures. Other driving mechanisms for tectonics include volume changes due to ice or water phase changes in the interior, thermoelastic stress, deformation of the surface above rising diapirs of warm ice, and motion of subsurface material toward large impact basins as they fill in and relax.

Summary

Venus has a pressure-corrected bulk density that is only 3% less than that of the Earth. In contrast, the surface environments of these two planets are very different. At the mean planetary radius the atmospheric pressure and temperature on Venus are 95 bars and 737 K, respectively. Liquid water cannot exist on the surface, which implies the absence of the processes most effective for erosion and sediment transport on Earth. The planet is completely shrouded in clouds, and temperatures of the lower atmosphere do not vary much from equator to poles, resulting in winds not capable of significant erosion. Most of the materials exposed on the surface of Venus apparently formed during approximately the last 20% of solar system history, with no significant clues to conditions on the planet during prior eons. Because the dense atmosphere has destroyed small bolides, the smallest surviving impact craters have diameters of ~2 km, and the total population of impact craters is less than 1000. The dominant terrain on Venus is plains, which constitute ~80% of the planet's surface. Impact craters are randomly distributed on these plains, and thus differences in the relative age of surface materials based on differences in crater frequency are not statistically robust.

The global topography of Venus does not include the diagnostic plate-boundary signatures that are present on Earth, and thus plate tectonics has not been active on Venus during the time represented by the current surface materials and features.

Having seen how the need for rational inference leads to the Bayesian approach for data analysis, we illustrate its use with a couple of simplified cosmological examples. While real problems require analytical approximations or Monte Carlo computation for the sums to be evaluated, toy ones can be made simple enough to be done with brute force. The latter are helpful for learning the basic principles of Bayesian analysis, which can otherwise become confused with the details of the practical algorithm used to implement them.

Introduction

In science, as in everyday life, we are constantly faced with the task of having to draw inferences from incomplete and imperfect information. Laplace (1812, 1814), perhaps more than anybody, developed probability theory as a tool for reasoning quantitatively in such situations where arguments cannot be made with certainty; in his view, it was ‘nothing but common sense reduced to calculation’. Although this approach to probability theory lost favour soon after his death, giving way to a frequency interpretation and the related birth of statistics (Jaynes 2003), it has experienced a renaissance since the late twentieth century. This has been driven, in practical terms, by the rapid evolution of computer hardware and the advent of larger-scale problems. Theoretical progress has also been made with the discovery of new rationales (Skilling 2010), but most scientists are drawn to Laplace's viewpoint instinctively.

In the past few years, several introductory texts have become available on the Bayesian (or Laplacian) approach to data analysis written from the perspective of the physical sciences (Sivia 1996; MacKay 2003; Gregory 2005).

Signal separation is a common task in cosmological data analysis. The basic problem is simple to state: a number of signals are mixed together in some manner, either known or unknown, to produce some observed data. The object of signal separation is to infer the underlying signals given the observations.

A large number of techniques have been developed to attack this problem. The approaches adopted depend most crucially on the assumptions made regarding the nature of the signals and how they are mixed. Often methods are split into two broad classes: so-called blind and non-blind methods. Non-blind methods can be applied in cases where we know how the signals were mixed. Conversely, blind methods assume no knowledge of how the signals were mixed, and rely on assumptions about the statistical properties of the signals to make the separation. There are some techniques that straddle the two classes, which we shall refer to as ‘semi-blind’ methods. They assume partial knowledge of how the signals are mixed, or that the mixing properties of some signals are known and those of others are not.

There is a large literature in the field of signal processing about signal separation, using Bayesian techniques or otherwise. For any cosmological signal separation problem, it is almost always the case that someone has already attempted to solve an analogous problem in the signal processing literature. Readers who encounter a problem of this type, which is not already addressed in the cosmological literature, are encouraged to look further afield for existing solutions.

Once planetesimals have formed, the dominant physical process that controls further growth is their mutual gravitational interaction. Conventionally the only further role the gas disk plays in terrestrial planet formation is to provide a modest degree of aerodynamic damping of protoplanetary eccentricity and inclination. In this limit the physics involved – Newtonian gravity – is simple and the problem of terrestrial planet formation is well posed. It is not, however, easy to solve. It would take 4 × 109 planetesimals with a radius of 5 km to build the Solar System's terrestrial planets, and it is infeasible to directly simulate the N-body evolution of such a system for long enough (and with sufficient accuracy) to watch planets form. Instead a hybrid approach is employed. For the earliest phases of terrestrial planet formation a statistical approach, similar to that used in the kinetic theory of gases, is both accurate and efficient. When the number of dynamically significant bodies has dropped to a manageable number (of the order of hundreds or thousands), direct N-body simulations become feasible, and these are used to study the final assembly of the terrestrial planets. Using this two-step approach has known drawbacks (for example, it is difficult to treat the situation where a small number of protoplanets co-exist with a large sea of very small bodies), but nevertheless it provides a reasonably successful picture for how the terrestrial planets formed.

Introduction

One of the principal aims of cosmology is to identify the correct cosmological model, able to explain the available high-quality data. Determining the best model is a two-stage process. First, we must identify the set of parameters that we will allow to vary in seeking to fit the observations. As part of this process we need also to fix the allowable (prior) ranges that these parameters might take, most generally by providing a probability density function in the N-dimensional parameter space. This combination of parameter set and prior distribution is what we will call a model, and it should make calculable predictions for the quantities we are going to measure. Having chosen the model, the second stage is to determine, from the observations, the ranges of values of the parameters which are compatible with the data. This second step, parameter estimation, is described in the cosmological context by Lewis and Bridle in Chapter 3 of this volume. In this article, we shall concentrate on the choice of model.

Typically, there is not a single model that we wish to fit to the data. Rather, the aim of obtaining the data is to choose between competing models, where different physical processes may be responsible for the observed outcome. This is the statistical problem of model comparison, or model selection. This is readily carried out by extending the Bayesian parameter estimation framework so that we assign probabilities to models, as well as to parameter values within those models.