Introduction to Earth Sciences

Geophysics section


Preface and Course Objectives

Imagine you are a visitor from another world and you have come to earth for one semester. You have been given the mission of learning enough to be able to make the entry under "Planet Earth" in the encyclopedia of your home world. What would you write? This is by no means a trivial question. You don't have much time and it is immediately apparent on arrival that the earth is a large and complex object. Solids, liquids and gases are present and all are in some sort of motion, even the solid part, and there are distinct interactions between these components. There are numerous life forms and it is apparent that one species - humans - has come to dominate the earth to such an extent that it can alter the earth's solid, liquid and gaseous systems. Some of the humans seem to be worried about the way they are changing these systems; others don't. Somehow the basics of this planet have to be described usefully, without an undue amount of precis.

The task of the visitor and the objective of this course are fairly similar. I will try to impart some of the essentials of what we know about our planet. To do this I will use some of the critical results of modern Earth science research, placed in a background of some historic studies of the Earth. I will emphasize physical aspects of the Earth -- Geophysics -- rather than the chemical aspects that will be described by Professor Langmuir in his lectures.

In addition to the simple transfer of information (me describing to you some things that we know about the Earth) I will explain howwe have come to know these things. Remember that most of the Earth is fundamentally inaccessible. Except for the surface layers we walk on, and some layers that have been exposed by tectonic motions from original depths of maybe 10 kilometers, the great majority of the Earth cannot be examined first hand. In this way the deep earth is like outer space or the inner atom; we are required to infer what is going on in the Earth's deep internal processes from expressions of those processes on the surface, a very great distance from where they are acting. Just how this inference is done is an underlying theme of these lectures.

This inference has limits which means that the knowledge we have always involves some measure of uncertainty. Almost nothing we know about the Earth is known with certainty. This is not unique to Earth science, of course, and actually applies to all of physical science. We are also going to discuss those limits and uncertainties, even though, in most college Earth science texts, such limits are almost never discussed. One of the most important reasons for attempting to understand limits and uncertainties is because they fundamentally govern our ability to predict the future behavior of the Earth; to say when an earthquake might take place, a hurricane might make landfall, or a dramatic shift might take place in the earth's climate.


The Meaning of "Understanding" in the Earth Sciences

The objective of Earth science is develop an understandingof how the Earth functions as a dynamic body in space. But first, we have to ask ourselves very clearly what it is we mean when we say we understand something that we generally cannot directly observe, and how the limits to understanding are described.

"Understanding" means very different things to scholars in different fields. The processes of knowledge creation in different epistemic cultures within science, even within the Earth sciences are surprisingly diverse. There are major differences between geochemistry and geophysics.

To most physical scientists the notion of understanding has a fairly restricted meaning - to say that a process is understood means that we have derived a theory or a model that can account for some observed behavior (of the Earth) which is the result of that process. As such, the theory can be thought of as something that connects one set of information with another.

To illustrate, information in the physical sciences can generally be separated into two types.


Our task, very often, is to derive what we want to know (the information we don't have) from what information we do have, and that requires a theory.

For a very simple example we observe that in most parts of the Earth the weather changes throughout the year in a repeatable manner which we call "seasons". We also know that the seasons oppose each other in north and south hemispheres - when its summer in New Zealand its winter in New York. This is what we know and we need a theory to explain this. The operative theory is one involving gravitational forces and other information - planetary motions and solar radiation. We could call this the "theory of the seasons" and it connects one set of information (planetary motions etc.) that we didn't observe, with another set of information (the global variation of seasons) that we did observe.

To state this in a little more detail: We usually refer to the information we have in hand as data because it is typically derived from a set of direct measurements or observable quantities (the temperature of the atmosphere, the topography of mountains or the seafloor). The inferred information is sometimes thought of as parameters (viscosity of the Earth's core, rate of convection in the mantle), information that is not measurable, but must be derived from measurable information. Scientists now have some very sophisticated measuring devices to produce data. It is critical to recognize that these measurements that produce data do not in and of themselves produce understanding, they only give descriptions of the Earth, ways of quantifying its behaviour and form. These data are typically both incomplete and inexact - we do not have measurements of rainfall everywhere, for instance. It's quite difficult to determine how much rain falls over the oceans. Similarly, earthquakes are very non-uniformly distributed (many around the Pacific rim, few in the eastern U.S.) and cannot be located to better than a few kilometers. Any uncertainty in the observed information will always be transmitted into uncertainties in the inferred information (the parameters); usually these uncertainties are amplified.


More generally we describe a system of interest by numerous quantities -


these quantities may be geophysical, geological or something else. All are included in a description of the system under study. As noted above we can divide them into data and parameters.

Let's call them the sets


for that data we can measure, and



for the parameters we have to infer from those data. To understand the system we say the following very important thing:

We seek to estimate the minimum set of parameters, , that fully describe the system; together with the physical laws that relate the parameters to the things we can observe.


The "laws" that connect the parameters to observed data can also be thought of as theories or models.

Going from left to right in this diagram is called the "forward" problem. Going from right to left (more normal because we go from observed data to inference) is called the "inverse" problem. Both are studied in geophysics.

One of the most important things we can do is solve this problem in a way that leads to a useful results. By this we typically mean ways in which the solution can be used to predictthe future behavior of the system. In our simple example the observed seasons (data) are connected to the way the Earth rotates on its axis and revolves around the sun and other factors. There exist a small number of orbital parameters which can be used with the theory of gravitation and solar heating to explain the seasons. This theory allows us not only to predict when the next season will arrive (not hard to do), but other things like the date and time of eclipses. Such predictions are very, very accurate. We can say that we understand the seasons, because we know what causes them, we know why they repeat and why they are opposed in north and south hemispheres, and we can predict ahead aspects of the changing seasons.

This example is perhaps a little trivial you might think because one hardly needs a theory to predict that winter will follow fall. Our experience is enough to tell us that. However, many aspects of climate and weather are not so predictable. The El Nino is a climate phenomenon that visits us from time to time (generally not more often that four years and almost always within seven years) and significantly impacts the economies of some developing countries, particularly in Latin America and Africa. Its predictability is much less that the seasons of course but the same ideas hold -- we make observations about the El Nino and construct a theory of its behavior which involves the physics of fluids and connects to a set of parameters that control the system. From that we can predict, but with quite a bit of uncertainty, when the next El Nino might occur.


Understanding Systems

What I have described above has validity for a single process. The visitor with the task of compiling the encyclopedia entry would quickly realize that the Earth is an interacting web of many processes -- a systemdriven by internal and external forces, responding as a complete whole. It is not apparent that the integrated behavior of the system can be deduced by simply summing the behavior of the components. How do we go about understanding a system.

Let's start with the way we deduce theories. The structure of the process often involves three components.


We make observations, analyze them, and derive a theory to explain them by connecting to other information.

Overlying this 3 component structure are two differing philosophies or epistemologies: One Reductionist, the other Holistic.

The reductionistapproach says that any physical system such as the Earth is too large and complex to study as a whole, so we reduce it to an irreducible unit, study it to gain an understanding of that unit, then infer the behavior of the system as a whole by somehow summing the behavior of many components, in a type of collage.

This approach has dominated the physical sciences for centuries, and is the basis on which we have constructed much of our understanding about the Earth.

The holisticor whole system view says that systems have systems behavior that cannot be predicted by simply summing the behavior of the component pieces. In fact, i would argue that there are no separable components, that everything interacts with and is affected by its environment. These systems properties are known as emergent properties, and may change as the systems evolve with time. To see them we need macroscopes, not microscopes.

This is a very new view and it has come about largely because it has been possible to produce simulationsof complex systems using large computers to describe their behavior. The reductionist view prevailed at a time when we had insufficient analytic capabilities to deal with systems as a whole.

To deal with entire systems there has evolved a whole new way of thinking, and alternate epistemology, and with it a whole new language. It is a new way of knowing and understanding. It involves such concepts as -

Chaos, Scale-invariance, Fractal Geometries, Self-similarity and

Self-organized criticality.

I'll try to explain the latter using a now-classic experiment performed by Per Bak. It involves a pile of sand.

Bak made an apparatus in which he dripped sand at a regulated rate from a sort of sand faucet onto a circular plate. Initially, a simple sand pile is built up. The slope on the sides of the pile (called the angle of repose) can be used to estimate the coherence of the sand grains - stickier grains make steeper sand piles. The pile grows at a rate governed by how fast the sand is dripped out. At some point, however, the pile will always begin to collapse with addition of more sand, without changing the rate at which the sand is dripped from the faucet. Avalanches begin to form down the sides of the sand pile, as illustrated.


When avalanches begin the pile has reached a critical state in which it is beginning to fall apart. Many different sizes of avalanches occur even though there is no change in the sand dripping rate or any other aspect of the experiment. So the system's observable response is highly variable although the driving force doesn't change. Most important Bak observed that the

time, location and size of avalanches were unpredictable

What that meant is that studying any one avalanche, no matter how carefully, cannot enlighten us as to when, or where, or how large the next one will be. That is, reductionism (study of the unit components) fails to lead to an understanding of the dynamic behavior of the system as a whole. Studying an avalanche can lead to an understanding of the physics of avalanches (why any one occurs) but not to the dynamics of the sand pile.

How then can we learn about the system ? We need to observe the system in a different way. Instead of focusing in on the individual avalanches we need to assemble information on all the avalanches.

So we collect up the sand from each avalanche and put it in a bag. Some will be small, some big, some in-between. Then arrange them in order of size, and determine if there is any information in the ordering by making a simple graph of the incidence of bags of a particular size.

Note that on this graph we have set out the axes in a different way from normal - equal increments go in powers of ten rather than unit steps. This is called a logarithmic scale and is critical to the analysis.

What we discover when we make such a plot is that there is a clear relationship between avalanche size and number of avalanches, even though we cannot predict the size of any particular avalanche in advance. Part of it may seem a bit obvious in that there are relatively few large avalanches and a great many small ones. But the straight line on a plot like this says that there is a "power law" relationshipbetween avalanche size and frequency of occurrences. That is, the greater occurrence of small landslides is related to the lesser occurrence of large ones. This type of power law behavior is typical of self-organized critical systems. Thus, in an overall system sense there is order in the system. The number of small avalanches is related to the number of large ones in a predictable way, even though individually they cannot be predicted. It turns out that this aspect of systems is very common indeed.

Earthquake magnitudes and many other important phenomena in the Earth are well known to behave the same way.






This power law behavior of earthquake magnitudes has been used to argue that, like the sand pile, the Earth is essentially falling apart; the crust is always near failure, having reached a critical state through accumulation of large scale stresses. Just like the sand pile avalanches, the study of any one earthquake can tell us very little about when, where or how big the next earthquake will be. We can learn about the mechanism of earthquakes, but not their system properties, and it is the latter that we need to predict them (we return to this topic later).


The following show actual earthquake data - one for global earthquakes with magnitudes greater than 5, the other for earthquakes in southern California with magnitude greater than 4. The earthquakes do not fall perfectly on a straight line, but are nevertheless quite close.



The rate of occurrence of forest fires in four different parts of the world follows the same power law distribution as earthquakes. Forest fires are, of course, a completely different phenomenon from earthquakes or sandpiles, yet they too display a power law relationship.



The near universality of the power law distribution of sizes has intrigued many scientists since it was first recognized. Some think it a deeply profound expression of how nature behaves as a system that leads to a deeper understanding of the Earth. For us, it says that often there is an ordering underlying systems that may seem to be quite disordered, and that the study of systems like the Earth requires approaches that acknowledge the system dynamics of the Earth as a whole, rather than focusing on a single part of the system.

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