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The Biggest Banana Peel on Earth

Understanding the San Andreas Fault and the Mechanics of Earthquake Generation

John Townend
Department of Geophysics
Stanford University
June 2001

What causes earthquakes? Many of us have pondered this question, but despite the devastating role in human society that earthquakes have played for millennia, the mechanisms by which earthquakes are triggered and interact are still poorly understood.  My work involves trying to measure stresses within the Earth in order to quantify the strength of big faults, such as the San Andreas, and to elucidate the mechanics of earthquake generation.

The San Andreas Fault (SAF) system, which runs the length of California, is in many ways archetypal: seismically active and geologically divisive, it forms a major component of the boundary between the Pacific and North American tectonic plates. Ironically, while the mechanics of smaller and less significant faults are well understood, those of the intensively studied SAF are highly enigmatic. In particular, the fault appears to behave as if it were extraordinarily weak (much like a slippery banana peel). In comparison, laboratory data and data from smaller faults indicate almost unequivocally that rocks have much higher friction and are generally resistant to slipping.

Two lines of evidence suggest that the SAF is weak: heat flow data and estimates of the forces driving motion.  Heat flow data relates to the fact that a slipping fault is expected to generate appreciable amounts of frictional heat, for exactly the same reason as rubbing your hands together warms them up.  Data collected from throughout California do not reveal any sign of the thermal anomaly expected after millions of years of rocks sliding past each other, and suggest, therefore, that the fault is perhaps lubricated. 

It has also been observed that the SAF slips in response to very low driving forces.  Small faults and laboratory samples behave similarly to your shoe on concrete; unless the ground slopes quite steeply, there is enough friction ("grip") for you to maintain balance. Stand on a wet banana peel, however, and no matter how gentle the slope, you're quite likely to fall over; the SAF behaves more like the banana peel than the concrete. This is a significant observation since it has strong implications for the manner in which a small earthquake might trigger a larger one nearby (and vice versa), and for the maximum size of earthquake any particular segment of the fault might produce.  Nevertheless, the data pertaining to the strength of the SAF have been, until recently, quite sparse, and have consequently led to much disagreement and controversy in the geophysical community about exactly how representative and trustworthy they are. To really understand the mechanics of the fault, we need to clearly understand what is driving the slip.

An earthquake occurs when rock breaks along a fault. Consider snapping a pencil in two. As you bend it further and further, the forces acting in the middle of the pencil increase to a point at which the wood itself is unable to sustain any more loading: crack! Whether or not the pencil breaks would seem intuitively to depend on whether you've subjected it to a force that exceeds its intrinsic strength.  Determining whether or not an earthquake will occur is, at least in principle, an analogous problem of comparing the various forces acting on a fault to the fault's overall strength.

Determining the forces acting on a fault and the fault's strength is not as straightforward as you might think.  For one thing, the very concept of "force" is not very convenient for describing earthquake mechanics, and it's generally force per unit area, or “stress,” that's important when we're thinking about things breaking. For example, it's quite comfortable to balance on one foot on the floor, but astonishingly painful to try balancing on a nail. The force you apply (your weight) is the same in both cases, but because the area of the patch of floor you stand on is 10,000 times larger than the area of a nail, the stress is 10,000 times less, and it's the stress that your foot and brain register.  Also, we need to keep track of stresses acting in all directions at different points in space. In terms of the pencil analogy, we need to be able to quantify the stress magnitudes in various directions throughout the entire pencil. To be completely thorough, this requires six separate stress components, usually given in the form of a matrix, referred to as the stress tensor. In these terms, my research is based on determining the components of the stress tensor and relating these to fault strength and earthquake mechanics.

Measuring stress in rocks several kilometers underground, however, is difficult when you're confined to the Earth's surface. One way to circumvent this problem is to make use of earthquakes themselves.  If we assume that all the earthquakes occurring in a sufficiently small volume of the Earth's crust are responding to the same stress tensor, we can then use the geometry of these earthquakes to tell us what this corresponding stress tensor is. Once again, though, we can only determine the geometry of the earthquakes indirectly, by means of surface-based seismometers.

The first seismic wave that arrives at a particular seismometer following an earthquake jolts the seismometer either towards or away from the earthquake source, depending on the relative location of the seismometer and the type of earthquake.  An earthquake occurring in the middle of a network of seismometers produces a systematic pattern of first motion polarities. The spatial distribution of these polarities is referred to as the earthquake's "focal mechanism" and is related to the geometry of the fault that produced the earthquake and to the corresponding slip vector. It is a group of these focal mechanisms (one for each earthquake in a small region) that we use in order to find the stress tensor, via a procedure known as stress inversion.

This is where my research comes into play. What we need to do is take all the earthquake focal mechanism data in a particular region and invert the data to find the stress tensor.  To "invert," in this context, means to find the stress tensor that is most consistent with all the focal mechanisms, a problem similar to that of finding the straight line which best fits a set of data. Each focal mechanism represents two pieces of information related mathematically by the stress tensor: fault orientation and the direction in which the fault slipped during an earthquake. We assume that all earthquakes obey the same physics, and this enables us to look for a single stress tensor which best relates the different fault orientations to their corresponding slip directions.

My contribution has been to develop a more sophisticated method of grouping focal mechanisms prior to inversion, so as to make the best use possible of the data while at the same time satisfying the constraint that the stress tensor affecting each of the earthquakes is the same. The stress tensor is likely to vary spatially and perhaps with time as well, and so ideally we would like to be able to determine it on as small a scale as possible. But the smaller the area we focus on, the fewer focal mechanism data we have and the less reliable the stress inversion becomes.  Using my method, we have found it possible to estimate the stress tensor at almost 400 locations in southern California, giving us a very detailed image of how stress varies in the vicinity of the SAF and its associated faults.

The independent results that emerge are reassuringly consistent with each other, and yet still difficult to explain.  Representing the stress tensor at each location by an arrow showing the orientation of the axis of greatest horizontal compressive stress, we have discovered that throughout most of southern California this direction is almost orthogonal to the SAF orientation. The greatest compressive stress (analogous to your weight) is almost perpendicular to the fault plane (the banana peel) and yet the fault (you!) slips. The component of stress driving slip on the fault is much smaller than the component of stress orthogonal to the fault (which simply pushes the two sides of the fault together), implying that the fault slips under very low levels of driving force.

For the SAF to continue slipping under these circumstances, it must probably be lubricated by, for instance, rocks of very low friction or a fluid such as water lining the fault.  Unfortunately, a suitably slippery rock has not been identified, nor has any conclusive evidence for the presence of fluids in the fault zone been obtained.  Determining which of these alternatives, or perhaps an as yet unconsidered mechanism, is responsible for the SAF's weakness is important because it is likely to elucidate how individual earthquakes are triggered and how they subsequently trigger other earthquakes.

With our new results, we can say quite confidently that the SAF slips in response to very low driving forces, and is correspondingly weak.  Why this is the case, given the discrepancy with laboratory measurements and data pertaining to much smaller faults, remains enigmatic.  Nevertheless, it appears that we have progressed from facing the question of whether the fault is weak, to the more specific questions of why and what it means in terms of producing earthquakes.