"The striking similarity of the coastlines of Africa and Brazil must have been made by Satan."

-- Schuchert, 1928

As we now turn our attention to the internal processes in the Earth that drive catastrophic earthquake and volcanoes, let us take stock of the Earth that resulted from the topics covered in the first part of the class. It is a planet born in fire and storm. There are vast stores of heat energy within the interior, residual from the energy of accretion, core-formation, and radioactive decay processes that we have reviewed. The Earth's fluid envelopes, the oceans and atmosphere, were progressively exhaled by volcanic eruptions. The surface was again and again struck by large meteorites, but most of the scars of bombardment have been healed by cycling of the ocean floor or erosion of the continental surface. Life evolved on the planet, punctuated by rapid catastrophic environmental changes due to massive volcanism, impacts, and sea-level changes.

While the bombardment from space has slowed, and now involves rare chance events (that may or may not intersect and/or terminate human existence), the Earth rumbles along, producing a steady diet of catastrophic upheavals for those that dwell on its surface. Those associated with the atmosphere and oceans (storms, glacial ages, changes in atmospheric chemistry, changes in ocean nutrients) are largely due to variations in solar energy influx. Earthquakes and volcanoes arise from deep-seated processes that we will strive to understand. It is the cooling of the Earth that supplies the energy for these phenomena, and the pace of cooling is such that there has always been and will be for long into the future a steady supply of both earthquakes and volcanic eruptions.

We begin by considering the Earth stripped of its fluid layers. The globe is then most dramatically a bimodal surface, with 30% elevated continents and 70% deep oceans. These surfaces are themselves not level, with high chains of mountains in both the continents and the oceans, and very deep ocean trenches around much of the Pacific ocean margin. There is rough topography on both the ocean floor and on the continents, which must withstand the flattening tendencies of erosion. We will see that the roughness is itself a manifestation of deep dynamics.

The continents are the most accessible regions, and have been extensively studied by humans, both in the pursuit of economic resources and in the quest for understanding of how they evolved. The crust of the continents is comprised of relatively low density rocks (relative to oceanic crustal rocks), which are the result of extensive melting of early Earth mantle and segregation of the lighter components into the continental crust. This process began early in the Earth, and so the rocks of the continents, which are too buoyant to sink back into the mantle, preserve a 4 billion year history of the planet's surface. The light continental crust has an average thickness of 40 km, with a root extending downward much as the root of an iceberg compensates for the high elevation of ice above the sea level. The crust is embedded within the lithosphere, the stiff, coherently translating portion of the upper mantle. The lithosphere under oceans is 70-100 km thick, while under continents it is as much as 350 km thick. Thus, there is a deep 'keel' of stiff material under the continents, extending downward in a conical shape that has remained attached to the continental crust for great periods of time.

So, do continents really 'drift'? This notion is one that dates back to the work of Alfred Wegener, a meteorologist working in the 1920's. He was a very experienced traveler and naturalist, and he argued that continental drift has occurred based on several lines of evidence. The first was the remarkable symmetry of the eastern South American and western African coast lines. If one closes up the Atlantic, the puzzle pieces of the continents fit together amazingly well, and North America also contracts well back onto the northern coast of Africa and the western coast of Europe. Wegener also argued that connecting up the continents was required in order to explain continuity of geological structures across the boundaries of South America and Africa. Furthermore, fossil dinosaurs (and plants) of the same species are found in Brazil and southwestern Africa. These organisms could not swim great distances, so there was either a land bridge across the Atlantic (now sunk out of sight?) or the continents were close together. Wegener also noted that there is evidence for past differences in locations of all continents, such as the presence of areas with scars of past glaciation located near the equator today.

But, the idea of large lateral motions of the continents, or Continental Drift, met great resistance. In part, this stemmed from the conservatism that had gripped the early geologists, fostered by the ideas of Uniformitarianism and the legacy of Hutton and Lyell. Moving continents around smacked of catastrophism, and was dismissed as improbable. In part, the human experience was again a limiting perspective. While the notion of slow vertical motions was broadly accepted, as required to explain the exposure of marine fossils high in the Alps, this was viewed as a consequence of localized buckling and folding of the surface, with changes in sea level. The Earth still seemed very rigid overall, and unable to endure large horizontal motions of continents. There was also a focus on local observations, the result of the intensive localized geological studies that were mapping out the fossil record and the history of rock formation at each site around the world. There was not a global perspective, sitting back from the planet and viewing it as a dynamic system.

Wegener published maps with continental reconstructions dating back 100 million years or so, and argued forcefully that this had taken place, but geologists and physicists responded by saying that there is no mechanism to propel continents through a sea of ocean floor, and despite the logic of some of Wegener's arguments, he must be wrong. Sir Harold Jeffreys quibbled with the continental reconstructions, arguing that the fit is not really all that good, and there are 15 degree mismatches (this overlooked the then unknown extent of the submarine continental shelves of Africa and South America). Other notions were proposed, and gained some currency in the frustrating search for a reconciliation. One was the notion advanced by Warren Carey of an Expanding Earth, which in the past had a smaller radius, bringing the continents back into connection. This idea persisted from the 1930s to the 1950s, and even finds some supported today. However, no mechanism for expanding the Earth could be found; there simply is no source of energy to do this, and the idea languished.

In the late 1950s and early 1960s there began a revolution in the thought about the Earth, and the mobility of the surface. This is the time of the Plate Tectonics revolution, and the old ideas of a geologic history dominated by localized vertical motions has given way to a history of vast horizontal motions of the surface continents and even of the ocean floors. The observations that underlay this hypothesis are numerous, and some were around for many decades prior to the synthesis that took place in the mid to late 1960s. However, some new observations were essential to making the puzzle fit together (so to speak), and as with many scientific advances, it was the confluence of completely unexpected lines of study that made the breakthrough possible.

One of the essential lines of evidence was the global observation of earthquake locations. This was mapped out in primitive form as early as the mid-1850s (at least on the continental regions where there was history of earthquakes occurring in long belts of activity). Advances in the study of earthquakes, or the field of Seismology, had led to accurate global earthquake locations around the world by the 1930s. If one looks at relatively shallow events, in the upper 60 miles of the Earth, the distribution of events is non-uniform, with long chains or bands of earthquake activity lying out in the oceans, and around the margins of the Pacific ocean. The latter region is also ringed with volcanoes, leading to the "Ring of Fire" observation. Following the 1906 San Francisco earthquake disaster, it was quite well established that earthquakes involve sliding of rock across breaks in the ground or faults. Thus, the earthquake distribution clearly reflects where there is active deformation and breaking of rock around the Earth. So, what causes the long chains of earthquake activity and the concentration in regions near volcanoes? Another puzzle was that by the 1920s it was clearly established that some earthquakes occur deep in the mantle, down as deep as 700 km. This was particularly difficult to understand, since the pressures and temperatures at such depths are such that rock is expected to deform ductily, and there should be no abrupt breaking of rock or sliding on faults. The physicists fought for a long time, arguing that deep earthquakes (below 100 km) could not exist, and the seismologists must be locating them incorrectly, but improved models of the seismic wave properties of the Earth reaffirmed the observation. The deep events are also not uniformly distributed, but occur in limited regions, primarily around the Pacific margin. No deep events are found out under the central oceans. The question then became; how to explain the occurrence and location of deep earthquakes? The answer was not forthcoming for many decades after the basic observations were accepted.

The most critical line of observations that broke through the resistance to large-scale horizontal motions came from the unlikely area of studying the Earth's magnetic field. The magnetic field is produced by a complex system of convection in the outer core. The spinning rotation of the Earth and the presence of the solid inner core cause outer core convection to occur in cylinders aligned with the spin axis. The motion of the molten iron alloy causes free electrons in the iron to move, which generates an electric current. Any electric current produces a magnetic field. While the flow in the core is very complex geometrically, the net result of the constructive and destructive interference of magnetic fields is that there Earth has an overall dipolar field aligned with the spin axis. The field is generated by what is called Dynamo action in the core flow.

For several hundred years, humans had exploited the general dipolar geometry of the Earth's magnetic field, as observed at the surface, primarily for navigation. The symmetry of the dipole field, which has north and south magnetic poles very close to the north and south poles of the rotation axis, causes a systematic variation of magnetic field direction with latitude on the surface. Magnetized needles align with the field to point north-south at the surface, but there is also a varying dip to the magnetic direction with latitude. For example, the field is nearly horizontal at the equator, and steeply dipping at the poles. From centuries of observations, it was recognized that the magnetic field of the Earth actually varies with time, and there are small deviations from a perfect dipole geometry. This is the result of the complex dynamo generation mechanism. But, there are also variations of intensity of the field, and for example, for the past few centuries the field has grown progressively weaker. If it were to continue to weaken at the current rate, in a few thousand years, the field would drop to zero. Has this ever happened? The answer lies in longer term records than available from the history of navigation.

Earth rocks often include small amounts of magnetic minerals, rich in iron, which act like little compasses at the Earth's surface. When a rock forms, by cooling from molten lava, or by sedimentation processes, the local magnetic field caused by the dipole, tends to make the cooling magnetic minerals align with the field. In effect, the little compass needles get frozen into the rock as it cools or sediments. Once hardened and cooled, these magnetic orientations are preserved. The rocks then record the direction of the magnetic field at their source of origin, and if the rocks move laterally, we can tell, because their magnetization will differ from that where they formed (if the latitude changes). Also, if the magnetic field points somewhere other than north as in the present field, we can tell that the rocks have either been deformed (tilted, bent, folded, etc.) or the magnetic field has changed with time.

What was found by geologists in the 1950s is that in a layer of rocks at a given site, which have not undergone significant deformation, the orientation of the magnetic directions tend to flip direction with time. For example, a sequences of lava flows near a volcano may have layer upon layer, but in some cases the magnetite is aligned with a field oriented toward the north pole, and in other layers of different ages the rock magnetic field is oriented to point southward. This remarkable observation provided evidence that the Earth's magnetic field REVERSES, while maintaining a nearly constant north-south alignment with the rotation axis, the field has alternated with time interchanging the north and south poles. This does not happen on a regular basis, but with a very erratic history of reversals. By dating the rocks, geologists established that the ancient magnetic field has flipped with a unique sequence, imprinting a bar code of magnetic orientations onto vertical sequences of rocks.

In the late 1950s and early 1960s, there was massive military sponsored mapping of the sea floor, particularly in the north Atlantic and north Pacific. This was largely for submarine warfare purposes, but included mapping of the detailed bathymetry (water depth) of the oceans and mapping of the magnetic properties of the seafloor (for aid in detailed navigation of submarines). The main magnetic property measured was simply the intensity of magnetic field (not direction) of the sea floor, obtained by trailing magnetometers behind large ships that made many tracks over the ocean floor. This revealed an amazing banded structure of ocean floor magnetization, with long, quasi-linear stripes of high or low magnetization. The zebra stripes suggested that somehow the ocean crust acquired bands of uniformly magnetized rock. Key observations were made across the mid-Atlantic ridge, where it was recognized that the stripes parallel the submarine volcanic chain of the ridge, and are symmetric on either side of the ridge. The sequence of stripes bore strong resemblance to the unique bar code of magnetic field history seen vertically in layered rocks. This suggested that somehow the ocean floor has a horizontally varying age analogous to the vertically varying age of a layer of rocks.

This led to the notion of Sea Floor Spreading, by which new rocks in the oceanic crust are created at mid-ocean ridges, by upwelling of molten rock. This rock that sunders and pulls apart laterally, allowing new rock to form in the gap in between the continued rifting apart of the crust, symmetrically spreading on either side of the ridge results in youngest rock at the ridge and increasingly older rock laterally in directions perpendicular to the ridge. The spreading occurs fairly steadily, and during the millions of years that pass by the magnetic field has reversed many times. This causes rock formed at different times (in long central bands at the ridge) to acquire alternating magnetization. The magnetic stripes are preserved in the rocks. The intensity variations detected by magnetometers reflect the constructive/destructive interference of alternately polarized magnetic directions relative to the Earth's present magnetic field.

This Sea Floor Spreading produces vast amounts of new ocean crust and underlying cooled and stiffened oceanic lithosphere that vary with age laterally from the sea floor volcanoes on the mid-Ocean ridge system. This system involves the mid-Atlantic, Indian, and Pacific ridges, which girdle the Earth. When rifting initiates, it may sunder overlying continents, as was the case for breaking apart South America and Africa, and the ongoing production of sea floor in between moves the continents laterally, resulting in Continental drift. The continents are not 'plowing through' the ocean floor, but are moving around as new ocean floor is created.

The production of new ocean floor must be balanced by destruction of old surface somewhere, if the net surface area of the Earth is to be conserved. Given the rapid acceptance of the overwhelming evidence for sea floor spreading, geologists looked for where the balancing mass flow could be located. Suddenly, it dawned on them that the areas of deep earthquakes, primarily in circum-Pacific regions represent areas of sinking old oceanic lithosphere. The unusually cold temperatures of the sinking lithosphere allow earthquakes to occur at depths where faulting does not normally exist. Regions where old oceanic lithosphere sinks into the mantle are called SUBDUCTION ZONES. These are areas with deep oceanic trenches, and large volcanoes exist in arcs on both continents and ocean islands, paralleling the deep trenches. These are the locations of the largest earthquakes and most explosive volcanic eruptions.

The long chains of earthquakes in oceans and on the Pacific margin are now recognized to outline the major chunks of the Earth's surface that constitute the plates of Plate Tectonics. These are large tracts of lithosphere that move coherently, growing on one side by the process of sea floor spreading, and being consumed on the other side by subduction. Where the edges of plates abut, there are different faulting processes that produce earthquakes, and there are melting processes that produce volcanoes. The entire surface of the planet is broken up into about 8 major plates and many smaller ones, all moving relative to one another.

Over time, plate tectonics has rafted continents around all over the surface of the Earth. We can use the magnetic record of seafloor to run the clock backward, closing up ocean basins such as the Atlantic and restoring past configurations of the continents. In doing this, we exploit the magnetic orientations preserved in continental rocks of varying ages to determine the latitude at which rocks formed. In addition, information about mountain building events, largely the result of collision between continents or subduction on continental margins, helps to constrain past positions of the continents. We can run the clock back with some confidence for a few hundred million years, and with diminishing confidence back to 600 million years. There have been intermittent aggregations of all of the continents into super continents such as Gondwanaland or Pangea, and also intervals of wide dispersal of the continents, much as we observe today. In addition, we can project the plate tectonic motions forward into the future for a few tens of millions of years, anticipating where new ocean floor will be produced at the mid-Atlantic ridge, and how the American continents will ride up onto the Pacific rise, subducting the ridge in the process.

The record of the large-scale lateral motions of plate tectonics is well established, and in fact can be actively measured today by space-based geodesy which allows instantaneous motions of the surface to be determined. The theory, now 30 years old has withstood many tests, and while some refinements have been made, it is the fundamental paradigm of the Earth Sciences, and guides most of our understanding of catastrophic processes such as earthquakes and volcanoes. The motions of the continents have also had direct effects on life, producing land bridges that allow lifeforms to expand from one continent to another, or long intervals of continental isolation, that allow one form of flora or fauna to come to dominate that may be distinct from other continents (as for the case of Australia and its dominance by marsupials). The connection of North and South America released a flood of highly competitive North American animals (tested in competition from Eurasian and African ancestors), which decimated more gentle forms that had dominated in South America. Plate tectonics has also affected climate, with continental collisions such as that which produced the high Himalayan mountains actually changing weather patterns and leading to the onset of the monsoon cycle which afflicts India and southeast Asia. When large continents are located at the high latitudes where ice can build up, sea level tends to decrease. There are many affects of plate tectonics that we will consider in the rest of this class. Our immediate attention will now turn to one of the most direct catastrophic by-products of Plate Tectonics: the occurrence of devastating EARTHQUAKES.

The 1995 Kobe, Japan earthquake caused more than $100,000,000,000 in damage, and took more than 5000 lives.

We have explored the evidence for large-scale motions of the Earth's surface involved in the process of sea floor creation, sea floor subduction, and continental motions. Over the very long time scale processes involved, the Earth's mantle can actually be viewed as a viscous fluid, flowing convectively in the attempt to get heat out of the interior. But, because the surface is relatively cold, this fluid-like behavior is modified, stiffening the fluid, and resulting in the brittle behavior of rocks. The realm of brittle behavior gives rise to rock fracture and frictional sliding, which is the source of earthquakes.

How can rock flow like a fluid on one hand, yet break brittly on the other? This is somewhat counterintuitive, given our day to day experience with rocky materials, but think back and you will recall times where you drove by a road cut and observed strongly distorted rock structures, folded and bent from their original horizontal layering without having fractured. There are two key factors that must be considered: The effects of time, and the effects of temperature. Time is important, for even under the action of a steady, but fairly weak force, such as gravity at the surface of the Earth, a rock can begin to flow like a fluid given long enough time. This is observed in ancient human structures, where pillars and columns of Greek temples are abnormally thickened in their lower extremes, and stained glass windows in old European cathedrals are very thin at the top. Yet, if you rap on the stone or glass with a hammer, the material will chip or shatter. In this case, rapid time scale forces produce a different behavior than long time scale forces.

In addition, the behavior of materials changes with temperature. As one heats up a rock it will behave more and more ductile for both short and long time forces. The composition of the rock also influences its time and temperature behavior, so not all rocks have identical properties. We call these mechanical properties Rheology, meaning the behavior of solid materials in response to applied forces. Because the temperature increases with depth into the Earth, the rheology varies with depth. This is accentuated by the chemical variations between crust and mantle. The region of Earth that is very high viscosity, or stiff and brittle, is the low temperature zone near the surface called the Lithosphere. This is stiff even for long-term forces, but can bend like a beam. In fact, oceanic lithosphere need not fracture to deform as it eventually sinks back into the mantle. The lithosphere under oceans varies from very thin (about 5-10 km) near ridges to about 70-100 km in the oldest regions (150-200 my) of oceanic plate. The upper portion of the lithosphere is the crust, which is about 6 km thick in oceanic regions, but most of the lithosphere is upper mantle rocks. Note the distinction here, the crust is different than the mantle because it differs in rock composition (oceanic crust is basalt, while the upper mantle under it is peridotite depleted in basaltic components). The lithosphere is not defined by chemistry, but by rheology, in that it is the stiff region that translates coherently as a quasi-rigid plate. Under a continent the stiff region may extend 150-300 km deep, making for very thick regions of plate.

Within the lithosphere, heat transports by conduction, which does not involve physical flow of the material as in convection. The temperature increases almost linearly with depth in a conducting region, as in the lithosphere, but near temperatures of about 1000 degrees the rheology of the rock begins to change very rapidly and it becomes more ductile. The material then flows readily, and does not translate laterally with the moving plate, but shears. This softer region, which accommodates the motions of the lithosphere is called the asthenosphere. It is not molten rock (although there may be small amounts of partial melting in some regions), but for both short and long term forces the material flows rather than breaks. So, if you hit it with a hammer, it would be gushy, not brittle.

While the lithosphere is pretty stiff for long-term forces, throughout much of the lower part of the lithosphere, the rock is too warm to be brittle for short term forces. This restricts brittle frictional sliding and earthquake faulting to the coldest, shallowest regions of the lithosphere. Typically this is only the upper 20 km of continental rocks and the oceanic crust. It is possible for some earthquakes to occur in the uppermost mantle, although these are fairly rare. Deeper earthquakes require the special conditions of downwelling lithosphere to provide sufficiently brittle material to rupture at large depths.

Given the rheological properties that make the lithosphere stiff and its shallowest regions brittle for short term forces, the motions of plates are accompanied by shallow breaking and sliding of rock, rather than plastic deformation. This means that earthquakes occur on the planet, as the result of deformations in the shallowest layer that are responding to deep-seated convective motions as the planet cools. The ultimate source of energy for driving earthquakes is thus the heat of the Earth, and the convection processes that result in surface motions are responsible for earthquake activity.

To begin to consider earthquakes, the intrinsically brittle response of the upper portions of the lithosphere, we must define the idea of faults, which allow movements in the brittle regime. Faults are surfaces within the crust across which there have been shearing motions of the rocks on either side of the break. These surfaces are two-dimensional, and you can think of them as the surface contact between two halves of a broken stone.

Not all faults have earthquakes, as it is possible for rock to slide steadily and continuously, offsetting the two rock masses on either side of a fault with no sudden jarring motion. An earthquake is produced by sudden shearing slip on a fault, where sudden implies a time scale of fractions of a second (for the smallest earthquakes) up to as much as two minutes for the greatest earthquakes. This is a very short time relative to the time scale of plate tectonic motions and mantle convection, so earthquake faulting is on a more familiar time scale for humans than most plate tectonic phenomena. Of course, that is what makes the events so much more catastrophic.

Sudden, shearing slip on a fault is generally understood as a frictional sliding instability. This means that we view earthquake faulting as a process associated with frictional resistance to either breaking of rock (creating a new fault) or resistance to sliding of a previously broken rock with a fault in it. In either case, we can study friction in the laboratory to begin to understand what controls earthquake behavior. In general, friction on a fault increases the harder the rock is squeezed together (i.e. with the normal stress on the fault). More deeply buried rocks are more squeezed, so there is a general increase in frictional resistance with depth in the brittle zone. But the instability of friction proves to be very complex, as the conditions under which frictional resistance is suddenly overcome by a gradually building shearing stress on the rock depends on many properties such as the temperature, rock composition, presence of fluids in the rock and the connectedness of those fluids (which controls whether the fluids drain away or build up pore water pressure). The previous history of sliding of a fault proves to be important too, as each slip event grinds up rock, producing a layer of rock powder or gouge in the fault zone.

Faults exist on all scalelengths, ranging from hand-samples up to rock outcrops in roadcuts up to great breaks in the Earth's crust such as the San Andreas fault. The earthquake behavior of this huge range of faults varies accordingly. If we look at a map of where there are historically 'active' faults, meaning faults that have slipped in the most recent geological time interval called the Holocene, we find that California is criss-crossed with faults of many scales. There is a complex array of faults along the western margin of the state, with the single most continuous fault being the San Andreas Fault, which stretches from Cape Mendocino all the way to the Imperial Valley. It runs through the San Francisco peninsula, from just offshore of the Golden Gate Bridge, down through San Bernadino. This fault is the principle plate boundary fault between the Pacific and North American plates, but many other faults accommodate some of the relative motion between the plates (about 5 cm/yr for the Pacific/North American relative motions).

Eastern California has large faults as well, primarily on the eastern side of the Sierra Nevada. Whereas the San Andreas involves horizontal shearing of the crust, with the western side moving northwestward relative to the eastern side, the faults in the Owens Valley involve largely vertical motion, as the Sierra block tilts upward and the valley drops downward. There are a great variety of faults in California, as in all areas of the crust. Some are inactive, awaiting new patterns of crustal deformation to reactivate them or not, while others are quite active but are buried under sediments and we may be unaware of their existence.

On the largest scale, the plate boundaries of the Earth are all faults that connect up in various ways to make a world circuiting connection of breaks, across which the relative motions of the steadily moving plates are taking place. Since we have a pretty clear idea of how fast plates are moving (10s of cm/yr is typical), and from magnetic stripes, fault geometries, and active measurements of motions using lasers and satellite methods we know the current directions of relative plate motions, we have good constraints on how fast various faults are accumulating deformation that will be released in earthquakes. For example, we know that the Pacific plate is moving northward at about 5 cm/yr relative to North America. This motion, driven by convection appears to be relatively steady over geological time periods. The edges of the plates are grinding past each other and must keep up with the overall motions, however, for most faults this is not a continuous sliding process, but a process of sticking and slipping, as friction resists sliding and is overcome in episodic events. Each sudden slip works to catch the plate offset up, but it may take multiple slips of a given strand of fault to catch up with the total plate offset over a given interval of time.

The San Andreas fault does not have uniform sliding properties, as there are long stretches of the fault that do not have small earthquakes, but appear to suddenly break every 100-150 years in very large earthquakes that involve 5-10 m of slip (thereby locally catching up with 100-150 years of relative plate motions at a steady rate of 5 cm/yr. There are other stretches of the fault that have multitudes of small earthquakes on a daily basis, apparently never suffering large ruptures. In some cases the offsets of the many small events may add up to keep up with the overall plate motion, but in some cases some of the motion is not accounted for by earthquakes, but involves steady sliding or creep of the fault. Clearly, the most catastrophic events are those that involve sudden great sliding of faults, but this tends to occur rarely, on a time scale that makes for a very limited record of past events upon which to base any prediction of the future behavior.

As we proceed to consider earthquake phenomena, we will need a few descriptive terms for describing faulting processes. These include:

1. Strike slip faulting. This is faulting involving purely horizontal shearing motions of the two sides of the fault. If you look across the fault and the other side moves to your right during an earthquake, you have right-lateral strike-slip faulting. If it moves to your left, you have left-lateral strike-slip faulting. The San Andreas fault is a right-lateral strike-slip fault.

2. For faulting which involves vertical motions, there are a few conventions of importance. If the fault is a vertical plane, with purely vertical motions you call it dip-slip motion. If the fault plane is dipping (not vertical), there will be some rock above the fault and some below the fault. The rock above the fault is called the hanging wall (a miner could hang a lamp on it), while the rock below the fault is called the foot wall (where the miner stands).

If the faulting causes the upper block to move downward relative to the lower block (hanging wall downward relative to footwall), the fault is a normal fault. This is the type of fault usually found in regions of extension, where the crust is being pulled apart. This includes mid-ocean ridges where sea floor spreading is taking place as well as continental rifts, like in Eastern Africa, where the crust is breaking apart. The Basin and Range region of Eastern California, Nevada, Utah, and Idaho is also a region of normal faults due to regional extension and opening of the region. The faults on the eastern flank of the Sierra Nevada are normal faults.

If the hanging wall moves upward relative to the footwall, you have reverse faulting, and if the dip (angle from the horizontal) of the fault is less than 30 degrees we call it thrust faulting. Reverse and thrust faulting occurs in regions of compression, where the surface is converging. This is common in subduction zones and in places where continents are colliding. The biggest thrust faults are those on the contact between underthrusting oceanic lithosphere and the overriding plate. The largest earthquakes tend to be thrust faulting events in subduction zones, and may be as large as magnitude 9.5.

The style of faulting reflects the regional tectonic process that is deforming the brittle crust, so it is very useful to be able to determine the faulting geometry whenever we can. In fact, we are able to do this without seeing the fault, as will be discussed later.

The 1906 San Francisco earthquake ruptured the northern 400 km of the San Andreas fault, with offsets of about 3-5 m along much of the length of the fault. This event caused a great destruction in San Francisco, in large part due to a conflagration that burned downtown. It was also an important event scientifically, as it involved the rupture of a vertically dipping right lateral strike slip fault, which offset the west side toward the northwest relative to the east side. This sense of displacement was readily observable in the fractured ground by offsets of fences, riverbeds, and other fault crossing features (including a railroad tunnel through the Santa Cruz mountains).

The clear observations of faulting and the intensive ensuing investigation of the earthquake prompted the articulation of the Elastic Rebound Theory, a conceptual model for how earthquake motions occur. The basic idea is that regional crustal movements, induced for example by plate tectonics, are acting over a region with a fault in it. If the fault were frictionless, the blocks of rock on either side would simply slide along steadily. Because of friction, the fault usually does not do this, and instead there is resistance to instantaneous motion. While rocks are brittle, they do have the ability to deform (strain) a tiny amount, as is true of any solid material. The rock on either side of the fault, in the so-called fault zone, strains to accommodate the regional motions, up to the point where the frictional resistance is exceeded. When this occurs, the rock slides on the fault surface, releasing the elastically accumulated strain energy in the fault zone, with the sudden fault slip catching up with the large scale offsets. The release of strain energy in the fault zone is fairly localized, controlled by the deformation properties of rock and the fact that fault zones are intrinsically weak regions in the crust because they are fractured.

Most of the energy released from the volume of strained rock around the fault goes into heat, as the sliding of rock heats up the fault surface. Some of the energy is released as seismic waves, which spread out through the rock, shaking the ground. It is the latter energy which causes most earthquake damage, as the waves expand outward and vibrate human structures. Fairly little damage occurs as the direct result of abrupt offsets in the fault zone, although there is a tendency for humans to build in fault zone regions (either they have carved convenient valleys and riverways which attract people, or there are exposed cliffs adjacent to fault scarps which have nice views).

Understanding the seismic waves is key to understanding how earthquakes cause catastrophes. There are 2 fundamental seismic waves. P (Primary) waves and S (Secondary) waves. P waves travel faster than S waves and are directly analogous to sound waves in a solid material. We are familiar with sound properties, which involve the excitation of air molecule vibrations by a source (such as a vibrating vocal cord), and the outward propagation of that sound as adjacent molecules are vibrated and then more distant ones vibrate etc., until finally some vibrate a sensor such as your eardrum and your brain translates the electrical impulses from the eardrum into an awareness of the disturbance. In sound waves the particles oscillate back and forth in the direction that the sound propagates (outward in all directions from the source on a spherical wavefront). After the sound passes the air particles return to where they were before the sound wave passed through the medium. Similar oscillations occur in a P wave in rock, in that the particles oscillate back and forth in the same direction as the wave is propagating, returning to their original position due to the restoring forces of the surrounding rock. When we hear a noise through a wall, we are simply hearing a sound that propagated through air, turned to a P wave as it went through the solid wall, and again became a sound wave that we eventually hear.

S waves involve shearing motions perpendicular to the direction in which the wave disturbance is propagating. In a rock, the adjacent material has a restoring force that causes the shearing particles to return elastically to their original position. If you try to shear a fluid, there is no effective restoring force, so S waves cannot propagate in water or air.

It is important to remember that waves spread in all directions away from the source, effectively on spherical wavefronts surrounding the source in the rock. So, at an instant of time after an earthquake fault slides, the source will be surrounded by an outward propagating P wave and an outward propagating S wave. The velocity of the P wave, or the velocity of sound in a rock, is faster so the P wavefront spreads through the rock faster. The P and S velocities are both controlled by material properties of the rock, in particular the P velocity is controlled by the bulk modulus or compressibility of the rock, its rigidity (resistance to shear), and its density. The shear velocity is controlled by rigidity and density.

The outward propagating P and S waves spread through the Earth, with the amplitude of the wave decreasing as the wave travels further. This is because the energy is spread over a larger and larger surface as a function of increasing time. Eventually, the wave is too small to detect. The larger the initial input of energy (i.e. the larger the earthquake), the more distant the perceptible shaking will be. With sensitive instruments we can detect the tiny motions of small earthquakes (say, magnitude 4.5) everywhere on the Earth, even though these events don't usually cause damage even right at the fault region. A large earthquake, such as a magnitude 7 earthquake, may cause destructive shaking for tens of miles, and the waves can be detected circling the planet again and again before they die down to imperceptible levels. A great, magnitude 9 earthquake can set the Earth to ringing like a bell for days.

We study the seismic waves from earthquakes because they tell us about the source (the earthquake faulting process) and they tell us about the Earth. Major results from the study of seismic waves include:

1. Locating the earthquake sources.

2. Measuring the relative sizes and energy release of earthquakes

3. Telling what is the fault geometry and how it slipped

4. Determining internal layering and structure of the Earth

The 1994 Northridge California caused about $30-40 billion damage and took over 60 lives. It was a magnitude 6.7 event. 2000 houses were destroyed or badly damaged, 40 apartment buildings collapsed, 500 apartment buildings had moderate to severe damage. The response of the U.S. government to this disaster was to cut funding for the earthquake monitoring and analysis efforts of the U.S. Geological Survey.....

Earthquakes release stored elastic energy in strained rock, a fraction of which spreads outward into the surrounding rock masses as elastic waves. These waves are then responsible for distant shaking by the earthquake, which may be catastrophic in its effects on human structures. Specialists in the design of structures to withstand the shaking induced by earthquakes are called earthquake engineers. Engineers recognize that structures all have some intrinsic mechanical flexibility, and thus they can be analyzed as vibrating mechanical systems. In fact, every structure has distinct natural harmonic periods at which they will undergo stable resonating vibrations, if the building is shook. The period of harmonic vibration depends on the building design, so engineers can influence it. The main problem is that if the ground shakes at the natural harmonic period of the building, the oscillations of the building are maximized. This tends to cause rapid damage to the structure. Basically the period is proportional to the square root of the mass and inversely proportional to the square root of the building stiffness. By making a building stiffer, the period is reduced (or the resonant frequency is increased). By increasing the mass, the period is increased (frequency reduced).

Building damage is a result of ground shaking induced by earthquake occurrence, but it does not directly tell us about the earthquake process. In order to study earthquakes we need to somehow record them. One approach is to describe the felt shaking and damage from an earthquake. This reveals the general location of the faulting, to the extent that there are any nearby human observers or structural effects. It also suggests something about how much energy was released in the degree of damage. But there are many factors which influence the damage that have nothing to do with the faulting. For example, variations in construction standards around the world enhance catastrophic building collapses and loss of life in some areas. Our understanding of the earthquake process itself must be independent of such human-induced variations.

About 100 years ago, scientists interested in studying earthquakes realized that what was needed was accurate recordings of how the ground actually shook at different places on the Earth, rather than how buildings responded to that shaking. This led to the invention of instruments called seismometers, which record the ground shaking at a given location as a function of time. Most seismometers work on an Inertial Pendulum System of one type or another. This involves some arrangement with a mass suspended on a spring. The spring is connected to the Earth, and when the Earth moves, the spring stretches instantly due to the inertia of the mass (inertia is the resistance to a change in motion). The stretching of the spring eventually causes the mass to move, but it is slightly delayed and shifted relative to the motions of the Earth, and it is that relative motion that we record onto a recording (either on paper or on magnetic tape) called a seismogram. Why is this all necessary? Remember, if you are trying to measure how the ground moves, you have to deal with the fact that the instrument you want to use to record the motion will move with the ground. You need to have some way of separating the recording sensor from the ground. You have seen film footage of earthquake shaking, often recorded at TV studios or on security cameras. The ground shaking is visible because the wall holding up the camera acts as a spring, delaying the motion of the camera relative to the ground.

Seismologists have developed very sensitive seismometers, capable of detecting very tiny ground motions that are imperceptible to humans. By continuously operating these seismometers at locations around the world, we have the ability to record shaking motions anywhere on the planet. The fact that seismic waves travel outward in all directions from the earthquake (or explosion) source allows the disturbance to be detected at many seismic recording stations. Each station keeps accurate time records, so that we know the time at which the ground at a particular location vibrated. Accurate recordings of the vibrations allow us to study earthquakes quantitatively.

The types of vibrations that are recorded involve the P and S waves radiated outward from the source by the release of elastic strain energy in the rock as a fault slides. P and S waves are called body waves, because they travel through the Earth's interior. Because the Earth has layers, as well as a free surface, the P and S waves can bounce around inside the earth, analogous to echoing sound in a canyon. This gives rise to many paths by which P and S wave energy can travel from the source to each point on the Earth's surface. Thus, the ground motion recordings from earthquakes tend to be rather complex, with a sequence of arrivals that are mainly controlled by the Earth structure, not by the source. The earthquake faulting may last only a few seconds, while the ground shaking will be more prolonged because the P and S waves travel with different velocities and there are many paths with different total travel times for the energy to get to the station.

The surface of the Earth causes P and S waves to interact with each other and with the layering of the crust and mantle to produce patterns of vibrations that we call surface waves. There are two main types of surface waves: Love waves and Rayleigh waves. Love waves travel faster than Rayleigh waves, but slower than S waves. Love waves involve only horizontal motions of the Earth, perpendicular to the direction in which the wave is propagating. They are trapped, reverberating S waves near the surface of the Earth. Rayleigh waves involve shaking in the vertical direction (up and down), as well as back and forth in the direction of propagation of the wave. They are a mix of P and S wave energy reverberating near the surface. These waves propagate along the surface, rather than through the body of the planet, thus, their energy is spread out on an expanding ring on the surface rather than over a spherical shell. This makes surface wave amplitudes larger than body wave amplitudes, and thus most damage from earthquake shaking is caused by Love or Rayleigh waves.

Because the P, S, Love and Rayleigh waves all involve different shaking motions, seismometers are designed to record all possible directions of shaking at the surface. This is achieved by having 3 instruments at each site, one recording vertical motions, and two recording perpendicular horizontal motions (usually North-South and East-West). Any motion of the surface can be described as time varying vector (with direction and amplitude), which has components on the three orthogonal axes recorded by the seismometer.

Thus, if we record the ground shaking at a site, and there is a nearby earthquake we will see a sequence of seismic waves pass by the site. First will come the P wave, then the S wave, then the Love wave and finally the Rayleigh wave. The velocity with which each wave type travels determines the time at which the corresponding energy passes by the site and shakes the seismometer, leaving a record of the amplitude, direction, and arrival time of various vibrations. This provides a quantitative record of the ground shaking that can be used to study the source or the layered Earth.

Typically, the first thing we want to do is to determine the origin time and location of the source of the seismic waves. Remember, we do not initially know when or where an earthquake has occurred. What we have are recordings of the times at which the ground began to shake at different places, along with the sense of motion of the shaking. Since the P wave is expected to be the first shaking, from several stations we can identify the arrival time of the P wave at each position. The time at which the wave arrived depends on when the source released the initial energy, and how far it was from each station. In order to determine those unknown quantities, we must know the velocity at which P waves travel through the rock. From a bunch of P wave arrival times, and knowing the P velocity appropriate for the region, one can estimate (by guessing or by more formal mathematical procedures called inversion) where and when the source had to be located in order to account for the observed arrival times at different locations. This is a form of triangulation, done in three dimensions, since the earthquake may be deep in the crust.

We can also use the arrival times of S waves at each station, as long as we know the S wave velocity. Since the S wave travels slower than the P wave, the time separation between their arrivals at a station increases with the distance from the source. Thus, the S-P difference in arrival time is proportional to the distance. Given some knowledge of the S and P velocities of rocks, we can take the S-P time at each station and draw a circle around it with a radius corresponding to the distance to the event. Intersections of the circles from multiple stations identify the unique common position for the source. Once the location is determined, the origin time is set by the absolute P arrival times.

The arrival times of waves are used to locate the event, and once it is known where the event was, we can use the amplitudes at different distances to determine how Big the event was. The basic fact that helps in this effort is that the amplitudes of the waves get progressively smaller with distance, and knowing the distance, we can correct for that effect to tell how big the motions were right at the fault. This gives an estimate of the total energy put into the ground, which is proportional to how big the area of fault slip is and how much slip occurred.

There are several measures of earthquake size that reflect the ground shaking amplitudes. The first is a qualitative measure called Intensity. This is actually a damage scale, in which the level of shaking felt or damage caused is categorized into ten or twelve categories. Intensities tend to give higher damage, and higher intensity values near the source. This does not use seismograms at all, but is very useful for historical events for which there are no seismic recordings. Intensities are also practical, in the sense of reflecting human effects rather than scientific measures of the source.

Seismograms give seismic wave amplitudes that are used to determine earthquake Magnitudes. These are based on the distance corrected amplitudes of seismic waves, but often have a mix of quantitative and empirical procedures. Magnitude scales are all logarithmic, meaning that they are based on powers of ten. For each increase in the magnitude value by one unit, the ground motions were 10 times larger. The energy required to produce 10 times larger motions is about 30 times larger. Thus, a magnitude 5.0 earthquake produces ground shaking at some given distances, say 10 km, that is ten times larger than a magnitude 4.0 event recorded at the same distance.

The earthquake magnitude that is determined depends on which seismic wave is measured, and there are different magnitude scales for P waves, for Rayleigh waves, and for different periods of motion. The Richter scale is just one of many magnitude scales, and really involves only events recorded in Southern California on a particular type of seismic instrument (sensitive to high frequency body wave shaking), corrected for distance by the special formulas appropriate for Southern California. While much more general magnitude scales are applied to events around the world, using a variety of seismic instruments, the media tends to call them all Richter magnitude.

The most quantitative measure of earthquake size determined by seismograms is called the Seismic Moment. This is an energy based measure that accounts for the actual geometry of the faulting (magnitudes do not, despite the fact that seismic wave radiation is affected by whether the fault is strike-slip, normal, or thrust faulting). The seismic moment is a quantity proportional to the permanent displacement on the fault. It is given by the product of the rigidity, the fault area that ruptured and the amount of slip. This quantity is determined by making a computer model of the faulting that matches the observed amplitudes of the complete seismogram, accounting for any differences in excitation (strength of radiation) of the P, S, Love and Rayleigh waves caused by fault depth, geometry, and slip process. A magnitude scale called the Moment Magnitude scale was determined to provide familiar logarithmic numbers. While all other magnitude scales only work for a limited range of events, the Moment Magnitude scale is good for all events. The largest earthquake that has been recorded this century was the 1960 Chile earthquake, which had a moment magnitude of 9.5! Richter magnitudes tend to saturate around magnitude 8.2-8.5, meaning that even if the event is bigger, you get the same Richter magnitude. Thus, the Moment Magnitude is particularly useful for very large events.

Some of the World's Worst Earthquakes (in lives lost)

856 Corinth, Greece 45,000

1038 Shansi, China 23,000

1057 Chihil, China 25,000

1170 Sicily 15,000

1268 Silicia, Asia Minor 60,000

1290 Chihil, China 100,000

1293 Kamakura, Japan 30,000

1456 Naples, Italy 60,000

1531 Lisbon, Portuga l30,000

1556 Shensi, China 830,000

1667 Shemaka, Caucasia 80,000

1693 Catania, Italy 60,000

1731 Peking, China 100,000

1737 Calcutta, India 300,000

1755 Northern Persia 40,000

1755 Lisbon, Portuga l70,000

1783 Calabria, Italy 50,000

1797 Quito, Ecuador 40,000

1811 New Madrid, MO several

1812 New Madrid, MO several

1819 Kutch, India1, 543

1822 Aleppo, Asia Minor 22,000

1828 Echigo, Japan 30,000

1847 Zenkoji, Japan 34,000

1868 Peru/Ecuador 25,000

1868 Ecuador/Colombia 70,000

1872 Owens Valley, CA 50

1875 Venezuela/Colombia 16,000

1886 Charleston, SC 60

1891 Mino-Owari, Japan 7,000

1896 Sanriku, Japan 22,000

1897 8.7 Assam, India 1,500

1899 8.6 Yakutat Bay, Alaska

1906 8.2 San Francisco, CA 700

1908 7.5 Messina, Italy1 20,000

1915 7.0 Avezzano, Italy 30,000

1920 8.5 Kansu, China 180,000

1923 8.2 Kwanto, Japan 143,000

1932 7.6 Kansu, China 70,000

1935 7.5 Quetta, India 60,000

1939 7.75 Chillan, Chile 30,000

1939 8.0 Ezrican, Turkey 23,000

1948 Fukui, Japan 5,131

1949 6.9 Pelileo, Ecuador 6,000

1949 Khait, USSR 12,000

1950 8.6 Assam, India 1,526

1957 Northern Iran 2,500

1960 9.5 Southern Chile 5,700

1960 5.9 Agadir, Morocco 14,000

1962 7.3 Northern Iran 14,000

1963 6.0 Skopje, Yugoslavia 1,200

1964 9.4 Alaska 131

1968 7.4 Iran 11,600

1970 7.8 Peru 66,000

1971 6.5 San Fernando, CA 65

1972 6.2 Managua, Nicaragua 5,000

1976 7.9 Guatemala 22,000

1976 7.6 Tangshan, China 250,000

1976 Philippines 3,100

1980 7.7 El Asnam, Algeria 3,500

1980 7.2 S. Italy 3,000

1981 6.9 S. Iran 3,000

1981 7.3 S. Iran 1,500

1982 6.0 Yemen 2,800

1983 6.9 Turkey 1,342

1985 7.9 Michoacan, Mexico 9,500

1986 5.4 El Salvador 1,000

1987 7.0 Colombia 1,000-5,000

1988 6.6 Nepal-India Border 1,450

1988 7.0 Spitak, Armenia 25,000

1989 6.9 Santa Cruz, CA 63

1990 7.7 Iran 40,000

1990 7.8 Luzon, Philippines 1,700

1992 7.3 Landers, CA 1

1994 6.5 Northridge, CA 65

1995 6.5 Kobe, Japan 5,000

The strain energy released in seismic waves spreads outward in all directions from the source region, which may be either a sliding earthquake fault, an underground explosion, or a volcanic eruption. The waves propagate with velocities determined by the rock properties at each position in the interior, and an initially spherical outward propagating wavefront quickly becomes contorted by the geological heterogeneity encountered. Given knowledge of how fast the waves propagate through rock, the arrival times of P and S wave disturbances recorded by seismometers at various positions around the Earth allow us to locate the event, specifying the origin time and spatial coordinates of the source. Once we know how far each station is from the source, we can correct for the geometric spreading effects of propagation. The observed amplitudes of ground shaking can then be used to compute the magnitude or seismic moment.

But, we can do even more. We can also identify the source type (explosion versus earthquake for example) and for earthquake sliding events we can determine the geometry of the fault and the sense of displacement on it. In addition, we can study the medium through which the waves have passed, learning about the layered and continuously varying properties of the interior. From the resulting understanding of how seismic waves traverse the Earth and what type of faulting is occurring in various locations, we can gain understanding of the dynamic processes responsible for the earthquake and can more effectively protect ourselves from the dangers of future earthquakes.

Different types of sources produce different patterns of motion on the outgoing P and S waves, and this can be used to distinguish between possible causes of shaking. For example, an underground explosion pushes the ground outward symmetrically in all directions, with the outgoing P wave initial sense of motion being away from the source in all directions. If we record the P waves from an explosion, the first sense of motion will be away from the source (after allowing for any distortions of the direction of propagation caused by variable velocity structure). In the ideal case of a perfectly symmetric explosion, no S waves are generated by the source radiation since there is no shearing at the source. On the other hand, a faulting event involving abrupt shear sliding on a planar surface produces an asymmetric pattern of alternating quadrants of compression and dilation of the rock. This is because the abrupt shearing motion will push on two quadrants of rock and will pull on two quadrants. Earthquakes also produce strong S waves at the source due to the shearing motion.

One of the most important attributes of elastic media is that the sense of initial motion is preserved as the wave propagates through the Earth. This is easiest to visualize if you think about P waves in a solid or acoustic waves in a fluid. In both cases the wave disturbance involves a transient, outward expansion of particle oscillations induced by some source. Each particle on a wavefront (the locus of the disturbance at a given instant in time) will initially move toward or away from the source, depending on the position relative to the source geometry. Each particle's motion is produced by the motion of an adjacent particle, closer to the source, and in turn the motions track back to other particles, all along a line connecting up right back to the source region, where the first particle moved either toward or away from the source. This preservation of the first motion of the P wave along the entire sequence of interacting particles is an elastic effect, and is essential to our ability to relate distant observations of particle motions to how the ground moved near the source, at what may be thousands of kilometers distance. Because the fault will have a regular four-lobed (quadripolar) distribution of particle motions with respect to the arbitrarily oriented fault plane, and we can use observations to figure out the orientation of the four-lobed pattern of alternating compression and dilation, we can determine the orientation of the fault plane and the sense of slip on it from ground motion recordings around the world.

To relate distant motions at the Earth's surface, recorded by seismometers, to the corresponding position that the energy was radiated away from the source, we must be able to correct for wave propagation effects, or how the Earth's velocity structure distorts the outward propagating wavefront. This is possible, because we now have a good understanding of how seismic waves travel through the Earth, and can account for the complex distortions that they incur.

This ability to remotely determine the geometry of earthquake faulting that produced a particular disturbance has played a key role in revealing the ongoing process of plate tectonics. Most faults are buried deep in the crust or are located under oceans where we cannot directly see the faulting motions that produce earthquakes. Despite this, the determination of the faulting geometry using seismic waves allows us to identify faulting in regions that are inaccessible to direct measurement. This has demonstrated that normal faulting (extensional events) dominate on mid-ocean ridge systems, the result of ocean floor pulling apart as sea-floor spreading occurs. It has shown that subduction zones are convergent regions, where old oceanic lithosphere thrusts back into the mantle, producing the largest earthquakes which tend to be thrust events on the contact between the underthrusting and overriding plates. It has revealed the existence of strike-slip, horizontally shearing boundaries that connect up ridges and subduction zones, such as the San Andreas, or large transform faults that offset the mid-ocean ridges. The present day direction of faulting, and the overall accumulation of offset is revealed by analysis of the fault mechanisms.

So, how do seismic waves tell us about the interior? Clearly we need to know something about the interior to even use the seismic waves for simple things like locating the source. How have we solved the two problems simultaneously? Well, it has been a boot-strapping effort, of progressively estimating the Earth structure, then locating events, then refining the Earth structure etc. Some earthquakes or large explosions have had precisely known locations and origin times. From measuring the arrival times of waves at various distances, we have determined how fast waves travel through the Earth to various distances. Then, we develop a model of the Earth, specifying how the velocity of P or S waves vary with depth in such a fashion as to account for the travel times of the waves to different distances. This model can then be used to locate events that are not independently constrained. As more events are located, the data base of arrival times at different distances expands, and an updated Earth model is determined, and the iterative procedure goes on.

An important idea associated with this iterative process is the idea that energy travels through the Earth on paths that can be represented by Seismic Rays. These are defined as the curves connecting the normal (perpendicular) to a local portion of a wavefront as that wavefront expands outward with time. If we think of P waves, which cause oscillations of particles back and forth along the direction in which the wave is propagating, we can imagine the curving line produced by one particular particle at the source, expanding outward, jostling a neighbor, which then jostles a neighbor, on and on, communicating along that unique trajectory the initial particle motion. Since the sense of P wave particle motion is always along the normal to the wavefront, i.e., in the direction of the normal to the wavefront, this curve is a seismic ray. We can thus draw a seismic ray for any particular path through the medium directly connecting back particle by particle from the receiver position to the source.

As the outward propagating wavefront expands, it will encounter changes in rock properties of two types. There will either be abrupt contrasts across rock boundaries, such as at a contact between two rock layers with different elastic wave velocities, or the velocity can vary smoothly, either increasing or decreasing with depth (or laterally). At a boundary the seismic wave energy can have three types of interaction:

1. Reflection - Some of the incident wave energy will reflect off of the boundary

2. Refraction - Some of the incident wave energy will transmit across the boundary

3. Conversion - Incident P (or S) wave energy can convert to S (or P) wave energy

The first two ideas are familiar from optics and acoustics, with Snell's Law governing the kinematic properties of seismic rays interacting with a boundary (the angle of incidence equals the angle of reflection, etc.). Refraction changes the direction of the ray, just as looking down at an object in a swimming pool gives an apparent shift of the location of the object because the light is refracted from a straight path in passing through the water versus the air. The conversion of P to S and S to P energy is unique to solid materials and elastic waves, and is partially responsible for the great complexity of seismic ground motions, as P wave that impinges on any boundary in the Earth has its energy partitioned into reflected and refracted P waves AND reflected and refracted S waves, as is the case for every S wave hitting a boundary. With the Earth having many internal boundaries between rock layers, the seismic wavefield becomes very complex.

Reflections are very useful for determining the presence of and nature of layering, and this is commonly applied in the oil industry as the main tool for finding oil and mineral resources. The basic idea is to put out many seismometers on the surface, and then to vibrate the ground with explosions or vibrating trucks that send P waves spreading down into the crust. Some of the P energy is reflected at each boundary at depth, and this gives rise to reflected arrivals observed at the surface. By working down, finding the shallow velocity first, and the depth to the first reflector, and then the deeper velocities and the depths to deeper reflectors, we can develop very high resolution images of the shallow layering of the crust. Often the layers are warped and deformed, and it is in the favorable geometries for capturing oil that we proceed to drill. Similarly, reflections are used to probe deeper, to the Moho (crust-mantle) boundary, to the core-mantle boundary and to the inner core-outer core boundary. At each boundary seismic wave energy reflects, refracts and converts, which gives a unique wavefield complexity that reveals the presence of and the properties of the boundary (such as the change in velocity or density across the boundary).

While there are many boundaries in the finely layered crust, and there are major boundaries in the upper mantle transition zone and between the Earth's major layers, for most of the Earth there are smooth variations of material properties that do not have sharp boundaries. These variations are primarily with depth, as the increasing pressure causes systematic increases in velocity in a uniform composition material, but there are also lateral temperature and compositional gradients that cause material properties to vary at a given depth (uniform pressure). There are two simple classes of seismic wave behavior in regions of smoothly increasing or decreasing velocities.

If the velocity increases smoothly with depth the result on a seismic wave is that it will bend back up to the surface of the Earth, with each part of the wavefront turning at a different depth in the Earth. Thus, if we measure the arrivals along the surface of the Earth as a function of distance from the source, the travel time from the source origin time to the arrival of the P or S wave at each position on the surface will produce a smoothly increasing curve (travel time curve). In detail, the slope of the travel time curve at each position is inversely proportional to the velocity at the depth at which the ray turned, or penetrated most deeply to. Thus, if we observe a smooth travel time curve, steadily increasing with distance, we can determine that the velocity at depths in the Earth for which the rays turn was itself smoothly increasing and we can give the absolute velocities involved.

If the velocity decreases with depth, the wave in the low velocity region turns downward, thus it is possible to have a region on the Earth's surface where no seismic energy will be observed, because the wavefront was deflected from ever arriving there. This is called a shadow zone. For the travel time curve as a function of distance, the shadow zone produces a break in the curve, or a gap with no arrivals at a particular distance range.

Well, if we consider the actual travel time curves for the Earth, we see a mix of effects of smooth velocity increases in much of the interior, abrupt boundaries at depth which cause strong reflections and refractions, and velocity decreases, which produces shadow zones and discontinuous travel time curves. The best way to see this is to plot all of the arrival times of various seismic waves at a given distance on a plot of travel time versus distance. When the arrivals at various distances correspond to a particular path through the Earth, they define continuous travel time curves. We can then analyze the travel time curves, identifying what type of wave was involved (P or S or some mixture of P and S segments), and deduce the structure at depth that is responsible.

In the early 1900s as the number of seismographic stations around the world increased, and the data set of well-located earthquakes accumulated, seismologists were able to plot up the travel time curves for the Earth, which can be viewed as a unique 'fingerprint' of the Earth, describing how the waves from any source of seismic wave energy will traverse the planet. This immediately revealed that the P wave travel time curve, the first line of arrivals is continuous out to distances about 1/4 of the way around the Earth (epicentral distances out to 90 degrees), but then there is a major shadow zone and discontinuity in the travel time curve. This reveals the presence of the low velocity core of the Earth. The S waves are also seen out to a distance of 90-100 degrees, but there the waves diminish and there is no discontinuous curve. This is the primary evidence that the low velocity core is actually molten, as no S wave can traverse a fluid. We also see travel time branches that correspond to waves reflected from the major boundaries, and the combined information of the travel time curves and proliferation of reflected phases provides enough information to accurately compute the P and S velocity with depth all the way to the center of the Earth. This gives a one-dimensional model of the Earth, as a layered planet with continuously increasing velocity with depth in the mantle and a low velocity molten core. Once we have a fairly accurate model for the velocity as a function of depth, we can use it locate earthquakes everywhere in the Earth with an accuracy of a few tens of kilometers or better, depending on the distribution of seismic stations relative to each source.

But, the Earth is a dynamic planet, and we know there are lateral variations that are not well represented by any one-dimensional model. For example, we know that the Moho discontinuity is about 6 km deep under oceans, but varies from 15-70 km deep under continents. Reflections and refractions from the Moho tell us this. Since there are downwelling oceanic lithosphere and upwelling partially molten regions, we expect there are even deeper seated lateral variations in material properties that should affect seismic velocities. Can we determine a model of the Earth's properties that includes all of these effects. If so, it would be a great tool for understanding the dynamic processes in the interior of the Earth.

In the 1970s and 1980s seismologists began to systematically 'map out' the variations in three-dimensions. They drew upon the remote imaging procedures that had been introduced in the medical world, such as CATSCAN tomography. This is the use of many crossing beams of radiation recorded at many sensors encircling a body. Typically, it is anomalous blockage of beam intensity which is sought, as this reveals the presence of localized zones of unusual tissue such as a tumor. Basically, beams that hit the anomalous zone show an effect, while beams that do not hit it have normal behavior. By using the crossing ray coverage, one can deduce where the paths encountering a common tissue anomaly intersect, and thus find the anomalous tissue. This boils down to solving a large system of simultaneous mathematical equations.

Seismologists drew upon this approach to define Seismic Tomography, which uses the travel times of waves from many sources to many receivers, to find regions of faster or slower than average seismic velocity. These are usually given as perturbations to some one-dimensional average Earth model, which has the background increase in velocity with depth. By exploiting the crossing ray coverage and the fact that seismic waves have local sensitivity (so that localized rays are affected in traversing an anomalous region), seismologists can locate the three-dimensional distribution of fast and slow regions, not just the variations with depth.

Visualizing the three-dimensional models is rather challenging, but various displays suggest how the velocities vary laterally at each depth, and how they vary relative to the background model as a function of depth. In the early 1980s, when global seismic tomography was first producing images of the planet's internal velocity variations, it was found that there are strong large-scale patterns of faster and slower material. At shallow depths in the mantle, in the upper 200-300 km, the lateral variations have strong correlations with surface tectonic features. For example the old stable core regions of continents (cratons) are found to be underlain by high velocity material, presumably due to both being colder regions and perhaps having a chemically differentiated keel of material in a thickened lithosphere. Young, active regions such as the mid-ocean rifts and continental rifts are seen to be underlain by low velocity material, which is presumably hotter and buoyant.

The interpretation that most of the lateral variations in seismic velocity are the result of thermal variations (200-1000 degree lateral variations in temperature are expected in the convecting mantle, which should give rise to 3-10% lateral variations in seismic velocity, as observed) has a major implication. Hot, slow seismic velocity regions are expected to be low density they will tend to rise, while cold, high seismic velocity regions will be high density and therefore sink. Thus, the seismic models from tomography can be interpreted in terms of upwellings and downwellings in the mantle, which are the direct convective pattern of the interior which drives plate tectonics. Thus, we are in the second generation of the plate tectonics revolution, where seismic imaging reveals the complete three-dimensional configuration of the system. Regions of particular interest include downwellings, which often have deep earthquakes, and can be studied in detail. It is often found that the high velocity slab extends well beyond the depth of the deepest earthquakes.

Thus, we see that the very same waves that cause destructive shaking from earthquakes provide a valuable tool for human investigation of the Earth system, and therefore a tool for understanding the causes of the earthquakes that generated the waves.