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:
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.
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