INTRODUCTION

Seismic tomography is the most complex seismic method that we’ll discuss in this class. Tomography allows us to deal with almost any distribution of velocities underground. The distribution can be either two- or three-dimensional. The velocity can vary continuously from place to place. We do not need distinct layers or interfaces. Before dealing with seismic tomography, let’s take a look at medical "CAT-SCAN" tomography.

CAT-SCAN IMAGING

This is an x-ray method for making images of the interior of people or geological entities such as rock samples or sand-box tectonic models. Using moving sources and receivers on rotating rings we can shoot x-ray beams through the patient in all directions in the plane of the rings. The beams or rays travel through the patient in a complex spider’s web of intersecting lines.

The x-rays travel at more or less constant velocity so there is no refraction and the rays are straight. The amplitude, in contrast, drops as the ray encounters different tissues and bones. To make an image we divide the sample space into zillions of pixels or picture elements and assign an attenuation value to each. Then, based on the attenuation of each relevant pixel, we calculate the total attenuation along each ray. By solving a huge set of simultaneous equations, we adjust the attenuation in each pixel until the calculated attenuations matched the measured attenuations of all rays. Thus the final image is a map of x-ray attenuation in the whole sample space. To make three-dimensional views we move the patient a short distance normal to the rings of sources and receivers and repeat the experiment.

SEISMIC FAN SHOOTING

In the 1920’s the German firm "Seismos" sent refraction crews to the Gulf Coast of Texas and Louisiana to find salt domes as they had at home. The instruments were basically mechanical with no electronic amplification. Recording was on photographic film and initially the direct air wave was used to compute the shot instant (travel-time equals zero).

The seismographs were laid out in an arc with the shot at the center so the rays spread out in a fan-shaped pattern. In the shales and sandstones of the region the velocity generally increased downward and thus the ray paths were concave up. Travel-times at any given distance were similar over large areas.

In contrast, a wave that encountered a salt dome would speed up and arrive earlier than normal for a given distance. Thus they could conclude that a salt dome lay somewhere along a particular ray or set of rays. To remove the ambiguity a second fan of different orientation was used. The fan lay at the intersection of two or more "early" ray paths.

Seismos had great success for about a decade until they were driven from the scene by American companies using seismic reflection equipment with electronic amplifiers.

TOMOGRAPHY BETWEEN WELLS

Perhaps the most common kind of tomography involves shooting from one well to receivers in another well nearby. The source is located in one well and the receivers in another. As many criss-crossing rays as practical are used. The interwell area is divided into pixels and first arrival travel-times calculated based on initial estimated velocities, Snell’s Law and the distance each ray travels in each pixel. The calculated times are compared to the measured ones and then the velocities are altered by computer until the times agree. More complex interpretations use wave amplitudes and shapes also.

Some uses include mapping fractures in bedrock, steam flooding in oil fields and in situ coal burning.

INTERIORS OF VOLCANOES

To predict eruptions and to develop geothermal energy geophysicists would like to map out velocity variations under volcanoes. Where are the magma chambers? What is their depth and shape? To answer these questions we can try two techniques using seismic waves.

One technique uses large, temporary arrays of seismographs to record small local earthquakes resulting in part from magma movement. The earth beneath the volcano is divided into "voxels" (three dimensional equivalent of pixels). Each voxel is assigned an initial seismic velocity and each arrival an initial origin time and hypocenter. Using thousands of rays we can invert the whole data set for velocity, hypocenter location and origin time. The magma chamber should have low velocity (it’s hot), no S-waves (it’s liquid) and be surrounded by a swarm of little ‘quakes (magma motion cracking rock at the periphery of the chamber).

A second technique uses waves from far away. These teleseimic arrivals have almost horizontal, vertically ascending wavefronts under the volcanic region. Arrivals at stations above the magma chamber should be late (again high temperature reduces the wave speed) and there should be an S-wave shadow zone (liquid). The two methods can, of course, be combined.

TESTING GLOBAL WARMING

Because of the low-velocity "SOFAR Channel" explosions at a depth of about one kilometer in the ocean can be detected world-wide. Given that sound wave speed increases with temperature, we expect that travel-times from repeated explosions should decrease year by year. To the extent that the rays sample most of the ocean we should get a very robust, integrated estimate of how much additional heat is being stored in the sea.

Preliminary study suggests that a source near Heard Island in the southern Indian Ocean would be heard (sorry about that!) throughout the world oceans. Additional source locations would help pin-point where warming has been occurring. At present the experiment is being delayed for fear that the sound source would damage marine mammals. (I just read in an old saga that in Viking times certain stretches of Icelandic beaches were prized for the large numbers of whales that would strand themselves there).

GLOBAL TOMOGRAPHY

Body waves in the mantle can be used to map out regions of abnormally high and low seismic velocities. Given the increase of velocity with depth, the rays of both P- and S-waves are concave up. Waves will arrive earlier if they sample a "fast" region somewhere on their path. Conversely, arrivals will be late for rays traversing a low-velocity region somewhere on their path. The travel-time differences can be inverted to map out the slow and fast regions of the mantle. If the velocity differences are caused by temperature differences we expect the slow regions to be hot, low density and rising. Fast regions might be cold, dense and sinking. Of course the velocity variations might be due to compositional differences, not to temperature ones. Thus we have a powerful tool for estimating the present directions of mantle convection.

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