Seismic tomography

Seismic tomography is a technique for constructing a cross-sectional image of a slice of the earth from seismic data. Measurements are made of seismic energy that propagates through or reflects from subsurface geological materials. The measured time of travel and amplitude of this energy are used to infer geometry and physical properties of the geological materials, from which an image of the inside of the earth is generated.

Method Pioneered

Seismic tomography is a means of making an image of a slice of the earth using seismic data. “Tomography” is derived from a Greek word meaning “section” or “slice.” Since the 1970's, seismic techniques have been used to create subsurface pictures. Although some methods that have been used in exploration geophysics for a number of years can be classified as tomographic, it is only since the mid-1980's that seismic tomography has been specifically developed for geophysical exploration and exploitation. Increased interest in seismic tomography in geophysical exploration and global seismology is the product of many factors, including the interaction between different scientific disciplines, along with advances in seismic field-data acquisition, imaging and inverse-problem theory, and computing speed.

The basic idea of tomography is to use data measured outside an object to infer values of physical properties inside the object. This method was pioneered by J. Radon in 1917. Radon showed that if data are collected all the way around an object, then the properties of the object can be calculated. In fact, Radon derived an analytical formula that relates the object's internal properties to the collected data.

Method Applied

Since the mid-1970's, the ideas of tomography have been applied to a number of fields of study. Applications of tomographic techniques are found in fields as diverse as electron microscopy and astronomical imaging. In medicine, the process of computed tomographic scanning (“CT” or “CAT” scanning) has developed rapidly since its inception in the early 1960's and its use has been integral in diagnostic medicine.

In tomography, geophysicists apply techniques similar to those of medicine to geophysical problems. Beginning in the early 1970's, interest and applications began rapidly expanding. Since then, a number of papers on the applications of seismic tomography have been presented. These range from attempts to estimate the internal velocity structure of the subsurface to formulations that provide a complete image of the subsurface geology. Since the late 1980's, tomographic reconstruction has become a standard technique in analyzing data between drill holes (crosshole analysis). Thus, while tomography is relatively new to exploration geophysics, it is a broad, powerful concept that has made a significant impact. Seismic tomography has led to many useful new applications as well as insightful reinterpretations of some existing imaging methods.

Seismic tomography is a type of “inverse pro-blem”—that is, measurements are first made of some energy that has propagated through and reflected from within a medium (in this case, the earth). The received travel times and amplitudes of this energy are then used to infer the values of the medium through which it has transmitted. The parameters that are extracted are velocities and depths; therefore, a gross model of the earth's structure can be derived. Initially, this was considered the ultimate goal of seismic tomography. However, accurate measurements can be used effectively for other purposes, such as constructing an accurate depth image of the subsurface.

In CT scanning, an X-ray source and a number of X-ray detectors are used to acquire data around the human body. The X-ray source sends out X-rays, and receivers record the transmitted X-ray intensity. This intensity is related to the attenuation of the X-rays along their ray paths inside the object. In turn, the amount of attenuation is related to the density of the object encountered by the X-rays. Thus, a CT scan is an actual estimate of the density distribution within a body. CT scans can be done over various parts of the body, and these scans can be put together to form a three-dimensional image. This kind of image can show with great clarity the internal structure of the body or damage inside the body. Interpreting three-dimensional images of the body's interior is similar in many ways to interpreting the interior of the earth from three-dimensional seismic data.

Seismic Surveys

Tomographic geophysical exploration attempts to determine from seismic data the velocities with which sound propagates through a section of the earth, as well as other properties of the earth, such as density and compressibility. Classical tomography is typically associated with transmitted energy and requires a distribution of sources and receivers around the object to be imaged. In medical X-ray tomography, the source and receiver rotate all the way around the object being imaged. In contrast, by far the most pervasive seismic measurement is the surface reflection survey. Its measurements are made on just the upper boundary of the medium of interest.

Since the first seismic detectors (seismometers or geophones) were placed on the surface of the earth near the end of the nineteenth century, seismic waves have been used to locate remote objects. The first applications involved the location of earthquake epicenters in faraway regions. Efforts to locate heavy artillery by seismic means during World War I later evolved into the first exploration methods for oil and gas. Imaging techniques in exploration seismics have continued to be improved ever since. At first, the process involved the interpretation of travel times of observed seismic pulses in terms of the depth and slope of reflecting surfaces. Beginning in the 1970's, complete seismic records were used, and imaging methods were developed that were based on sophisticated mathematical techniques.

In a seismic survey, geophysicists typically arrange seismic detectors along a straight line and then generate sound waves by vibrating the earth. Earthquakes release the large amounts of energy needed to probe the deep layers (mantle and core) of the earth. Other methods can produce seismic waves that can be focused on the geologic features closer to the earth's surface. These waves can be generated by explosions, such as a charge of dynamite, or by dropping a weight or pounding the ground with a sledgehammer. To eliminate environmental risks associated with the use of explosives, a system called “vibroseis” is used. In this system, a huge vibrator mounted on a special truck repeatedly strikes the earth to produce sound waves. A seismograph records how long it takes the sound waves to travel to a rock layer, reflect, and return to the surface. The recorded data display the amplitudes of the reflected sound waves as a function of travel time. Such a graphic record is called a “seismogram.” The equipment is then moved a short distance along the line, and the process is repeated. This procedure is known as the seismic reflection profiling method.

Method Adapted to Seismic Data

Since seismic waves traveling in the earth readily spread, refract, reflect, and diffract, classical tomographic methods must be adapted to produce realistic seismic pictures, and effective software and interactive graphics are required to process the seismic data into a relevant image. It has taken some time for tomographic concepts to spread to seismic imaging, for appropriate data to be acquired, and for effective processing and interpretation techniques to be developed. Using a variety of computer programs, seismograms are processed to yield seismic sections that represent the earth's reflectivity in time. Geologists, though, would really like to have a lithologic picture illustrating such features as rock velocity, seismic wave attenuation, and elastic constants of the rocks as a function of depth.

Reflectivity is a property associated with interfaces between rocks; a rock sample held in one's hand does not have an intrinsic reflectivity. Therefore, reflectivity is not an actual rock property, and it must be converted to some parameter that really describes the rock. In addition, seismic time data must be converted to depth measurements in the imaging process. Consequently, conventional reflection sections are being greatly improved by the use of tomographic techniques to produce subsurface images as a function of depth and to estimate rock properties from some of the images.

The basic procedure of seismic tomography is an extension of the notion of transmission tomography. This process can also be classified as a generalized linear inversion of travel times. The first part of the procedure is to locate reflected events on the raw seismograms and then associate these events with the structure of a proposed or guessed geological model. Next, the laws of physics are applied to trace ray paths of seismic waves through the proposed model from given seismic sources down to a particular reflector and back to the seismic detectors. The ray-traced travel times are then compared through the model with the travel times recorded on the seismogram, and the geological model is updated to make the ray tracing consistent with the observed data. Seismic tomography is distinct from classical tomography in that only reflected waves are used, and the source-detector coverage of the object or area of interest is far from complete. These aspects of the problem create difficulties, but the tomographic velocity determination is still very useful, especially in areas of significant lateral velocity variations. By including all available data in the tomographic process, as well as any other available geophysical data, the resolution and certainty of subsurface images can be greatly improved. In 2009 the Federal Lands Highway Program of the U.S. Department of Transportation used cross-borehole seismic tomography to investigate an active sinkhole causing damage to property in a residential neighborhood of central Florida. Personnel were able to obtain images that showed the “throat” of the sinkhole at a depth of 24 meters.

Resource Exploration

Various survey geometries and tomographic constructions are used to assist the solving of geophysical problems. Geophysicists can use the velocities of seismic waves recorded by a seismograph to determine the depth and structure of many rock formations, since the velocity varies according to the physical properties of the rock through which the wave travels. In addition, seismic waves change in amplitude when they are reflected from rocks that contain gas and other fluids. Sometimes the fine details of seismic records can be used to infer the type of rocks (lithology) in the subsurface. Some tomographic studies have used subsurface velocities determined from the inversion of seismic travel times to construct geological cross sections of the geology inside the earth, while other studies have used reflection amplitudes for the same purpose. Based on the characteristic geometries and amplitudes for oil and gas traps and for mineral ore deposits, these tomographic images are used to predict where oil, natural gas, coal, and other resources such as groundwater and mineral deposits are most likely to be found in the subsurface. The tomographic cross sections constructed from seismic data make the odds of finding such resources much greater than would be the case if exploration were based on mere random drilling.

In seismic tomography, various source and detector geometries are used, such as drill-hole-to-drill-hole, surface-to-drill-hole, and surface-to-surface. The greater the degree of angular coverage around the rock mass, the greater the reliability of the constructed tomographic image. By making numerous measurements from various source-detector positions and analyzing the travel times and amplitudes from a number of source-detector locations, the velocity and attenuation of the intervening rock can be calculated from the recorded energy—energy that is either reflected or transmitted. This technique has found applications not only in locating subsurface natural resources but also in areas such as determining the location of nuclear-waste dumps and the monitoring of stream floods, which are used to help produce hydrocarbons from a reservoir.

Exploitation of Hydrocarbon Reservoirs

In many hydrocarbon development areas, adjacent drill holes may be available. In these situations, it is desirable to have a very high-resolution description of the rock mass between the drill holes. For this purpose, it is often effective to use crosshole tomography. A seismic source, such as dynamite caps or downhole air guns, is placed in one drill hole, and appropriate detectors are placed in an adjacent drill hole. The source is fired, and the resulting seismic energy propagates through the rock and is detected in the other drill hole. The travel times and amplitudes of seismic waves that have been reflected or transmitted through the rock mass between the drill holes are recorded. The source and detectors are then moved to another position, and the process is repeated. This procedure is continued until the region of interest is adequately covered by the propagating energy. Seismic crosshole tomography has been used for a number of applications, including mineral exploration in mines, fault detection in coal seams, stress monitoring in coal mines, delineation of the sides of a salt dome, investigation of dams, and mapping of dinosaur-bone deposits. The resolution of crosshole tomography is typically better than for surface reflection tomography.

The broad objective of geophysics is to produce images that represent the subsurface geology as accurately as possible, and tomography-based imaging algorithms provide seismic depth sections that are consistent with drill-hole data in regions of resource exploration and exploitation. Integrating drill-hole and surface seismic reflection data in a tomographic approach can provide a better, less ambiguous subsurface picture. This correlation holds considerable promise to increase knowledge of the subsurface. The resulting seismic depth sections assist in interpreting the structure (geometry), stratigraphy (depositional environment), and lithology (rock and fluid types) of potential and established hydrocarbon reservoirs and mineral deposits.

The geologic detail needed to develop most hydrocarbon reservoirs substantially exceeds the detail required to find them. For effective planning and drilling, a complete understanding of the lateral extent, thickness, and depth of the reservoir is absolutely essential. This can be found only with detailed seismic interpretation of three-dimensional seismic reflection surveys integrated with drill-hole data. A common practice in three-dimensional seismic reflection surveying is to place the seismic detectors at equal intervals and collect data from a grid of lines covering the area of interest. Based upon integrated seismic tomographic imaging of the drill-hole and seismic reflection data, more wells are drilled in the area, and the three-dimensional data volume evolves into a continuously utilized and updated management tool that influences reservoir planning and evaluation for years after the seismic data were originally acquired and imaged.

Global Seismology

Imaging in global seismology (whole-earth geophysics) has lagged behind the developments in exploration geophysics for several reasons. In contrast to artificial sources, earthquakes are uncontrolled, badly placed sources of seismic-wave energy, and the earth is only sparsely covered with seismometers. In addition, instrument responses were for a long time widely different, and recording was not done digitally. Thus, seismologists were faced with the paradox that the available data, despite the enormous volume, often contained crucial gaps.

In global seismology, the whole three-dimensional earth is considered as an object to be imaged. Seismic energy generated by earthquakes travels through the earth and is recorded by a distribution of seismic detectors, such as the World Wide Standardized Seismographic Network. By examining the travel times of the propagating energy for a number of earthquakes and stations, researchers can construct a model representing the velocity structure inside the earth. Likewise, by measuring the shapes and sizes of the amplitudes of the recorded energy, they can estimate a seismic attenuation model of the earth. Based upon these models, a three-dimensional tomographic image of the earth can be constructed. In 2004, seismic tomography revealed large pieces of subducted lithosphere “floating” in the upper mantle.

Global seismic tomography has been used to image convective flow within the mantle. Changes in seismic wave velocity have been used to identify sinking (cold) and rising (warm) mantle materials. Estimates can be made of the variation of seismic velocities inside the earth using seismic tomography, and these variations in turn depend upon the variations in composition, structure, and temperature of the materials inside. Mantle regions that are relatively hot have lower velocities compared to cooler regions at the same depth, because the higher temperatures reduce the values of the elastic constants of the mantle material. Seismic tomography supports a hybrid convection theory that postulates the existence of shallow, small-scale convection currents as well as of deep, large-scale convection currents in the mantle. Convection of the mantle is the primary driving force of plate tectonics. In general, tomographic results show a strong correlation at shallow depths with present plate boundaries, such as fast movement under cold, old shields and in subduction zones, and slow movement under hot, spreading ridges and other volcanically active areas. Three-dimensional images of the earth's interior reconstructed with seismic tomographic procedures have had a major effect on the understanding of the structure and dynamics of the earth.

Principal Terms

amplitude: the maximum departure (height) of a wave from its average value

attenuation: a reduction in amplitude or energy caused by the physical characteristics of the transmitting medium

imaging: a computer method for constructing a picture of subsurface geology from seismic data

inversion: the process of deriving from measured data a geological model that describes the subsurface and that is consistent with the measured data

lithology: the description of rocks, such as rock type, mineral makeup, and fluid in rock pores

resolution: the ability to separate two features that are very close together

seismic reflection method: measurements made of the travel times and amplitudes of events attributed to seismic waves that have been reflected from interfaces where changes in seismic properties occur

seismometer: an instrument used to record seismic energy; also known as a geophone or a seismic detector

travel time: the time needed for seismic energy to travel from the source into the subsurface geology and arrive back at a seismometer

Bibliography

Bording, R. P., et al. “Applications of Seismic Travel-Time Tomography.” Geophysics 90 (1987): 285-303. Discusses the basic principles of tomography and how they can be applied to seismic data to create a velocity model of the earth from recorded travel times.

Iyer, H. M., et al., eds. Seismic Tomography: Theory and Practice. London: Chapman and Hall, 1993. Various essays explore all aspects of seismic tomography and the inversion of seismic data.

Lines, L. R. “Cross-Borehole Seismology.” Geotimes 40 (January 1995): 11. Discusses applications of seismic tomography to the shallow subsurface.

Lo, Tien-When, and Philip L. Inderwiesen. Fundamentals of Seismic Tomography. Tulsa, Okla.: Society of Exploration Geophysicists, 1994. Provides a fine introduction to seismic tomography for students with little knowledge on the subject.

Nolet, Guust. A Breviary of Seismic Tomography. New York: Cambridge University Press, 2008. A text accessible to undergraduate students, this book provides an introduction to seismic tomography, wave propagation theory, travel-time tomography and more.

Nolet, Guust, ed. Seismic Tomography. Boston: D. Reidel, 1987. Describes the methods and reliability of seismic tomography. Contains many qualitative discussions that will be useful to the general reader as well as more technical discussions for those with the appropriate background. Primarily discusses applications of tomography to whole-earth geophysics, with some discussion of applications to exploration geophysics.

Poupinet, Georges. “Seismic Tomography.” Endeavour 14, no. 2 (1990): 52. Good description of seismic tomography as it is applied to the study of the deep structure of the earth by integrated analysis of seismic wave patterns generated from earthquakes.

Russell, B. H. Introduction to Seismic Inversion Methods. Tulsa, Okla.: Society of Exploration Geophysicists, 1988. Discusses techniques used for the inversion of seismic data, including principles of seismic tomography. Good illustrations.

Stewart, R. R. Exploration Seismic Tomography. Tulsa, Okla.: Society of Exploration Geophysicists, 1991. Recounts the historical development of tomography. Reviews the fundamentals of seismic tomographic techniques and discusses applications of seismic tomography, mainly to exploration geophysics.

Tarbuck, Edward J., Frederick K. Lutgens, and Dennis Tasa. Earth: An Introduction to Physical Geology. 10th ed. Upper Saddle River, N.J.: Prentice Hall, 2010. This college text provides a clear picture of the earth's systems and processes that is suitable for the high school or college reader. It has excellent illustrations and graphics. Bibliography and index.

Valentine, Andrew P., and John H. Woodhouse. “Reducing Errors in Seismic Tomography: Combined Inversion for Sources and Structure.” Geophysical Journal International 180 (2009): 847-857. Presents new solutions to problems in seismic tomography. A background in mathematics is necessary. The paper focuses on full-waveform inversion, but the authors suggest solutions may be useful in other areas.