Skip to main content

Definition of the Subject

Seismic tomography refers to a number of techniques designed to investigate the interior of the earth using arrival times and/or waveforms from natural and artificial sources. The most common product of a tomographic study is a velocity model, although other parameters, such as attenuation, are also studied. The importance of seismic tomography stems from two facts. One, it generally has higher resolution than that provided by other geophysical methods. Two, it provides information that (a) can help solve fundamental problems concerning the internal structure of the earth at a global scale, and (b) has been used in tectonic and seismic hazards studies at a local scale. Seismic tomography has also been applied to data collected in boreholes, but because of the high expenses associated with drilling, borehole tomography is relatively little used.

Introduction

In the most general terms, seismic tomography problems are inverse problems, and before...

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Institutional subscriptions

Bibliography

  1. Aki K (1993) Overview. In: Iyer H, Hirahara K (eds) Seismic tomography. Chapman, London, pp 1–8

    Google Scholar 

  2. Aki K, Lee W (1976) Determination of three‐dimensional velocity anomalies under a seismic array using first P arrival times from local earthquakes, 1. A homogeneous initial model. J Geophys Res 81:4381–4399

    ADS  Google Scholar 

  3. Aki K, Richards P (1980) Quantitative seismology, vol 2. Freeman, San Francisco

    Google Scholar 

  4. Aki K, Christoffersson A, Husebye E (1977) Determination of the three‐dimensional seismic structure of the lithosphere. J Geophys Res 82:277–296

    ADS  Google Scholar 

  5. Allen M, Isaacson E (1998) Numerical analysis for applied science. Wiley, New York

    MATH  Google Scholar 

  6. Ambrose J (1973) Computerized transverse axial scanning (tomography): Part 2. Clin Appl Br J Radiol 46:1023–1047

    Google Scholar 

  7. Bai C-Y, Greenhalgh S (2005) 3‑D multi-step travel time tomography: imaging the local, deep velocity structure of Rabaul volcano, Papua New Guinea. Phys Earth Planet Inter 151:259–275

    ADS  Google Scholar 

  8. Bai C-Y, Greenhalgh S (2006) 3D local earthquake hypocenter determination with an irregular shortest‐path method. Bull Seism Soc Am 96:2257–2268

    Google Scholar 

  9. Bai C-Y, Greenhalgh S, Zhou B (2007) 3D ray tracing using a modified shortest‐path method. Geophysics 72(4):T27–T36

    ADS  Google Scholar 

  10. Bard Y (1974) Nonlinear parameter estimation. Academic Press, New York

    MATH  Google Scholar 

  11. Barret H, Hawkins W, Joy M (1983) Historical note on computed tomography. Radiology 147:172

    Google Scholar 

  12. Bates R, Peters T (1971) Towards improvements in tomography. NZ J Sci 14:883–896

    Google Scholar 

  13. Beck J, Arnold K (1977) Parameter estimation in engineering and science. Wiley, New York

    MATH  Google Scholar 

  14. Benz H, Smith R (1984) Simultaneous inversion for lateral velocity variations and hypocenters in the Yellowstone region using earthquake and refraction data. J Geophys Res 89:1208–1220

    ADS  Google Scholar 

  15. Benz H, Chouet B, Dawson P, Lahr J, Page R, Hole J (1996) Three‐dimensional P and S wave velocity structure of Redoubt Volcano, Alaska. J Geophys Res 101:8111–8128

    ADS  Google Scholar 

  16. Boschi L, Ampuero J-P, Peter D, Mai P, Soldati G, Giardini D (2007) Petascale computing and resolution in global seismic tomography. Phys Earth Planet Inter 163:245–250

    ADS  Google Scholar 

  17. Bracewell R (1956) Strip integration in radio astronomy. Aust J Phys 9:198–217

    MathSciNet  ADS  MATH  Google Scholar 

  18. Bracewell R, Riddle A (1967) Inversion of fan-beam scans in radio astronomy. J Astrophys 150:427–434

    ADS  Google Scholar 

  19. Broad W (1980) Riddle of the Nobel debate. Science 207:37–38

    ADS  Google Scholar 

  20. Brooks R, Di Chiro G (1976) Principles of computer assisted tomography (CAT) in radiographic and radioisotopic imaging. Phys Med Biol 5:689–732

    Google Scholar 

  21. Červený V (2001) Seismic ray theory. Cambridge University Press, Cambridge

    Google Scholar 

  22. Červený V, Molotkov I, Pšenčik I (1977) Ray method in seismology. Charles University, Prague

    Google Scholar 

  23. Chapman C (1987) The Radon transform and seismic tomography. In: Nolet G (ed) Seismic tomography. Reidel, Dordrecht, pp 25–47

    Google Scholar 

  24. Chen H, Chiu J-M, Pujol J, Kim K, Chen K-C, Huang B-S, Yeh Y-H, Chiu S-C (2006) A simple algorithm for local earthquake location using 3D V P and V S models: test examples in the central United States and in central eastern Taiwan. Bull Seis Soc Am 96:288–305

    Google Scholar 

  25. Claerbout J (1985) Imaging the Earth's Interior. Blackwell Scientific Publications, Boston

    Google Scholar 

  26. Cormack A (1963) Representation of a function by its line integrals, with some radiological applications. J Appl Phys 34:2722–2727

    ADS  MATH  Google Scholar 

  27. Cormack A (1964) Representation of a function by its line integrals, with some radiological applications, II. J Appl Phys 35:2908–2913

    ADS  MATH  Google Scholar 

  28. Cormack A (1973) Reconstruction of densities from their projections, with applications in radiological physics. Phys Med Biol 18:195–207

    Google Scholar 

  29. Cormack A (1980) Recollections of my work with computer assisted tomography. Mol Cell Biochem 32:57–61

    Google Scholar 

  30. Cormack A (1982) Computed tomography: some history and recent developments. Proc Symp Appl Math 27:35–42

    MathSciNet  Google Scholar 

  31. Creager K (1984) Geometry, velocity structure, and penetration depths of descending slabs in the western Pacific. Ph D dissertation, University of California, San Diego

    Google Scholar 

  32. Creager K, Boyd T (1992) Effects of earthquake mislocation on estimates of velocity structure. Phys Earth Planet Inter 75:63–76

    ADS  Google Scholar 

  33. Crosson R (1976) Crustal structure modeling of earthquake data. 1. Simultaneous least squares estimation of hypocenter and velocity parameters. J Geophys Res 81:3036–3046

    ADS  Google Scholar 

  34. Crowther R, DeRosier D, Klug A (1970) The reconstruction of a three‐dimensional structure from projections and its application to electron microscopy. Proc R Soc Lond Ser A 317:319–340

    ADS  Google Scholar 

  35. Deans S (1983) The Radon transform and some of its applications. Wiley, New York

    MATH  Google Scholar 

  36. DeRosier D, Klug A (1968) Reconstruction of three dimensional structures from electron micrographs. Nature 217:130–134

    ADS  Google Scholar 

  37. Dietz L, Ellsworth W (1990) The October 17, 1989 Loma Prieta, California, earthquake and its aftershocks: Geometry of the sequence from high‐resolution locations. Geophys Res Lett 17:1417–1420

    ADS  Google Scholar 

  38. Dietz L, Ellsworth W (1997) Aftershocks of the Loma Prieta earthquake and their tectonic implications. In: P Reasenberg (ed) The Loma Prieta, California, earthquake of October 17, 1989 – Aftershocks and postseismic effects. US Geol Surv Prof Pap 1550-D, D5-D47

    Google Scholar 

  39. Dines K, Lytle R (1979) Computerized geophysical tomography. Proc Inst Electr Electron Eng 67:1065–1073

    Google Scholar 

  40. Durrani T, Bisset D (1984) The Radon transform and its properties. Geophysics 49:1180–1187; Errata, 1985, 50:884–886

    ADS  Google Scholar 

  41. Dziewonski A (2003) Global seismic tomography: What we really can say and what we make up. Geol Soc Am Penrose Conference, Plume IV: Beyond the Plume Hypothesis, Abstracts (available at: www.mantleplumes.org/Penrose/PenPDFAbstracts/Dziewonski_Adam_abs.pdf)

  42. Eberhart‐Phillips D (1986) Three‐dimensional velocity structure in northern California Coast Ranges from inversion of local earthquake arrival times. Bull Seism Soc Am 76:1025–1052

    Google Scholar 

  43. Eberhart‐Phillips D, Stuart W (1992) Material heterogeneity simplifies the picture: Loma Prieta. Bull Seism Soc Am 82:1964–1968

    Google Scholar 

  44. Eliseevnin V (1965) Analysis of rays propagating in an inhomogeneous medium. Sov Phys Acoust 10:242–245

    Google Scholar 

  45. Evans J, Achauer U (1993) Teleseismic velocity tomography using the ACH method: theory and application to continental‐scale studies. In: Iyer H, Hirahara K (eds) Seismic tomography. Chapman, London, pp 319–360

    Google Scholar 

  46. Forsythe G, Malcolm M, Moler C (1977) Computer methods for mathematical computations. Prentice‐Hall, Englewood Cliffs

    MATH  Google Scholar 

  47. Franklin J (1970) Well-posed extensions of ill-posed linear problems. J Math Anal Appl 31:682–716

    MathSciNet  MATH  Google Scholar 

  48. Gilbert P (1972) Iterative methods for the three‐dimensional reconstruction of an object from projections. J Theor Biol 36:105–117

    Google Scholar 

  49. Gill P, Murray W, Wright M (1981) Practical optimization. Academic Press, London

    MATH  Google Scholar 

  50. Gordon R (1974) A tutorial on ART. Inst Electr Electron Eng Trans Nucl Sci NS-21:78–93

    Google Scholar 

  51. Gordon R, Bender R, Herman G (1970) Algebraic reconstruction techniques (ART) for three‐dimensional electron microscopy and X-ray photography. J Theor Biol 29:471–481

    Google Scholar 

  52. Grand S (1987) Tomographic inversion for shear velocity beneath the North American plate. J Geophys Res 92:14065–14090

    ADS  Google Scholar 

  53. Groetsch C (1993) Inverse problems in the mathematical sciences. Vieweg, Braunschweig

    MATH  Google Scholar 

  54. Gubbins D (1981) Source location in laterally varying media. In: Husebye E, Mykkeltveit S (eds) Identification of seismic sources – Earthquake or underground explosion. Reidel, Dordrecht, pp 543–573

    Google Scholar 

  55. Hansen P (1992) Analysis of discrete ill‐posed problems by means of the L-curve. SIAM Rev 34:561–580

    MathSciNet  MATH  Google Scholar 

  56. Hansen P (1994) Regularization Tools: A Matlab package for analysis and solution of discrete ill‐posed problems. Num Algorithms 6:1–35; (Software available at: http://www2.imm.dtu.dk/%7Epch/Regutools/)

    ADS  MATH  Google Scholar 

  57. Hanson K (1987) Bayesian and related methods in image reconstruction from incomplete data. In: Stark H (ed) Image recovery: theory and applications. Academic, Orlando, pp 79–125

    Google Scholar 

  58. Hauksson E (2000) Crustal structure and seismicity distribution adjacent to the Pacific and North America plate boundary in southern California. J Geophys Res 105:13875–13903

    ADS  Google Scholar 

  59. Hauksson E, Haase J (1997) Three‐dimensional V P and \( { V_P/V_S } \) velocity models of the Los Angeles basin and central Transverse Ranges, California. J Geophys Res 102:5423–5453

    ADS  Google Scholar 

  60. Hauksson E, Jones L, Hutton K (1995) The 1994 Northridge earthquake sequence in California: seismological and tectonic aspects. J Geophys Res 100:12335–12355

    ADS  Google Scholar 

  61. Hawley B, Zandt G, Smith R (1981) Simultaneous inversion for hypocenters and lateral velocity variations: an iterative solution with a layered model. J Geophys Res 86:7073–7086

    ADS  Google Scholar 

  62. Herman G (1980) Image reconstruction from projections. Academic Press, New York

    MATH  Google Scholar 

  63. Herman G, Lent A (1976) Iterative reconstruction algorithms. Comput Biol Med 6:273–294

    Google Scholar 

  64. Herman G, Hurwitz H, Lent A, Lung H-P (1979) On the Bayesian approach to image reconstruction. Inform Contr 42:60–71

    MathSciNet  MATH  Google Scholar 

  65. Hounsfield G (1973) Computerized transverse axial scanning (tomography): Part 1. Description of system. J Br Radiol 46:1016–1022

    Google Scholar 

  66. Hounsfield G (1979) Computed medical imaging, Nobel Lecture. (available at: nobelprize.org/nobel_prizes/medicine/laureates/1979/hounsfield-lecture.pdf)

  67. Hounsfield G (1980) Autobiography. In: Wilhelm O (ed) The Nobel Prizes 1979. The Nobel Foundation, Stockholm (available at: nobelprize.org/nobel_prizes/medicine/laureates/1979/hounsfield-autobio.html)

  68. Hudnut K et al (1996) Co‐seismic displacements of the 1994 Northridge, California, earthquake. Bull Seism Soc Am 86(1B):S19–S36

    Google Scholar 

  69. Hudson J (1980) The excitation and propagation of elastic waves. Cambridge University Press, Cambridge

    MATH  Google Scholar 

  70. Humphreys E, Clayton R (1988) Adaptation of back projection tomography to seismic travel times problems. J Geophys Res 93:1073–1085

    ADS  Google Scholar 

  71. Hurwitz H (1975) Entropy reduction in Bayesian analysis of measurements. Phys Rev A 12:698–706

    ADS  Google Scholar 

  72. Inoue H, Fukao Y, Tanabe K, Ogata Y (1990) Whole mantle P‑wave travel time tomography. Phys Earth Planet Inter 59:294–328

    ADS  Google Scholar 

  73. Ivansson S (1983) Remark on an earlier proposed iterative tomographic algorithm. J Geophys R Astr Soc 75:855–860

    Google Scholar 

  74. Jackson D (1979) The use of a priori data to resolve non‐uniqueness in linear inversion. J Geophys R Astr Soc 57:137–157

    ADS  Google Scholar 

  75. Julian B, Gubbins D (1977) Three‐dimensional seismic ray tracing. J Geophys 43:95–113

    Google Scholar 

  76. Kak A, Slaney M (1988) Principles of computerized tomographic imaging. Inst Electr Electron Eng Press, New York

    MATH  Google Scholar 

  77. Kim K-H (2003) Subsurface structure, seismicity patterns, and their implication to tectonic evolution in Taiwan. Ph D dissertation, University of Memphis, Memphis

    Google Scholar 

  78. Kim K-H, Chiu J-M, Pujol J, Chen K-C, Huang B-S, Yeh Y-H, Shen P (2005) Three‐dimensional V P and V S structural models associated with the active subduction and collision tectonics in the Taiwan region. J Geophys Int 162:204–220

    ADS  Google Scholar 

  79. Koch M (1985) Non‐linear inversion of local seismic travel times for the simultaneous determination of 3D‐velocity structure and hypocenters – application to the seismic zone Vrancea. J Geophys 56:160–173

    Google Scholar 

  80. Koch M (1993) Simultaneous inversion for 3‑D crustal structure and hypocenters including direct, refracted and reflected phases – I Development, validation and optimal regularization of the method. J Geophys Int 112:385–412

    ADS  Google Scholar 

  81. Komatitsch D, Tsuboi S, Tromp J (2005) The spectral‐element method in seismology. In: Levander A, Nolet G (eds) Seismic earth: array analysis of broadband seismograms. Geophysical Monograph Series, vol 157. Am Geophys Union, Washington DC, pp 205–227

    Google Scholar 

  82. Langenheim V, Griscom A, Jachens R, Hildenbrand T (2000) Preliminary potential‐field constraints on the geometry of the San Fernando basin, southern California. US Geol Survey Open-File Report 00–219

    Google Scholar 

  83. Lawson C, Hanson R (1974) Solving least squares problems. Prentice‐Hall, Englewood Cliffs

    MATH  Google Scholar 

  84. Lee W, Pereyra V (1993) Mathematical introduction to seismic tomography. In: Iyer H, Hirahara K (eds) Seismic tomography. Chapman, London, pp 9–22

    Google Scholar 

  85. Lee W, Stewart S (1981) Principles and applications of microearthquake networks. Academic Press, New York

    Google Scholar 

  86. Lees J, Crosson R (1989) Tomographic inversion for three‐dimensional velocity structure at Mount St. Helens using earthquake data. J Geophys Res 94:5716–5728

    ADS  Google Scholar 

  87. Levenberg K (1944) A method for the solution of certain non‐linear problems in least squares. Quart Appl Math 2:164–168

    MathSciNet  MATH  Google Scholar 

  88. Lewitt R (1983) Reconstruction algorithms: transform methods. Proc Inst Electr Electron Eng 71:390–408

    Google Scholar 

  89. Liang W-T, Chiu J-M, Kim K (2007) Anomalous Pn waves observed in eastern Taiwan: implications of a thin crust and elevated oceanic upper mantle beneath the active collision‐zone suture. Bull Seism Soc Am 97:1370–1377

    Google Scholar 

  90. Ma K-F, Wang J-H, Zhao D (1996) Three‐dimensional seismic velocity structure of the crust and uppermost mantle beneath Taiwan. J Phys Earth 44:85–105

    Google Scholar 

  91. Magistrale H, Day S, Clayton R, Graves R (2000) The SCEC southern California reference three‐dimensional seismic velocity model version 2. Bull Seism Soc Am 90(6B):S65–S76

    Google Scholar 

  92. Marquardt D (1963) An algorithm for least‐squares estimation of nonlinear parameters. J Soc Ind Appl Math 11:431–441

    MathSciNet  MATH  Google Scholar 

  93. Martin M, Ritter J, CALIXTO Working Group (2005) High‐resolution teleseismic body‐wave tomography beneath SE Romania – I. Implications for three‐dimensional versus one‐dimensional crustal correction strategies with a new crustal velocity model. J Geophys Int 162:448–460

    ADS  Google Scholar 

  94. Meskò A (1984) Digital filtering: applications in geophysical exploration for oil. Wiley, New York

    Google Scholar 

  95. Monna S, Filippi L, Beranzoli L, Favali P (2003) Rock properties of the upper-crust in Central Apennines (Italy) derived from high‐resolution 3‑D tomography. Geophys Res Lett 30(61):1–4 doi:10.1029/2002GL016780

    Google Scholar 

  96. Morelli A (1993) Teleseismic tomography: core‐mantle boundary. In: Iyer H, Hirahara K (eds) Seismic tomography. Chapman, London, pp 163–189

    Google Scholar 

  97. Mori J, Wald D, Wesson R (1995) Overlapping fault planes of the (1971) San Fernando and 1994 Northridge, California earthquakes. Geophys Res Lett 22:1033–1036

    ADS  Google Scholar 

  98. Moser T (1991) Shortest path calculation of seismic rays. Geophysics 56:59–67

    ADS  Google Scholar 

  99. Moser T, Nolet G, Snieder R (1992) Ray bending revisited. Bull Seismol Soc Am 82:259–288

    Google Scholar 

  100. Moser T, Van Eck T, Nolet G (1992) Hypocenter determination in strongly heterogeneous earth models using the shortest path method. J Geophys Res 97:6563–6572

    ADS  Google Scholar 

  101. Nakanishi I, Yamaguchi K (1986) A numerical experiment on nonlinear image reconstruction from first‐arrival times for two‐dimensional island arc structure. J Phys Earth 34:195–201

    Google Scholar 

  102. Nelson G, Vidale J (1990) Earthquake locations by 3‑D finite‐difference travel times. Bull Seism Soc Am 80:395–410

    Google Scholar 

  103. Noble B, Daniel J (1977) Applied linear algebra. Prentice‐Hall, Englewood Cliffs

    MATH  Google Scholar 

  104. Nolet G (1993) Solving large linearized tomographic problems. In: Iyer H, Hirahara K (eds) Seismic tomography. Chapman, London, pp 227–247

    Google Scholar 

  105. Okubo P, Benz H, Chouet B (1997) Imaging the crustal magma sources beneath Mauna Loa and Kilauea Volcanoes, Hawaii. Geology 25:867–870

    ADS  Google Scholar 

  106. Oldendorf W (1961) Isolated flying spot detection of radio density discontinuities – Displaying the internal structural pattern of a complex object. IRE Trans Biomed Elec BME-8:68–72

    Google Scholar 

  107. Oransky I (2004) Obituary. Sir Godfrey N Hounsfield. Lancet 364:1032

    Google Scholar 

  108. Paige C, Saunders M (1982) LSQR: An algorithm for sparse linear equations and sparse least square problems. ACM Trans Math Softw 8:43–71

    MathSciNet  MATH  Google Scholar 

  109. Parker R (1994) Geophysical inverse theory. Princeton University Press, Princeton

    MATH  Google Scholar 

  110. Pavlis G, Booker J (1980) The mixed discrete‐continuous inverse problem: application to the simultaneous determination of earthquake hypocenters and velocity structure. J Geophys Res 85:4801–4810

    ADS  Google Scholar 

  111. Penrose R (1955) A generalized inverse for matrices. Proc Camb Phil Soc 51:406–413

    MathSciNet  ADS  MATH  Google Scholar 

  112. Pereyra V, Lee W, Keller H (1980) Solving two-point seismic‐ray tracing problems in a heterogeneous medium. Bull Seism Soc Am 70:79–99

    Google Scholar 

  113. Podvin P, Lecomte I (1991) Finite difference computation of traveltimes in very contrasted velocity models: a massively parallel approach and its associated tools. J Geophys Int 105:271–284

    ADS  Google Scholar 

  114. Press W, Teukolsky S, Vetterling W, Flannery B (1992) Numerical Recipes. Cambridge University Press, Cambridge

    Google Scholar 

  115. Prothero W, Taylor W, Eickemeyer J (1988) A fast, two-point, three‐dimensional raytracing algorithm using a simple step search method. Bull Seism Soc Am 78:1190–1198

    Google Scholar 

  116. Pujol J (1995) Application of the JHD technique to the Loma Prieta, California, mainshock‐aftershock sequence and implications for earthquake location. Bull Seism Soc Am 85:129–150

    Google Scholar 

  117. Pujol J (1996) Comment on: “The 1989 Loma Prieta earthquake imaged from inversion of geodetic data” by Thora Árnadóttir and Paul Segall. J Geophys Res 101:20133–20136

    ADS  Google Scholar 

  118. Pujol J (1996) An integrated 3D velocity inversion – joint hypocentral determination relocation analysis of events in the Northridge area. Bull Seism Soc Am 86(1B):S138–S155

    Google Scholar 

  119. Pujol J (2000) Joint event location – The JHD technique and applications to data from local seismic networks. In: Thurber C, Rabinowitz N (eds) Advances in seismic event location. Kluwer, Dordrecht, pp 163–204

    Google Scholar 

  120. Pujol J (2003) Elastic wave propagation and generation in seismology. Cambridge University Press, Cambridge

    Google Scholar 

  121. Pujol J (2007) The solution of nonlinear inverse problems and the Levenberg‐Marquardt method. Geophysics 72(4):W1–W16

    Google Scholar 

  122. Pujol J et al (1989) 3‑D P- and S‑wave velocity structure of the Andean foreland in San Juan, Argentina, from local earthquakes. Eos Trans Am Geoph Union 70(43):1213

    Google Scholar 

  123. Pujol J, Mueller K, Peng S, Chitupolu V (2006) High‐resolution 3D P‑wave velocity model for the East Ventura–San Fernando basin, California, and relocation of events in the Northridge and San Fernando aftershock sequences. Bull Seism Soc Am 96:2269–2280

    Google Scholar 

  124. Ramachandran G, Lakshminarayanan A (1971) Three‐dimensional reconstruction from radiographs and electron micrographs: application of convolutions instead of Fourier transforms. Proc Natl Acad Sci USA 68:2236–2240

    MathSciNet  ADS  Google Scholar 

  125. Ratchkovsky N, Pujol J, Biswas N (1997) Relocation of earthquakes in the Cook Inlet area, south central Alaska, using the joint hypocenter determination method. Bull Seism Soc Am 87:620–636

    Google Scholar 

  126. Rau R-J, Wu F (1995) Tomographic imaging of lithospheric structures under Taiwan. Earth Planet Lett 133:517–532

    ADS  Google Scholar 

  127. Robinson E (1982) Spectral approach to geophysical inversion by Lorentz, Fourier, and Radon transforms. Proc Inst Electr Electron Eng 70:1039–1054

    Google Scholar 

  128. Roecker S, Yeh Y, Tsai Y (1987) Three‐dimensional P and S wave velocity structures beneath Taiwan: deep structure beneath an arc‐continent collision. J Geophys Res 92:10547–10570

    ADS  MATH  Google Scholar 

  129. Romanowicz B (2003) Global mantle tomography: Progress status in the past 10 years. Annu Rev Earth Planet Sci 31:303–328

    ADS  Google Scholar 

  130. Sage A, Melsa J (1971) Estimation theory with applications to communications and control. McGraw‐Hill, New York

    MATH  Google Scholar 

  131. Sandoval S, Kissling E, Ansorge J, Svekalapko Seismic Tomography Working Group (2003) High‐resolution body wave tomography beneath the Svekalapko array: I, A priori three‐dimensional crustal model and associated traveltime effects on teleseismic wave fronts. J Geophys Int 153:75–87

    Google Scholar 

  132. Shepp L, Kruskal J (1978) Computerized tomography: the new medical X-ray technology. Am Math Mon 85:420–439

    MathSciNet  MATH  Google Scholar 

  133. Shepp L, Logan B (1974) The Fourier reconstruction of a head section. Inst Electr Electron Eng Trans Nucl Sci NS-21:21–43

    Google Scholar 

  134. Snoke J, Lahr J (2001) Locating earthquakes: at what distances can the Earth no longer be treated as flat? Seism Res Lett 72:538–541

    Google Scholar 

  135. Soldati G, Boschi L, Piersanti A (2006) Global seismic tomography and modern parallel computers. Ann Geophys 49:977–986

    Google Scholar 

  136. Sorenson H (1980) Parameter estimation: principles and problems. Dekker, New York

    MATH  Google Scholar 

  137. Spakman W (1993) Iterative strategies for non‐linear travel time tomography using global earthquake data. In: Iyer H, Hirahara K (eds) Seismic tomography. Chapman, London, pp 190–226

    Google Scholar 

  138. Stanton L (1969) Basic medical radiation physics. Appleton‐Century‐Crofts, New York

    Google Scholar 

  139. Stewart J, Choi Y, Graves R, Shaw J (2005) Uncertainty of southern California basin depth parameters. Bull Seism Soc Am 95:1988–1993

    Google Scholar 

  140. Süss M, Shaw J (2003) P wave seismic velocity structure derived from sonic logs and industry reflection data in the Los Angeles basin, California. J Geophys Res 108(13):1–18 doi:10.1029/2001JB001628

  141. Tarantola A, Valette B (1982) Inverse problems = quest for information. J Geophys 50:159–170

    Google Scholar 

  142. Tarantola A, Valette B (1982) Generalized nonlinear inverse problems solved using the least squares criterion. Rev Geophys Space Phys 20:219–232

    MathSciNet  ADS  Google Scholar 

  143. Teng T-L, Aki K (1996) Preface to the 1994 Northridge earthquake special issue. Bull Seism Soc Am 86(1B):S1–S2

    Google Scholar 

  144. Thurber C (1983) Earthquake locations and three‐dimensional crustal structure in the Coyote Lake area, central California. J Geophys Res 88:8226–8236

    ADS  Google Scholar 

  145. Thurber C (1992) Hypocenter‐velocity structure coupling in local earthquake tomography. Phys Earth Planet Inter 75:55–62

    ADS  Google Scholar 

  146. Thurber C (1993) Local earthquake tomography: velocities and \( { V_{\mathrm{P}}/V_{\mathrm{S}} } \) – theory. In: Iyer H, Hirahara K (eds) Seismic tomography. Chapman, London, pp 563–583

    Google Scholar 

  147. Thurber C, Kissling E (2000) Advances in travel‐time calculations for three‐dimensional structures. In: Thurber C, Rabinowitz N (eds) Advances in seismic event location. Kluwer, Dordrecht, pp 71–99

    Google Scholar 

  148. Tihonov A (1963) Solution of incorrectly formulated problems and the regularization method. Sov Math 4:1035–1038; (Note: a more common transliteration of this author's Russian name is Tikhonov.)

    MathSciNet  Google Scholar 

  149. Titchmarsh W (1948) Introduction to the theory of Fourier integrals. Oxford University Press, Oxford

    Google Scholar 

  150. Trampert J, Van der Hilst R (2005) Towards a quantitative interpretation of global seismic tomography. In: Van der Hilst R, Bass J, Matas J, Trampert J (eds) Earth's deep mantle: structure, composition, and evolution. Geophysical Monograph Series, vol 160. Am Geophys Union, Washington DC, pp 47–62

    Google Scholar 

  151. Tryggvason A, Bergman B (2006) A traveltime reciprocity discrepancy in the Podvin & Lecomte time3d finite difference algorithm. J Geophys Int 165:432–435

    ADS  Google Scholar 

  152. Um J, Thurber C (1987) A fast algorithm for two-point seismic ray tracing. Bull Seism Soc Am 77:972–986

    Google Scholar 

  153. Van der Hilst R, Engdahl E (1992) Step-wise relocation of ISC earthquake hypocenters for linearized tomographic imaging of slab structure. Phys Earth Planet Inter 75:39–53

    ADS  Google Scholar 

  154. Van der Sluis A, Van der Vorst H (1987) Numerical solution of large, sparse linear algebraic systems arising from tomographic problems. In: Nolet G (ed) Seismic tomography. D Reidel, Dordrecht, pp 49–83

    Google Scholar 

  155. Van Tiggelen R (2002) In search for the third dimension: from radiostereoscopy to three‐dimensional imaging. JBR-BTR 85:266–270

    Google Scholar 

  156. Van Tiggelen R, Pouders E (2003) Ultrasound and computed tomography: spin-offs of the World Wars. JBR-BTR 86:235–241

    Google Scholar 

  157. Vidale J (1988) Finite‐difference calculation of travel times. Bull Seism Soc Am 78:2062–2076

    Google Scholar 

  158. Vidale J (1990) Finite‐difference calculation of travel times in three dimensions. Geophysics 55:521–526

    ADS  Google Scholar 

  159. Villaseñor A, Benz H, Filippi L, De Luca G, Scarpa R, Patanè G, Vinciguerra S (1998) Three‐dimensional P‑wave velocity structure of Mt. Etna, Italy. Geophys Res Lett 25:1975–1978

    Google Scholar 

  160. Wald D, Graves R (1998) The seismic response of the Los Angeles basin, California. Bull Seism Soc Am 88:337–356

    Google Scholar 

  161. Woodhouse J, Dziewonski A (1989) Seismic modelling of the Earth's large-scale three‐dimensional structure. Phil Trans Roy Soc Lond A 328:291–308

    ADS  Google Scholar 

  162. Zhao D, Kanamori H (1995) The 1994 Northridge earthquake: 3‑D crustal structure in the rupture zone and its relation to the aftershock locations and mechanisms. Geophys Res Lett 22:763–766

    ADS  Google Scholar 

  163. Zhao D, Hasegawa A, Horiuchi S (1992) Tomographic imaging of P and S wave velocity structure beneath northeastern Japan. J Geophys Res 97:19909–19928

    ADS  Google Scholar 

  164. Zhdanov M (2002) Geophysical inverse theory and regularization problems. Elsevier, Amsterdam

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag

About this entry

Cite this entry

Pujol, J. (2009). Tomography, Seismic. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_553

Download citation

Publish with us

Policies and ethics