Skip to main content
Log in

Radon Transform Methods and Their Applications in Mapping Mantle Reflectivity Structure

  • Published:
Surveys in Geophysics Aims and scope Submit manuscript

Abstract

This paper reviews the fundamentals of Radon-based methods using examples from global seismic applications. By exploiting the move-out or curvature of signal of interest, Least-squares and High-resolution Radon transform methods can effectively eliminate random or correlated noise, enhance signal clarity, and simultaneously constrain travel time and ray angles. The inverse formulation of the Radon transform has the added benefits of phase isolation and spatial interpolation during data reconstruction. This study presents a ‘cookbook’ for Radon-based methods in analyzing shear wave bottom-side reflections from mantle interfaces, also know as SS precursors. We demonstrate that accurate and flexible joint Radon- and frequency-domain approaches are particularly effective in resolving the presence and depth of known and postulated mantle reflectors.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14

Similar content being viewed by others

References

  • An Y, Gu YJ, Sacchi M (2007) Imaging mantle discontinuities using least-squares Radon transform. J Geophys Res 112:B10303. doi:10.1029/2007JB005009

  • Anderson DL (2005) Scoring hot spots: the plume and plate paradigms. In: GR Foulger, JH Natland, DC Presnall, DL Anderson (eds) Plates, plumes, and paradigms, Geol. Soc. Am. Special Volume 388, 31–54

  • Bassin C, Laske G, Masters MG (2000) The current limits of resolution for surface wave tomography in North America. EOS Trans, AGU, 81, Fall. Meet. Suppl. F897

  • Bercovici D, Karato S-J (2003) Whole mantle convection and the transition-zone water filter. Nature 425:39–44

    Article  Google Scholar 

  • Beylkin G (1985) Imaging of discontinuities in the inverse scattering problem by inversion of a causal generalized radon transform. J Math Phys 26:99–108

    Article  Google Scholar 

  • Beylkin G (1987) Discrete radon transform. IEEE Trans Acoust 2:162–172 ASSP-2

    Article  Google Scholar 

  • Bina CR, Helffrich GR (1994) Phase transition clapeyron slopes and transition zone seismic discontinuity topography. J Geophys Res 99:15853–15860

    Article  Google Scholar 

  • Bostock NG (1996) Ps conversions from the upper mantle transition zone beneath the Canadian landmass. J Geophys Res 101:8393–8402

    Article  Google Scholar 

  • Bracewell RN (1956) Strip integration in radio astronomy. Aust J Phys 9:198–201

    Google Scholar 

  • Braunmiller J, Nabelek J (2002) Seismotectonics of the explorer region. J Geophys Res 107:2208. doi:10.1029/2001JB000220

    Article  Google Scholar 

  • Chapman CH (2004) Fundamentals of seismic wave propagation. Cambridge University Press, p 632

  • Clayton RW, McMechan GA (1981) Inversion of refraction data by wave field continuation. Geophysics 46:860–868

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Courtier AM, Revenaugh J (2008) Slabs and shear wave reflectors in the midmantle. J Geophys Res 113:B08312. doi:10.1029/2007JB005261

    Article  Google Scholar 

  • Courtillot V, Davaillie A, Besse J, Campbell IH (2003) Three distinct types of hotspots in the Earth’s mantle. Earth Planet Sci Lett 205:295–308

    Article  Google Scholar 

  • Davies D, Kelly EJ, Filson JR (1971) Vespa process for analysis of seismic signals. Nat Phys Sci 232:8–13

    Google Scholar 

  • Deuss A (2007) Seismic observations of transition-zone discontinuities beneath hotspot locations. In: Foulger GR, Jurdy DM (eds) Plates, plumes and planetary processes, Geological Society Special Paper 430, 121–136, doi: 10.1130/2007.2430(07)

  • Deuss A, Woodhouse JH (2001) Seismic observations of splitting of the mid-transition zone discontinuity in the Earth’s mantle. Science 294:354–357

    Article  Google Scholar 

  • Deuss A, Woodhouse JH (2002) A systematic search for mantle discontinuities using SS-precursors. Geophys Res Lett 29:1–4

    Article  Google Scholar 

  • Du Z, Vinnik LP, Foulger GR (2006) Evidence from P-to-S mantle converted waves for a flat “660-km” discontinuity beneath Iceland. Earth Planet Sci Lett 241:271–280

    Article  Google Scholar 

  • Dziewonski AM, Anderson DL (1981) Preliminary reference Earth model. Phys Earth Planet Inter 25:297–356

    Article  Google Scholar 

  • Dziewonski AM, Gilbert F (1976) Effect of small, aspherical perturbations on travel times and re-examination of the corrections for ellipticity. Geophys J R astr Soc 44:7–16

    Google Scholar 

  • Escalante C, Gu YJ, Sacchi M (2007) Simultaneous iterative time-domain deconvolution to teleseismic receiver functions. Geophys J Int 171:316–325. doi:10.1111/j.1365-246x.2007.03511.x

    Article  Google Scholar 

  • Estabrook H, Kind R (1996) The nature of the 660-kilometer upper-mantle seismic discontinuity from precursors to the PP phase. Science 274:1179–1182

    Article  Google Scholar 

  • Ekström G, Dziewonski AM (1998) The unique anisotropy of the Pacific upper mantle. Nature 394:168–172

    Article  Google Scholar 

  • Flanagan MP, Shearer PM (1998) Global mapping of topography on transition zone velocity discontinuities by stacking SS precursors. J Geophys Res 103:2673–2692

    Article  Google Scholar 

  • Foulger GR (2007) The “plate” model for the genesis of melting anomalies. Geol Soc Am 430:1–28 Special Paper

    Google Scholar 

  • Gorman A, Clowes R (1999) Wave-field tau-p analysis for 2-D velocity models: application to western North American lithosphere. Geophys Res Lett 26:2323–2326

    Article  Google Scholar 

  • Gossler J, Kind R (1996) Seismic evidence for very deep roots of continents. Earth Planet Sci Lett 138:1–13

    Article  Google Scholar 

  • Grand SP, van der Hilst RD, Widiyantoro S (1997) Global seismic tomography: a snapshot of convection in the Earth. GSA Today 7:1–7

    Google Scholar 

  • Gu YJ, Dziewonski AM, Agee CB (1998) Global de-correlation of the topography of transition zone discontinuities. Earth Planet Sci Lett 157:57–67

    Article  Google Scholar 

  • Gu YJ, Dziewonski AM (2002) Global variability of transition zone thickness. J Geophys Res 107:2135. doi:10.1029/2001JB000489

    Article  Google Scholar 

  • Gu YJ, Dziewonski AM, Ekstrom G (2003) Simultaneous inversion for mantle shear velocity and topography of transition zone discontinuities. Geophys J Int 154:559–583

    Article  Google Scholar 

  • Gu YJ, Dziewonski AM, Su W-J, Ekström G (2001) Models of the mantle shear velocity and discontinuities in the pattern of lateral heterogeneities. J Geophys Res 106:11169–11199

    Article  Google Scholar 

  • Gu YJ, An Y, Sacchi M, Schultz R, Ritsema J (2009) Mantle reflectivity structure beneath oceanic hotspots. Geophys J Int. doi:10.1111/j.1365-246x.2009.04242.x

    Google Scholar 

  • Hampson D (1986) Inverse velocity stacking for multiple elimination. J Can Soc Expl Geophys 22(1):44–55

    Google Scholar 

  • Hirose K (2002) Phase transitions in pyrolitic mantle around 670-km depth: implications for upwelling of plumes from the lower mantle. J Geophys Res 107:2078. doi:10.1029/2001JB000597

    Article  Google Scholar 

  • Houser C, Masters G, Flanagan GM, Shearer PM (2008) Determination and analysis of long-wavelength transition zone structure using SS precursors. Geophys J Int 174:178–194. doi:10.111/j.1365-246X.2008.03719.x

    Article  Google Scholar 

  • Ito E, Takahashi E (1989) Postspinel transformations in the system Mg2SiO4–Fe2SiO4 and some geophysical implications. J Geophys Res 94:10637–10646

    Article  Google Scholar 

  • Kappus ME, Harding AJ, Orcutt J (1990) A comparison of tau-p transform methods. Geophysics 55:1202. doi:10.1190/1.1442936

    Article  Google Scholar 

  • Karato S-I, Jung H (1998) Water, partial melting and the origin of the seismic low velocity and high attenuation zone in the upper mantle. Earth Planet Sci Lett 157:193–207

    Article  Google Scholar 

  • Katsura T, Ito E (1989) The system Mg2SiO4–Fe2SiO4 at high pressures and temperatures; precise determination of stabilities of olivine, modified spinel, and spinel. J Geophys Res 94:15663–15670

    Article  Google Scholar 

  • Kawakatsu H, Watada S (2007) Seismic evidence for deep water transportation in the mantle. Science 316:1468–1471

    Article  Google Scholar 

  • Kruger F, Weber M, Scherbaum F, Schittenhardt J (1993) Double beam analysis of anomalies in the core-mantle boundary region. Geophys Res Lett 20:1475–1478

    Article  Google Scholar 

  • Lawrence JF, Shearer PM (2006) A global study of transition zone thickness using receiver functions. J Geophys Res 111:B06307. doi:10.1029/2005JB003973

    Article  Google Scholar 

  • Lehmann I (1959) Velocities of longitudinal waves in the upper part of the Earth’s mantle. Geophys J R Astron Soc 15:93–113

    Google Scholar 

  • Li X, Kind R, Priestley K, Sobolev SV, Tilmann F, Yuan X, Weber M (2000) Mapping the Hawaiian plume conduit with converted seismic waves. Nature 427:827–829

    Article  Google Scholar 

  • Ma P, Wang P, De Hoop MV, Tenorio L, Van der Hilst RD (2007) Imaging of structure at and near the core-mantle boundary using a generalized radon transform: 2. Statistical inference of singularities. J Geophys Res 112:B08303. doi:10.1029/2006JB004513

    Article  Google Scholar 

  • Menke W (1989) Geophysical data analysis: discrete inverse theory. Academic Press Inc., San Diego, p 289

    Google Scholar 

  • Miller D, Oristaglio M, Beylkin G (1987) A new slant on seismic imaging: migration and integral geometry. Geophysics 52(7):943–964

    Article  Google Scholar 

  • Montelli R, Nolet G, Dahlen FA, Masters G, Engdah ER, Hung SH (2004) Finite-frequency tomography reveals a variety of plumes in the mantle. Science 303:338–343

    Article  Google Scholar 

  • Morgan WJ (1971) Convection plumes in the lower mantle. Nature 230:42–43

    Article  Google Scholar 

  • Neele F, de Regt H (1997) Imaging upper-mantle discontinuity topography using underside-reflection data. Geophys J Int 137(1):91–106

    Article  Google Scholar 

  • Niu F, Kawakatsu H (1995) Direct evidence for the undulation of the 660-km discontinuity beneath Tonga: comparison of Japan and California array data. Geophy Res Lett 22(5):531–534

    Article  Google Scholar 

  • Niu F, Kawakatsu H (1997) Depth variation of the mid-mantle seismic discontinuity. Geophys Res Lett 24(4):429–432

    Article  Google Scholar 

  • Papoulis A (1962) The Fourier integral and its applications. McGraw-Hill, New York

    Google Scholar 

  • Parker RL (1994) Geophysical inverse theory. Princeton University Press, Princeton, p 386

    Google Scholar 

  • Preston LA, Creager KC, Crosson RS, Brocher TM, Trehu AM (2003) Intraslab earthquakes: dehydration of the Cascadia slab. Science 302(5648):1197–1200. doi:10.1126/science.1090751

    Article  Google Scholar 

  • Radon J (1917) Uber die Bestimmung von Funktionen durch ihre Integralverte langs gewiusser Mannigfaltigkeiten, Berichte Sachsische Academie der Wissenschaften, Leipzig. Math Phys Kl 69:262–267

    Google Scholar 

  • Revenaugh J, Sipkin SA (1994) Seismic evidence for silicate melt atop the 410-km mantle discontinuity. Nature 369:474–476

    Article  Google Scholar 

  • Ringwood AE (1975) Composition and petrology of the earth’s mantle. McGraw-Hill, New York, p 630

    Google Scholar 

  • Ritsema J, Van Heijst HJ, Woodhouse JH (1999) Complex shear wav velocity structure imaged beneath Africa and Iceland. Science 286:1925–1928

    Article  Google Scholar 

  • Ritsema JH, van Heijst J, Woodhouse JH (2004) Global transition zone tomography. J Geophys Res 109:B02302. doi:10.1029/2003JB002610

    Article  Google Scholar 

  • Romanowicz B (2003) Global mantle tomography: progress status in the last 10 years. Annu Rev Geophys Space Phys 31(1):303

    Google Scholar 

  • Rondenay S, Abers G, van Keken P (2008) Seismic imaging of subduction metamorphism. Geology 36(4):275–278. doi:10.1030/G24112A

    Article  Google Scholar 

  • Rost S, Garnero E (2004) A study of the uppermost inner core from PKKP and P’P’ differential travel times. Geophys J Int 156:565–574. doi:10.1111/j.1365-246X.2004.02139.x

    Article  Google Scholar 

  • Rost S, Thomas C (2002) Array seismology: methods and applications. Reviews of Geophysics 40: 2-1–2-27. doi:10.1029/2000RG000100

    Article  Google Scholar 

  • Sacchi M, Ulrych TJ (1995) High-resolution velocity gathers and offset space reconstruction. Geophysics 60:1169–1177

    Article  Google Scholar 

  • Schmerr N, Garnero EJ (2006) Investigation of upper mantle discontinuity structure beneath the central Pacific using SS precursors. J Geophys Res 111:B08305. doi:10.1029/2005JB004197

    Article  Google Scholar 

  • Shearer PM (1990) Seismic imaging of upper-mantle structure with new evidence for a 520-km discontinuity. Nature 344:121–126

    Article  Google Scholar 

  • Shearer PM (1991) Imaging global body-wave phases by stacking long-period seismograms. J Geophys Res 96:20353–20364

    Article  Google Scholar 

  • Shearer PM (1993) Global mapping of upper mantle reflectors from long-period SS precursors. Geophys J Int 115:878–904

    Article  Google Scholar 

  • Shearer PM (1996) Transition zone velocity gradients and the 520-km discontinuity. J Geophys Res 101:3053–3066

    Article  Google Scholar 

  • Shearer PM (1999) Introduction to seismology. Cambridge Univ. Press, Cambridge, p 260

    Google Scholar 

  • Shen Y et al (2002) Seismic evidence for a tilted mantle plume and north-south mantle flow beneath Iceland. Earth Planet Sci Lett 197:262–272

    Article  Google Scholar 

  • Shen Y, Wolfe CJ, Solomon SC (2003) Seismological evidence for a mid-mantle discontinuity beneath Hawaii and Iceland. Earth Planet Sci Lett 214:143–151

    Article  Google Scholar 

  • Steinberger B, Sutherland R, O’Connell RJ (2004) Prediction of emperor-Hawaii seamount locations from a revised model of global plate motion and mantle flow. Nature 430:167–173

    Article  Google Scholar 

  • Stock JM, Molnar P (1988) Uncertainties and implications of the Cretaceous and Tertiary position of North America relative to Farallon, Kula, and Pacific plates. Tectonics 7:1339–1384

    Article  Google Scholar 

  • Su WJ, Woodward RL, Dziewonski AM (1994) Degree-12 model of shear velocity heterogeneity in the mantle. J Geophys Res 99:6945–6980

    Article  Google Scholar 

  • Tauzin B, Debayle E, Wittlinger G (2008) The mantle transition zone as seen by global Pds phases: no clear evidence for a thin transition zone beneath hotspots. J Geophys Res 113:B08309. doi:10.1029/2007JB005364

    Article  Google Scholar 

  • Thorson J, Claerbout J (1985) Velocity-stack and slant-stack stochastic inversion. Geophysics 50:2727–2741

    Article  Google Scholar 

  • Tonegawa T, Hirahara K, Shibutani T, Takuo S, Iwamori IH, Kanamori H, Shiomi K (2008) Water flow to the mantle transition zone inferred from a receiver function image of the Pacific slab. Earth Planet Sci Lett 274:346–354. doi:10.1016/j.epsl.2008.07.046

  • Trad D, Ulrych TJ, Sacchi M (2002) Accurate interpolation with high-resolution time-variant Radon transforms. Geophysics 67:644–656

    Article  Google Scholar 

  • van der Hilst RD, Karason H (1999) Compositional heterogeneity in the bottom 1000 kilometers of Earth’s mantle: toward a hybrid convection model. Science 286:1925–1928

    Article  Google Scholar 

  • Vidale JE, Benz HM (1992) Upper-mantle seismic discontinuities and the thermal structure of subduction zones. Nature 356:678–683

    Article  Google Scholar 

  • Walker D, Agee C (1989) Partitioning “equilibrium”, temperature gradients, and constraints on Earth differentiation. Earth Planet Sci Lett 96:49–60

    Article  Google Scholar 

  • Wang P, De Hoop MV, Van der Hilst RD, Ma P, Tenorio L (2006) Imaging of structure at and near the core mantle boundary using a generalized Radon transform: 1- construction of image gathers. J Geophys Res 111, B12, B12304. doi:10.1029/2005JB004241

  • Wessel P, Smith WHF (1995) The generic mapping tools (GMT) version 3.0 Technical Reference & Cookbook, SOEST/NOAA

  • Wilson CK, Guitton A (2007) Teleseismic wavefield interpolation and signal extraction using high resolution linear radon transforms. Geophys J Int 168:171–181

    Article  Google Scholar 

  • Weidner DJ, Wang Y (1998) Chemical and Clapeyron-induced buoyancy at the 660 km discontinuity. J Geophys Res 103:7431–7441

    Article  Google Scholar 

  • Weidner DJ, Wang Y (2000) Phase transformations: implications for mantle structure. In: Karato S et al (eds) Earth’deep interior: mineral physics and tomography from the atomic to the global scale. Geophys. Monogr. Ser, vol 117. AGU, Washington, D. C, pp 215–235

    Google Scholar 

  • Yilmaz O (1987) Seismic Data Processing. Soc Expl Geophys, Tulsa (Oklahoma), p 526

  • Zhou Y, Nolet G, Dahlen FA, Laske G (2006) Global upper-mantle structure from finite-frequency surface wave tomography. J Geophys Res 111:B04304. doi:10.1029/2005JB003677

    Article  Google Scholar 

Download references

Acknowledgments

We sincerely thank Yuling An, Ryan Schultz and Jeroen Ritsma for their scientific contributions and discussions. In particular, much of the work presented here was based on the MSc. thesis of Yuling An (currently at CGGVeritas) and an undergraduate summer project conducted by Ryan Schultz. We also thank IRIS for data archiving and dissemination. Some of the figures presented were prepared using the GMT software (Wessel and Smith 1995). Finally, we thank Surveys in Geophysics, particularly Michael Rycroft and Petra D. van Steenbergen, for inviting us to contribute to this Special Issue. The research project is funded by Alberta Ingenuity, National Science and Engineering Council (NSERC) and Canadian Foundation for Innovations (CFI).

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yu Jeffrey Gu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Gu, Y.J., Sacchi, M. Radon Transform Methods and Their Applications in Mapping Mantle Reflectivity Structure. Surv Geophys 30, 327–354 (2009). https://doi.org/10.1007/s10712-009-9076-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10712-009-9076-0

Keywords

Navigation