## Applications of *finite-frequency* tomography

**Principal Investigators:**

Tony Dahlen

Guust Nolet

Tony Dahlen

Guust Nolet

**Postdocs:**

Raffaella Montelli (now at Exxon-Mobil Research, Houston)

Raffaella Montelli (now at Exxon-Mobil Research, Houston)

**Graduate students:**

Ying Zhou (now at Virginia Tech)

Karin Sigloch

Yue Tian

Ying Zhou (now at Virginia Tech)

Karin Sigloch

Yue Tian

**Until recently, seismic tomography provided little direct evidence for lower mantle plumes. The existence of the African and Pacic superplumes (vast piles of material with lowered seismic velocity and probably a higher density) was uncontested, but as recently as 2003 Ritsema and Allen concluded:**

*Whole-mantle plumes are well established through both numerical and analog experiments, but conclusive evidence for their existence remains elusive on Earth*. At that time the first, still tentative, images of plumes were appearing in the literature, but agreement between different models was poor. One of the major hurdles is the (presumed) narrow conduit of plumes, which makes it easy for seismic waves to diffract around them, thus masking any delay acquired by the wave energy that actually travels through the plume by earlier arrivals that have found a way around the low velocities.**Over the past ten years, Tony Dahlen and I have been working together to develop ways to take wave diffraction into account in seismic tomography, in such a way that it could be applied to the gigantic systems of equations we use to interpret delays of seismic P and S waves (see also the ongoing discussion regarding these theoretical developments). When Raffaella Montelli started to apply the newly developed theory of**

*finite-frequency*tomography, we unexpectedly discovered evidence for twenty plumes penetrating deeply into the lower mantle (Montelli et al., 2004b). Resolution analysis, published in a (widely ignored...) appendix to that paper, showed that the evidence for lower mantle plumes was conclusive for at least a dozen of them. The discovery came at a time that the plume hypothesis itself was under attack (see for example www.mantleplumes.org ). Not everyone was immediately convinced. "I think it is fair to at least suspect that they are overinterpreting their data set (...) I think it is a leap of faith to claim a discovery", said Barbara Romanowicz (Berkeley) in Dick Kerr's News of the Week article in the same issue of Science.**With time, however, confirming evidence accumulated. Ray-theoretical inversions of data including core phases by Dapeng Zhao in Japan confirmed the existence of some of the stronger lower mantle plumes (Nolet et al., 2006). Raffaella Montelli inverted S wave delays (long period data only), and improved the earlier P wave model by removing noise introduced by a faulty crustal correction algorithm. The resulting catalogue of mantle plumes (Montelli et al., 2006b) shows that most deep mantle plumes are confirmed by the S wave interpretations, even though the limitation to a single frequency for S waves degrades the resolution of finite frequency tomography considerably. The interesting exception is Iceland - the S waves do detect a lower mantle plume signal where the P waves show nothing, despite a high enough resolution (neither type sees a plume in midmantle, though).**

**At the same time, Ying Zhou has inverted a global data set of phase velocities from Gabi Laske, and discovered a strong correlation between the spreading velocity of oceanic ridges and the depth of the low velocity zone under the ridge imaged with finite frequency tomography of Love wave phase velocities (Zhou et al., 2006). So far we have been working with existing data sets. But finite-frequency theory is most effective if delay times are measured at a series of frequencies, because this allows us to make use of the varying sensitivity. For example, if a nonzero delay time shows no dispersion over the full frequency band, it means that the structure that causes it must extend at least to the size of the "fattest" Frechet-kernel. A single high-frequency "ray" would show the delay, but carries no information about the size of the anomaly. Delays are easy to measure at very long periods (by cross-sorrelation) or at very short periods (by picking of the onset). It is clear that cross-correlation is the preferred way of measuring delay times, but how to do that at intermediate to short periods is far from clear. For example, the P waveform changes as a function of the varying contributions of the surface reflections pP and sP, depending on the radiation pattern of the source. Karin Sigloch solved this problem in a way that is as elegant as efficient (Sigloch and Nolet, 2006), and efforts are now under way by Karin, and new graduate student Yue Tiang, to measure frequency-dependent delay times and amplitudes for all major events in the IRIS data base.**

**Relevant publications:**

**Dahlen, F.A. and G. Nolet, Comment on the paper "On sensitivity kernels for wave-equation transmission tomography" by de Hoop and van der Hilst, Geophys. J. Int., 163, 949-951, 2005.**

Levander, A. and G. Nolet, Perspectives on array seismology and US Array, in A. Levander and G. Nolet (eds.), Seismic Earth: Analysis of broadband seismograms, AGU Monograph Series, 1-6, 2005.

Lebedev, S., G. Nolet, T. Meier and R.D. van der Hilst, Automated multimode inversion of surface and S waveforms, Geophys. J. Int., 162, 951-964, 2005.

Montelli, R., G. Nolet, G. Masters, F.A. Dahlen and S.H.-Hung, P and PP global traveltime tomography: Rays versus waves, Geophys. J. Int., 158, 637-654, 2004a.

Montelli, R., G. Nolet, F.A. Dahlen, G. Masters, E.R. Engdahl and S.H.-Hung, Finite-frequency tomography reveals a variety of plumes in the mantle, Science, 303, 338-343, 2004b.

Montelli, R., G. Nolet and F.A. Dahlen, Comment on `Banana-doughnut kernels and mantle tomography' by van der Hilst and de Hoop, in press, Geophys. J. Int., 2006a.

Montelli, R. G. Nolet, F.A. Dahlen and G. Masters, A catalogue of deep mantle plumes: new results from finite-frequency tomography, subm. to Geochem. Geophys. Geosys. (G3), 2006b.

Nolet, G. and R. Montelli, Optimum parameterization of tomographic models, Geophys. J. Int., 161, 365-372, 2005.

Nolet, G., F.A. Dahlen and R. Montelli, Traveltimes and amplitudes of seismic waves: a re-assessment, in A. Levander and G. Nolet (eds.), Seismic Earth: Analysis of broadband seismograms, AGU Monograph Series, 37-48, 2005.

Nolet, G., Plume Imagery, in: McGraw-Hill Yearbook of Science and Technology, 240-245, 2006.

Sigloch, K. and G. Nolet, Measuring finite-frequency body wave amplitudes and travel times, subm. to Geophys. J. Int., 2005.

Zhou, Y., F.A. Dahlen and G. Nolet, Three-dimensional sensitivity kernels for surface wave observables, Geophys. J. Int., 158, 142-168, 2004.

Zhou, Y., F.A. Dahlen, G. Nolet and G. Laske, Finite-frequency effects in global surface-wave tomography, Geophys. J. Int., 163, 1087-1111, 2005.

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

Levander, A. and G. Nolet, Perspectives on array seismology and US Array, in A. Levander and G. Nolet (eds.), Seismic Earth: Analysis of broadband seismograms, AGU Monograph Series, 1-6, 2005.

Lebedev, S., G. Nolet, T. Meier and R.D. van der Hilst, Automated multimode inversion of surface and S waveforms, Geophys. J. Int., 162, 951-964, 2005.

Montelli, R., G. Nolet, G. Masters, F.A. Dahlen and S.H.-Hung, P and PP global traveltime tomography: Rays versus waves, Geophys. J. Int., 158, 637-654, 2004a.

Montelli, R., G. Nolet, F.A. Dahlen, G. Masters, E.R. Engdahl and S.H.-Hung, Finite-frequency tomography reveals a variety of plumes in the mantle, Science, 303, 338-343, 2004b.

Montelli, R., G. Nolet and F.A. Dahlen, Comment on `Banana-doughnut kernels and mantle tomography' by van der Hilst and de Hoop, in press, Geophys. J. Int., 2006a.

Montelli, R. G. Nolet, F.A. Dahlen and G. Masters, A catalogue of deep mantle plumes: new results from finite-frequency tomography, subm. to Geochem. Geophys. Geosys. (G3), 2006b.

Nolet, G. and R. Montelli, Optimum parameterization of tomographic models, Geophys. J. Int., 161, 365-372, 2005.

Nolet, G., F.A. Dahlen and R. Montelli, Traveltimes and amplitudes of seismic waves: a re-assessment, in A. Levander and G. Nolet (eds.), Seismic Earth: Analysis of broadband seismograms, AGU Monograph Series, 37-48, 2005.

Nolet, G., Plume Imagery, in: McGraw-Hill Yearbook of Science and Technology, 240-245, 2006.

Sigloch, K. and G. Nolet, Measuring finite-frequency body wave amplitudes and travel times, subm. to Geophys. J. Int., 2005.

Zhou, Y., F.A. Dahlen and G. Nolet, Three-dimensional sensitivity kernels for surface wave observables, Geophys. J. Int., 158, 142-168, 2004.

Zhou, Y., F.A. Dahlen, G. Nolet and G. Laske, Finite-frequency effects in global surface-wave tomography, Geophys. J. Int., 163, 1087-1111, 2005.

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