What do seismic waves really resolve in an isotropic 3D Earth?

Guust Nolet, Henk Marquering, Tony Dahlen, Sergei Lebedev, Jun Tong (1) and Thomas Meier (2)

(1) Department of Geosciences, Princeton University
(2) Friedrich Schiller Universität, Jena

poster/oral: poster

On regional scales, there is often disagreement between tomographic models. Noise in the seismograms is probably a minor factor in causing such differences (although phase velocity measurements at low frequencies may be affected by atmospheric disturbances). More important, in our view, are the errors introduced by various assumptions made in the interpretation process, such as:

The interference of higher mode energy is no problem if waveforms are fitted, and no attempt is made to isolate a particular mode. However, waveform tomography currently disregards the interaction with higher modes due to scattering.

We have used Born theory for the scattering of surface wave modes (Snieder and Nolet, J. Geophys., 61:55-63,1987) to analyze different aspects of mode-mode conversions. Using a surface wave formalism for mode coupling greatly increases the efficiency of such calculations with respect to methods using discrete modes, and this enables us to calculate Frechet kernels in 3D. We show how one seismogram, which shows severe Love wave energy on the vertical component, can be fitted with 100% variance reduction assuming a 3D model of reasonable scattering strength. In a synthetic test, we show how scattered waves allow us to reconstruct a point scatterer using only one seismogram (Meier et al, JGR 1997, in press). We are currently implementing the theory in a new method of diffraction tomography for S waves.

We also show how the theory can be applied to compute 3D Frechet kernels for body waves. We do this for waveforms as well as for travel time anomalies as determined by crosscorrelation. The resulting kernels often defy intuition. For example, under certain conditions the sensitivity of the Earth to the travel time of a body wave is minimal on the ray itself, and greatest on a tube around the ray. Minimax phases such as SS have very complicated Frechet kernels. Conversions between the fundamental mode and higher modes induce a crustal sensitivity to body waves over large segments of the wavepath, remote from the ray location.

Finally, we show results from finite difference calculations. Large differences may exist between 'actual' travel times (from the FD simulations), ray-theoretical times determined with or without the Fermat approximation, and travel times as predicted by first-order Born theory. Again results are sometimes unexpected: we shall show an example where a negative velocity anomaly induces a faster arrival time as determined by crosscorrelation, and offer an explanation in terms of higher order Fresnel zones.

These results are very relevant when discussing a new reference Earth model. What started as a theoretical curiosity, is quickly turning out to become a major investigation into the validity of many assumptions that are commonly accepted to be true, and that underlie most if not all of the seismological imaging of the deep Earth. We conjecture that errors in theoretical assumptions are currently the major hurdle to get agreement about the extent and shape of 3D heterogeneity in the Earth.

Guust Nolet ( guust@geo.princeton.edu)

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