Princeton University
Email:
nolet@princeton.edu
poster/oral: oral
| Geodynamical models of convection in the Earth predict temperature differences of 500 K or more and a minimum size for significant heterogeneities of the order of 100 km. Tomographic images of the mantle generally do not show anomalies corresponding to such large temperature contrasts, and the difference is large enough to shed doubts on mineralogical interpretations of tomographic images. Two major causes can be identified for this possible lack of resolution: the data resolution is limited by shortcomings in the ray path coverage (the "Backus-Gilbert limit"), but even if we had ideal data coverage the effects of wavefront healing would still bias the recovered amplitude of smaller heterogeneities (smaller than the "Fresnel limit"). To compound the problem, the amplitude bias may actually lead to artifical structure in the images if the resolution varies strongly over short distances. A backprojection technique can be used to estimate the resolution even for very large inverse problems, and adaptive parametrization can alleviate this effect. Until recently, the Backus-Gilbert limit was more significant than the Fresnel limit for body wave tomography. This may still be the case for high frequency global studies, but long period data modeling is now reaching the Fresnel limit, and high-resolution studies of D" with short period data may have gone beyond it. Born (or "banana doughnut") theory offers a significant improvement over ray theory in predicting travel time delays at finite frequency near the Fresnel limit. It may be used to extend the validity of delay time inversions beyond this limit. But not too far - wavefront healing satisfies a diffusion equation and the inverse problem is ill posed. If appropriately damped, an inversion can still handle this and should give more consistent results. Born theory is also needed to interpret PP and SS delays correctly, since their sensitivity differs markedly from a ray-theoretical sensitivity even at high frequency. All this may serve to improve the reliability of the amplitudes of velocity anomalies. But how can we extend the data set and push the Backus-Gilbert limit to smaller length scales? To improve resolution and resolve true amplitudes of velocity anomalies, the use of P and S amplitudes is still largely unexplored. Though influenced by the effects of focusing, and therefore sensitive to velocity heterogeneities, the challenge is to separate the effects due to source and receiver structure, as well as attenuation along the path, from the focusing effects. Results of a pilot study on deep earthquakes shows that such a separation is feasible. Instrument drift and errors in source mechanism contribute to amplitude errors that are of the order of 5-10% or less, whereas amplitudes easily vary by 30% or more. Amplitude information is complementary to delay time information. |