Dept. of Geophysics and Center for Wave Phenomena
Colorado School of Mines
Golden CO 80401
Email:
rsnieder@mines.edu
poster/oral: oral
| Seismic tomography provides detailed images of the Earth's mantle while exploration seismology allows us to image the internal structure of hydrocarbon reservoir with great detail. Despite the insights that these images give, they should be taken with a grain of salt, because they provide a blurred image of the Earth's interior. This was noted by George Backus and Freeman Gilbert who showed in the late 1960's that with a finite data set one can never fully reconstruct a medium. For this reason they introduced the concept of ``data functionals'', which reflects the notion that instead of reconstructing the medium locally one can only obtain weighted averages of the medium. Backus Gilbert theory can be extended to weakly nonlinear problems, and nonlinear resolution kernels can be computed. An example of the inversion of normal mode data is used to illustrate that for a finite data set the nonlinearity always leaves an imprint on the model estimation. There is another reason why we should not exclusively focus on images. There are many applications where we are primarily interested in changes in a medium over time. By analyzing the change in the data directly without creating an image of the change, it is possible to measure minute changes in a medium. A table-top experiment is shown where a relatively velocity change of 0.1% can be measured with an accuracy of 0.02%. This is applied to infer the nonlinear dependence of granite on temperature and the relation to acoustic emissions. |