FURTHER THOUGHTS ON POPPERIAN GEOPHYSICS--THE EXAMPLE OF DECONVOLUTION"

ZIOLKOWSKI, A. 1982, Further Thoughts on Popperian Geophysics-The Example of Deconvolution, Geophysical Prospecting, 30, 155-165. Popper's demarcation criterion should be applied to all our theories in geophysics to ensure that our science progresses. We must expose our theories to tests in which they stand some risk of being refuted. But if we have a theory which has no rivals it may be difficult in practice to devise a test in which the theory risks being refuted conclusively. The example of the deconvolution problem for seismic data is considered for the case where the source wavelet is unknown. It is shown that all our existing theories of deconvolutions are not scientific in Popper's sense; they are statistical models. We cannot compare these models in a way that is independent of the geology, for each model requires the geology to have a different set of statistical properties. Even in our chosen geology it may be extremely difficult to determine the most applicable model and hence determine the " correct " deconvolution theory. It is more scientific to attempt to solve the deconvolution problem (a) by finding the source wavelet first, deterministically, or (b) by trying to force the wavelet to be a spike-that is, by devising a " perfect " seismic source. A new method of seismic surveying, which has been proposed to tackle the deconvolution problem by the first of these approaches, is based on a theory which is open to refutation by a simple Popperian test. Since the theory makes no assumptions about the geology, the test has equal validity in any geology. It pays to frame our theories in such a way that they may easily be put at risk. Only in this way will we establish whether we are on firm ground. The alternative is simply to take things on trust.