In the three publications:
- Dorman, LM, Lewis BTR. 1970. Experimental Isostasy .1. Theory of Determination of
the Earths Isostatic Response to a Concentrated Load.
Journal of Geophysical Research. 75:3357.
- Lewis, BTR, Dorman LM. 1970. Experimental Isostasy .2. An Isostatic Model for USA
Derived from Gravity and Topographic Data. Journal of Geophysical Research. 75:3367.
- Dorman, LM, Lewis BTR. 1972. Experimental Isostasy .3. Inversion of Isostatic Green-Function and
Lateral Density Changes. Journal of Geophysical Research. 77:3068
Brian and I showed that the relationship between the earth’s topography and its gravity field could be represented as a Fredholm integral equation of the first kind*.
Moreover, the kernel of this equation could be extracted from gravity and topographic data. And, that this kernel, could be transformed into a function of depth for the case of ‘local compensation’, which represents an earth whose lithosphere can support topography only ‘locally’. This is called the Pratt model, after John Henry Pratt.
The transformation from the kernel, or Greens Function, into the variation of density with depth is through application of an inverse Laplace Transform, which is a process which amplifies high spatial frequencies, and requires regularization, such as use of the method of Backus and Gilbert.
Thus we claim to have solved the inverse problem of Pratt Isostasy.
Brian and I were students of Robert P. Meyer, who was a student of George P Woollard, who devoted much effort to the prediction of gravity from geology. So we had an appropriate scientific heritage.
* See http://mathworld.wolfram.com/FredholmIntegralEquationoftheFirstKind.html and
Seismic refraction and reflection profiles of the East Pacific Rise lead to the discovery of a shallow melt region under the ridge crest near 9 degrees North.
Orcutt, J., Kennett, B., Dorman, L., & Prothero, W. (1975). Evidence of Low Velocity Zone Underlying a Fast-Spreading Rise Crest. Nature, 256(5517), 475-476. doi: 10.1038/256475a0
Orcutt, J. A., Kennett, B. L. N., & Dorman, L. M. (1976). Structure of the East Pacific Rise from an Ocean Bottom Seismometer Survey. Geophysical Journal International, 45(2), 305-320. doi: 10.1111/j.1365-246X.1976.tb00328.x
Rosendahl, B. R., Raitt, R. W., Dorman, L. M., Bibee, L. D., Hussong, D. M., & Sutton, G. H. (1976). Evolution of Oceanic-Crust .1. Physical Model of East Pacific Rise Crest Derived from Seismic Refraction Data. Journal of Geophysical Research, 81(29), 5294-5304. doi: 10.1029/JB081i029p05294
Much of this work was accomplished using several generations of Ocean-Bottom Seismographs, continuing the work of
W. A. Prothero and James Brune.