|
楼主 |
发表于 2019-6-25 02:02:18
|
显示全部楼层
A few popular books on inversion or retrieval theories and applications in geophysics or atmospheric science:
Hanel, R. A., b. J. Conrath, D. E. Jennings, and R. E. Samuelson, 1992: Exploration of the Solar System by Infrared Remote Sensing. Cambridge Univ. Press, Cambridge, 458 pp.
Houghton, J. T., F. W. Taylor and C. D. Rodgers, 1984: Remote Sounding of Atmospheres. Cambridge Univ. Press, 343 pp.
Menke, W., 1989: Geophysical Data Analysis: Discrete Inverse Theory. Revised Edition. Academic Press, Inc., 289 pp.
Rodgers, C. D., 2000: Inverse Methods for Atmospheric Sounding, Theory and Practice. World Scientific, London, 238 pp.
Twomey, S., 1970: Introduction to the Mathematics of Inversion in Remote Sensing and Indirect Measurement. Elsevier, Amsterdam, 243 pp.
In general, given known parameters such as the properties of materials or localized relationships among different parameters, a forward problem describes a spatial relationship and its temporal evolution of the physical state. On the other hand, an inverse or a retrieval problem is to find the values of those parameters or the localized relationship among different parameters built into those equations describing the forward problems.
For example, in the field of fluid mechanics or gasdynamics, the so-called Rankine-Hugoniot relations describe the mass, momentum and energy conservation laws across a shock. Given the values of gas constants and the localized equation of state (p=rho*R*T or p=(gamma-1)*rho*E for ideal gas) Rankine-Hugoniot relations can be used to solve many forward problems such as design good numerical schemes to solve the Euler equations. In the field of solid mechanics, on the other hand, Rankine-Hugoniot relations are often or also used to derive the localized equation of state, i.e., to find the parametric relationship between pressure and density for different materials. This is clearly an inverse problem. Here is a book that contains an overview on this subject:
Asay, J. R., and M. Shahinpoor (editors), 1993: High-Pressure Shock Compression of Solids. Springer Science+Business Media, LLC, 393 pp.
|
|