Approximations In Geophysics

A relatively large fraction of theoretical formulations as well as fundamental numerical data in geophysics are based on approximations. Unfortunately in many instances this fact is not realized sufficiently. Theoretical approximations are used for various reasons. For example, very frequently in differential equations only first derivatives are used, and second or higher derivatives are neglected. While this procedure usually does not lead to large errors, there are occasional cases where second derivatives approach, and even surpass the first derivatives in magnitude. Under such conditions results may be misleading and even may prevent progress in the investigation of the problem involved. Other approximations occur in connection with the use of series, where only terms with one or two powers of a quantity are retained regardless of the fact that the neglected terms may contribute appreciably to the results under certain conditions.