POTENTIAL FIELD CONTINUATION BETWEEN GENERAL SURFACES*

The theory of potential field continuation is studied with a view of extending it to include continuation between non-linear surfaces. This theoretical extension is regarded as useful in reducing observed potential fields along one general surface to another general surface. It is demonstrated that the continuation operators considered in past geophysical literature are special cases of the generalized operators. In view of the tremendous growth in the art of high-speed computing it is possible to consider applications of the generalized operators. In worked examples upward continuation between a general surface and a datum is considered for the gravity field due to geometrically simple sources; this in order to test the accuracy of the digital applications. It is indicated that for observations on an undulating surface it is possible to account for considerable errors when, during interpretation, the observation locations are taken to be along a datum. For aids to profile interpretation in areas of considerable topographic relief some simple convolution operators for continuation between linear, non-parallel surfaces are proposed.     

ON THE UPWARD CONTINUATION OF POTENTIAL FIELD DATA BETWEEN IRREGULAR SURFACES*

The potential field and its derivatives at points above an irregular surface can be approximately obtained from the sampled potential field data acquired on that surface. A method of minimizing the truncation effect, which appears when gravity and magnetic maps are processed with the aid of surface integrals, is derived. The results are compared with those of the most relevant similar methods by using a theoretical, but realistic, model.