Hermite関数による地磁i気・重力異常の解析

抄録

A method of potential analysis by use of Hermite functions is worked out in relation to geomagnetic and gravity anomaly. A potential field on a plane surface is expressed with a series of orthogonal functions involving Hermite functions. The coefficients of the series are useful for estimating potential values at different levels in height. The method is especially useful when it is applied to a problem of isolated anomaly because the functions involved tend to become zero at points distant from the anomaly. In actual problems, a number of infinite integrals, which involve Hermite functions, are to be evaluated for specified sets of coordinates. Such numerical integrations can readily be performed fairly accurately because the orthogonal functions tend to vanish very quickly for a large value of distance from the center of the anomaly. Two- and three-dimensional analyses are given in the paper taking the magnetic anomaly at Kursk, that over a magnetized cone and that over Izu-Oshima Island, an active volcano about 110 km southwest of Tokyo, as examples. It is demonstrated that upward continuation of the anomaly is successfully completed for these cases.