Determination of optimum second derivative weight coefficient sets for various grid systems

Abstract EN

This paper describes a possible approach to determine the optimum second derivative weight coefficient sets for various ring systems with amplitude responses approximating the theoretical response of the second derivative operation.

Weight coefficient sets for many ring systems are derived as follows.

In each system, the average radial gravity for each circle is given a weight of \lrnm, where rm is the radius of circle and n is a real number.

For each n value, the overall similarity between the calculated amplitude response of each derived set and the theoretical response of the second derivative operation is determined by computing the correlation coefficient between the mapped variables.

Similarity between the calculated and the theoretical responses measured by the highest correlation may generally be considered a criterion for determining the optimum n and consequently the optimum weight coefficient set for second derivative.

For a given ring system, the derived coefficient set by this technique is considered the best one.

Moreover, to calculate the second vertical derivative, a new weight coefficient set, which uses the least number of circles to obtain average gravity values and at the same time yields best results has been developed.

To test its validity, the proposed method has been applied to the Bouguer gravity anomaly in the Central Salt Province of the Gulf of Suez region, Egypt