Depth estimation of spherical bodies using Differential Operators (Gradient PgP r , Laplacian ر2Z and Biharmonic ر4Z ) to its gravity fields.

Abstract

Differential Operators (Gradient, Laplacian and Biharmonic) have been used to determine anomaly characteristics using theoretical gravity field for spherical bodies with different depths, radius and density contrasts. The intersection between the gravity field and the three differential operator's fields could be used to estimate the depth to the center of the spherical bodies regardless their different radius, depths and density contrasts. The Biharmonic Operator has an excellent result, were two zero closed contours lines produced. The diameter of the internal closed zero contour line define almost precisely the depth to the center of spherical bodies. This is an attempt to use such technique to estimate depths. Also, the Biharmonic Operator has very sensitivity to resolve hidden small anomaly due the effect of large neighborhood anomaly, the 2nd derivative Laplacian Filter could reveal these small anomaly but the Biharmonic Operator could indicate the exact depth. The user for such technique should be very care to the accuracy of digitizing the data due to the high sensitivity of Biharmonic Operator.The validity of the method is tested on field example for salt dome in United States and gives a reasonable depth result.

Keywords

• depth
• spherical bodies
• differential operators
• gradient pgp r
• laplacian z
• gravity fields