HIGH ACCURACY PRACTICAL DERIVATIVE TRANSFORMATIONS IN POTENTIAL-FIELD GEOPHYSICS USING CUBIC B-SPLINES

Potential field and gradient data are applied to tackle a variety of important issues in both exploration and solid Earth studies. Potential, potential field data and potential-field gradient data are supplementary to each other for resolving sources. Derivative computations are fundamentally important for source boundary detection and resolution improvement, for gradients-based inversion and interpretation methods and for data comparison. However, high accuracy noise resistant derivative computations are very difficult to achieve, especially for second or higher order derivatives. Here we propose a set of flexible high accuracy practical techniques to perform 2D and 3D derivative transformations from potential to potential-field components and from potential-field components to potential-field gradient components in the space domain using cubic B-splines. The spline-based techniques are applicable to either uniform or non-uniform rectangular grids for the 3D case, and applicable to either regular or irregular grids for the 2D case. The spline-based horizontal derivative computations can be done at any point in the computational domain. Comparisons through synthetic 3D gravity (x-derivative and second order vertical derivative obtained from the noisy gravity data) transformation examples show that the spline-based techniques are much more noise resistant and substantially more accurate and may provide better insights into understanding the sources than the fast Fourier Transform (FFT) techniques. Real 3D gravity transformation example from the slightly noisy observed gravity to gravity-gradient (y-derivative) component shows that the spline-based results are more noise resistant and more consistent with the corresponding observed data than the FFT results. The spline techniques are useful in real data applications. If certain desired components of the potential field or gradient data are not or not satisfactorily measured, they can be obtained using the spline-based transformations.