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Enhanced isotropic gradient operator
- Source: Geophysical Prospecting, Volume 62, Issue 3, Apr 2014, p. 507 - 517
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- 01 Sep 2011
- 01 Sep 2013
- 04 Mar 2014
Abstract
We present a two‐dimensional (2D) gradient operator that produces more accurate results than known traditional operators such as Ando, Sobel and the so‐called Isotropic operator. We further extend the derivation to three‐dimensional (3D), a powerful feature missing in all conventional operators.
We start by constructing a parameterized formula that generically represents all 2D numerical gradient operators. We then solve for the required parameter by equating this numerical gradient with that obtained analytically from a single Fourier harmonic (or, equivalently here, a stationary plane wave). As this parameter is frequency‐ and direction‐dependent (by virtue of the underlying Fourier harmonic), we construe a pragmatic version of it that is independent of these two variables yet capable of significantly reducing the error associated with traditional operators. Extension to 3D is achieved similarly; it requires dealing with two parameters as opposed to only one in the 2D case. Synthetic and real‐data results confirm higher accuracy from this operator than from traditional ones.