Teacher's Aide: Modeling Hole-Effect Variograms of Lithology-Indicator Variables

Authors: Ma Y.Z.¹; Jones T.A.²

Source: Mathematical Geology, Volume 33, Number 5, July 2001 , pp. 631-648(18)

Publisher: Springer

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Abstract:

Common variogram models, such as spherical or exponential functions, increase monotonically with increasing lag distance. On the other hand, a hole-effect variogram typically exhibits sinusoidal waves that form peaks and troughs, thereby conveying the cyclicity of the underlying phenomenon. In order to incorporate this cyclicity into a stochastic simulation, hole effects in the experimental variogram must be fitted appropriately. In this paper, we recommend use of several multiplicative-composite variogram models to fit hole-effect experimental variograms. These consist of a cosine function to provide wavelength and phase of cyclicity, multiplied by a monotonic model (e.g., spherical) to attenuate amplitudes of the cyclical peaks and troughs. These composite models can successfully fit experimental lithology-indicator variograms that contain a range of cyclicities, although experimental variograms with poor cyclicity require special considerations.

Keywords: cyclicity; hole effect; variogram fitting; multiplicative-composite model; sinusoid; attenuation

Language: English

Document Type: Regular paper

Affiliations: 1: ExxonMobil Upstream Research Company, P. O. Box 2189, Houston, Texas 77252-2189; yuan.ma@exxon.sprint.com 2: ExxonMobil Upstream Research Company, P. O. Box 2189, Houston, Texas 77252-2189; tajones@upstream.xomcorp.com

Publication date: 2001-07-01