Teacher's Aide: Modeling Hole-Effect Variograms of Lithology-Indicator Variables |
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| Authors: | Yuan Z Ma and Thomas A Jones |
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| Institution: | (1) ExxonMobil Upstream Research Company, P. O. Box 2189, Houston, Texas, 77252-2189 |
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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. |
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| Keywords: | cyclicity hole effect variogram fitting multiplicative-composite model sinusoid attenuation |
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