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Initial import
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|-
| Arithmetic mean
| Arithmetic mean
| <math>\bar{k} = \displaystyle\frac{1}{H_{t}} \displaystyle\sum\limits_{i = 1}^{N}k_{i}h_{i}</math>
| <inline-formula> <tex-math notation="TeX"> $\begin{align*}\bar{k} = \displaystyle\frac{1}{H_{t}} \displaystyle\sum\limits_{i = 1}^{N}k_{i}h_{i}\end{align*}$ </tex-math> </inline-formula>
| Average of uniform, horizontal, parallel layers in linear flow. ''k''<sub>''j''</sub> and ''h''<sub>''j''</sub> are the [[permeability]] and thickness of layer ''j'' . ''H''<sub>''t''</sub> is the total thickness.
| Average of uniform, horizontal, parallel layers in linear flow. ''k''<sub>''j''</sub> and ''h''<sub>''j''</sub> are the [[permeability]] and thickness of layer ''j'' . ''H''<sub>''t''</sub> is the total thickness.
|-
|-
| Harmonic mean
| Harmonic mean
| <math>\bar{k} = H_{t} \left(\displaystyle\sum\limits_{i = 1}^{N}\displaystyle\frac{h_{i}}{k_{i}}\right)^{-1}</math>
| <inline-formula> <tex-math notation="TeX"> $\begin{align*}\bar{k} = H_{t} \left(\displaystyle\sum\limits_{i = 1}^{N}\displaystyle\frac{h_{i}}{k_{i}}\right)^{-1}\end{align*}$ </tex-math> </inline-formula>
| Average of uniform, horizontal, serial layers in linear flow. Used for vertical [[permeability]] estimates in shale-free sands.
| Average of uniform, horizontal, serial layers in linear flow. Used for vertical [[permeability]] estimates in shale-free sands.
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|-
| Geometric mean
| Geometric mean
| <math>\bar{k} = \left(\displaystyle\prod\limits_{i = 1}^{N}k_{i}\right)^{1/N}</math>
| <inline-formula> <tex-math notation="TeX"> $\begin{align*}\bar{k} = \left(\displaystyle\prod\limits_{i = 1}^{N}k_{i}\right)^{1/N}\end{align*}$ </tex-math> </inline-formula>
| Approximate average of an ensemble of uncorrelated random permeabilities in globally linear flow. ''k''<sub>''j''</sub> is the [[permeability]] of each element in the ensemble
| Approximate average of an ensemble of uncorrelated random permeabilities in globally linear flow. ''k''<sub>''j''</sub> is the [[permeability]] of each element in the ensemble
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|-
| Radial flow
| Radial flow
| <math>\bar{k} = (k_{\rm max} \cdot k_{\rm min})^{1/2}</math>
| <inline-formula> <tex-math notation="TeX"> $\begin{align*}\bar{k} = (k_{\rm max} \cdot k_{\rm min})^{1/2}\end{align*}$ </tex-math> </inline-formula>
| Radial inflow (well) [[permeability]] in homogeneous, anisotropic media. ''k''<sub>max</sub> and ''k''<sub>min</sub> are the major and minor axes permeabilities.
| Radial inflow (well) [[permeability]] in homogeneous, anisotropic media. ''k''<sub>max</sub> and ''k''<sub>min</sub> are the major and minor axes permeabilities.
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|-
| Cross bedding
| Cross bedding
| <math>\bar{k} = \frac{\cos^{2}\alpha}{k_{0}} + \frac{\sin^{2}\alpha}{k_{90}}</math>
| <inline-formula> <tex-math notation="TeX"> $\begin{align*}\bar{k} = \frac{\cos^{2}\alpha}{k_{0}} + \frac{\sin^{2}\alpha}{k_{90}}\end{align*}$ </tex-math> </inline-formula>
| [[Permeability]] in a direction at an angle a to cross bedding. ''k''<sub>0</sub> and ''k''<sub>90</sub> are the permeabilities parallel and perpendicular to cross bedding.
| [[Permeability]] in a direction at an angle a to cross bedding. ''k''<sub>0</sub> and ''k''<sub>90</sub> are the permeabilities parallel and perpendicular to cross bedding.
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|}
* X = sample value
* X = sample value
* <inline-formula><tex-math notation="TeX">$\begin{align*}\bar{x}\end{align*}$</tex-math></inline-formula> = sample mean
* <math>\bar{x}</math> = sample mean
* ''n'' = number of samples
* ''n'' = number of samples
where
where
:<math>\bar{x}_{1} \mbox{ and } \bar{x}_{2} &= \mbox{sample means}\\s_{\bar{x}_{1}}^{2} \mbox{ and } s_{\bar{x}_{2}}^{2} &= \mbox{sample variances}</math>
:<math>\bar{x}_{1} \mbox{ and } \bar{x}_{2} = \mbox{sample means}</math>
:<math>s_{\bar{x}_{1}}^{2} \mbox{ and } s_{\bar{x}_{2}}^{2} &= \mbox{sample variances}</math>
The hypothetical value can be obtained from generally available tables of ''t'' values, listed under the null hypothesis probability that was selected. If the ''t'' statistic exceeds the table value, then the null hypothesis, H<sub>o</sub>, is rejected in favor of the alternate. Another way of phrasing this result is that the means are statistically different.
The hypothetical value can be obtained from generally available tables of ''t'' values, listed under the null hypothesis probability that was selected. If the ''t'' statistic exceeds the table value, then the null hypothesis, H<sub>o</sub>, is rejected in favor of the alternate. Another way of phrasing this result is that the means are statistically different.
==External links==
==External links==
{{search}}
* [http://store.aapg.org/detail.aspx?id=612 Find the book in the AAPG Store]
* [http://store.aapg.org/detail.aspx?id=612 Find the book in the AAPG Store]
[[Category:Geological methods]]
[[Category:Geological methods]]