Gardner公式

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This page is a translated version of the page Dictionary:Gardner’s equation and the translation is 100% complete.

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SheriffsDictionary.jpg
Term Gardner's equation
Pronunciation gard’ n∂r
Series Geophysical Reference Series
Author Robert E. Sheriff
DOI http://dx.doi.org/10.1190/1.9781560802969
ISBN 978-1-56080-118-4
Store SEG Online Store

“Gardner公式”或者“Gardner关系”是以G. H. F. Gardner和L. W. Gardner的名字命名的一个经验公式。该经验公式建立起了地震纵波速度与地震波传播所经过的岩石体积密度的关系。Gardner公式具体表示如下:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \rho = \alpha V_p^{\beta}}

其中Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \rho } 为体积密度,其单位为g/cm3, Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle V_p} 为纵波速度,其单位为ft/s,Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \alpha}Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \beta} 是两个通过经验选取的常量,其数值依赖于地质情况。Gardner等提出当选取Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \alpha = 0.23}Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \beta = 0.25} 时,经验公式可以取得一个较好的匹配效果.[1]基于这样的假设,Gardner公式可以简化为:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \rho = 0.23 V_p^{0.25}.}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle V_p} 的单位取为m/s时,我们应取Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \alpha = 0.31} ,此时Gardner公式可以表示为:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \rho = 0.31 V_p^{0.25}.}

因为Gardner公式可以基于从地震数据中得到的层速度提供岩性信息,因此其在石油勘探领域很受欢迎。公式中的常量Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \alpha}Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \beta} 一般可以通过声波密度测井信息来确定。当缺乏测井信息时,Gardner提出的常量依然可以提供一个良好近似。

经验公式说明密度与纵波速度的1/4次方成正比:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \rho = a V_\mathrm{P}^\frac14 , }

其中“a”取0.31当“V”的单位为m/s,“a”取0.23当“V”的单位为ft/s[1]


参考文献

  1. 1.0 1.1 Gardner, G.H.F.; Gardner L.W. & Gregory A.R. (1974). "Formation velocity and density -- the diagnostic basics for stratigraphic traps". Geophysics 39: 770–780. doi:10.1190/1.1440465.