Daily Dose of Exploration Geophysics: Gardners Expression as a Linear Regression

Gardner's Coefficients Revealed!

I have a added a new IPython notebook to my github account that shows how you can find the coefficients in Gardner's expression for the basin you happen to be working in. follow the link to myIPythonNotebooks - Gardner's Expression Regressed. For some reason, github is not showing the mathjax equations well, but if you download the notebook and open it locally, you should have no problem viewing them. I'll write them here just in case to give you a sample of what can be found in the notebook:

********************************************************************************************************************* One option is to linearize the equation and do a regression for the 2 parameters. This ipython notebook will show you how. Start with the general equation: $$\rho = \alpha * V_{P}^\beta$$ Take the natural log of both sides: $$ln(\rho) = ln(\alpha * V_{P}^\beta)$$ Use the properties of logarithms to make a linear equation: $$ln\rho = ln\alpha + ln(V_{P}^\beta)$$ $$ln\rho = ln\alpha + \beta*lnV_{P}$$ Rewrite: $$D = A + BV$$ where A is the intercept, B is the slope, V is the independent variable, and D is the dependent variable. *********************************************************************************************************************

Finally, below is a screen shot of the final regression:

GREAT LINK to SUBSURF WIKI: Gardner's equation