Analysis of Time-Depth Data in Sand Dunes from the Empty Quarter Desert of Southeastern Saudi Arabia

Theoretical and field studies show that P-wave velocity increases continuously with depth in unconsolidated sands. Many analytical and empirical models have been proposed to account for this phenomenon in near-surface layers. This study presents five new uphole data sets acquired in sand dunes located in the Empty Quarter (Rub’ Al-Khali) Desert in southeastern Saudi Arabia. Furthermore, the study compares the following velocity-depth functions: constant-velocity, Al-Shuhail, and Liner by fitting them to these data sets in addition to the sand curve data set. The constant-velocity function estimates an average P-wave velocity equal to 641 m/s in the dunes with an average sum of squared errors (SSE)=0.00101\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {(SSE)} = 0.00101$$\end{document}. Liner’s velocity function estimates an average surface P-wave velocity = 450 m/s and an average porosity (ϕ)=38.33%\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\phi ) = 38.33\%$$\end{document} in the dunes with an average SSE=0.000133\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {SSE} = 0.000133$$\end{document}. Al-Shuhail’s velocity function estimates an average surface P-wave velocity =25.78m/s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ = 25.78\,\hbox {m/s}$$\end{document} and an average velocity-depth gradient =662m-1/3\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ = 662\,\hbox { m}^{-1/3}$$\end{document} in the dunes with an average SSE=0.0000877\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {SSE} = 0.0000877$$\end{document}.