Time‐depth and velocity‐depth relations in sedimentary basins—A study based on current investigation in the Arctic Islands and an interpretation of experience elsewhere

Abstract

Velocities of P‐waves in the Arctic Islands obey the same power‐law equations (1) [Formula: see text], (2) [Formula: see text] that apply to Western Canada (Acheson, 1963). They appear to be closely related to the theoretical one‐sixth power law (n = 5/6) derived by Gassmann (1950), Brandt (1955), and others. Equations (1) and (2) are piece‐wise continuous at any given location and consist of a number of discrete segments corresponding to geologic units, each characterized by a distinct set of values for a, b, c, and n. Except for a limited number of velocity anomalies such as permafrost, these units relate to formations or groups of formations. Velocity changes in a, c, and n correspond to major changes in lithology, pressure, or compaction. Velocity fluctuations within the formations caused by variation in grain size, porosity, fluid‐to‐matrix coupling, and so on are not indicated in this analysis, and the velocity‐depth relation refers to secular velocity variation only. Correlation of reported velocity findings from many parts of the world through a common relationship to the one‐sixth power law suggests this system of equations has widespread, possibly global, application to important geophysical problems of many kinds.