Determination of vertical recent crustal movements by levelling and gravity data

Abstract

Abstract Recent vertical crustal movements are generally studied by comparing either repeated levellings or repeated gravity measurements; neither of these procedures gives strictly true vertical displacements of points. A theoretically more satisfactory approach can be based on a Stokes-like integral formula, requiring both types of data. Assuming a constant linear relationship between temporal changes of gravity and temporal changes of levelled “heights” in an area of interest, two variants of the original integral formula are derived, either variant requiring essentially only one type of data. The first variant can be used if, besides extended repeated levellings, the constants of the linear relationship are available (by using both types of data on some common points). Equivalently the second variant is based on repeated gravity measurements. Both variants contain a small surface integral term which is numerically estimated by model computations. Finally the theory is applied to the determination of real crustal movements in western Hokkaido, Japan. The temporal changes of gravity and of height at twenty points gave a correlation coefficient−0.66 which is statistically significant at the 1 per cent level. Neglecting the temporal changes of geoid undulations could cause systematic errors in indicated recent crustal movements in the area reaching the magnitude of one standard deviation of the relative height of the extreme points in the area. Further numerical investigations require the collection of precise data at some geodynamic test areas.