A quantitative study of isobaric equilibrium and gravity anomalies in the hawaiian islands

The deformation of a strong elastic lithosphere supported by an underlying weak magma is calculated for a long mountainous load. The deformations, produce vertical superposed stresses in the lithosphere that contribute to the support of the mountain and distribute its weight over a large area.Employing the principle of isobaric equilibrium, the distribution of the vertical supporting stress and the associated gravity anomalies may be determined by analysis.The results of the analysis are applied to the Hawaiian chain and it is shown that the calculated physical properties and gravity anomalies are remarkably like those observed. It is inferred from the study that: (a) a strong lithosphere underlies the Hawaiians and this section is practically identical with those underlying other regions; (b) the lithosphere will support one-sided stresses approximating 10⁹ dynes/cm.² for long periods of time; (c) the distribution of gravity anomaly may be described quantitatively in terms of the calculated deformations; (d) the principle of isobaric equilibrium is obeyed throughout the region whereas the isostatic principle is generally violated; and (e) the distribution of compensating masses is not at all like that demanded by the principle of isostasy.It is concluded that isostasy leads to results that are clearly wrong when applied to mountains or other deformed regions. The principle of isobaric equilibrium appears, however, to be well established by the investigation.