Principal Component Analysis of Geodetically Measured Deformation in Long Valley Caldera, Eastern California, 1983–1987

Abstract

Typical geodetic measurements of deformation consist of repeated surveys of a particular geodetic network. Such deformation data can be interpreted as a consequence of one or more self‐coherent sources by means of principal component analysis. A self‐coherent source is defined as any source that produces deformation that is time and space separable. Principal component analysis then gives the time and space factors that characterize the deformation attributed to each self‐coherent source. Geodetic measurements of deformation at Long Valley caldera provide two examples of the application of principal component analysis. A 40‐line trilateration network surrounding the caldera was surveyed in midsummer 1983, 1984, 1985, 1986, and 1987. Principal component analysis indicates that the observed deformation can be represented by a single coherent source. The time dependence for that source displays a rapid rate of deformation in 1983–1984 followed by less rapid but uniform rate in the 1984–1987 interval. The spatial factor seems consistent with expansion of a magma chamber beneath the caldera plus some shallow right‐lateral slip on a vertical fault in the south moat of the caldera. An independent principal component analysis of the 1982, 1983, 1984, 1985, 1986, and 1987 leveling across the caldera requires two self‐coherent sources to explain the deformation. The deformation pattern produced by the larger of these two sources appears to be roughly consistent with that found from the trilateration data. The deformation due to the second source is a nearly uniform tilt in the uplift profile. Presumably, that tilt is simply an artifact of systematic error in the leveling.