Tectonic Deformation Estimation using Stream Gradients: Nonparametric Function Estimation from Difference Data using Splines and Conjugate Gradients

摘要

In 1811-1812 three great (8.0+) earthquakes occurred near New Madrid, Missouri. We estimate coseismic deformation in this area using stream elevation data from topographic maps. Streams have a natural profile, the gradient of which depends on the resistance of underlying sediment and the volume of stream flow. If tectonic processes elevate the upstream end of a segment a different amount than the downstream end, the stream will attempt to return to its natural gradient by incising, aggrading, or altering its sinuousity. This adjustment takes time, so deviations from the natural gradient may indicate geologically recent deformation.We use penalized regression splines to estimate the natural stream profile and the deformation of the ground surface Estimation of the natural profile and deformation is based on nonparametric regression of the form y_2 - y_1 = f(x_2) - f(x_1). This may be formulated as a linear regression problem, potentially with millions of parameters when estimating large-scale surfaces; the system may be solved using conjugate gradient methods.