This paper discusses the progression of a novel algorithm that uses a wavelet‐transform approach. The transform is a generalization of the decimated, discrete wavelet transform (DWT) that is the undecimated DWT or stationary wavelet transform (SWT) also known as the undecimated á trous algorithm. It forms the basis for recovering displacements from acceleration time histories. The approach recovers a low‐frequency fling that is usually an almost sinusoidal or cosinusoidal pulse responsible for the big ground motions in strong motion events. The algorithm implements a well known and non‐linear, denoising scheme and is applied to the low‐frequency sub‐band and, in particular, succeeds in recovering the acceleration‐fling pulse. The progression is that in order to obtain estimates of displacements, the algorithmic baseline‐correction scheme can now locate an acceleration transient (i.e., a spike), which creates the DC shift in velocity and the linear trend in displacement, and is therefore the baseline error. Once this acceleration transient is corrected for or eliminated, double‐time reintegration recovers the velocity‐fling pulse and residual displacement. The paper infers that these acceleration transients may be due to ground rotation, embedded in the translational data. The scheme provides for easier integration once the low‐ and higher‐frequency accelerations are extracted.
Online Material: Additional results for the Chi‐Chi TCU068 (1999) station, the New Zealand Darfield Station (2010), and the Ölfus Earthquake (2008) in Iceland.