REMEDY FOR LOAD DISCONTINUITY IN TIME HISTORY ANALYSIS

Discontinuity at the end of an impulse will lead to an amplitude distortion in a time history analysis. This amplitude distortion can be effectively reduced, if a very small time step is used to perform a complete step-by-step integration procedure. As a result, a lot of computational effort is involved. In this study, it will be shown that a significant amplitude distortion may also occur for a dynamic loading, which is not classified as an impulse. Furthermore, a remedy is proposed to overcome the difficulty caused by the load discontinuity. This remedy is very simple and it involves adjusting the input load at the time instant of discontinuity. In fact, the average of the two discontinuity values at the load discontinuity is taken to be the adjusting input load for the time instant of load discontinuity. The feasibility of this remedy is analytically verified and confirmed with numerical examples not only for impulses but also for dynamic loadings. Apparently, there is no extra computational effort needed for the remedy and it will not complicate the programming of dynamic analysis codes.

Averaging and sampling for magnetic-observatory hourly data

A time and frequency-domain analysis is made of the effects of averaging and sampling methods used for constructing magnetic-observatory hourly data values. Using 1-min data as a proxy for continuous, geomagnetic variation, we construct synthetic hourly values of two standard types: instantaneous "spot" measurements and simple 1-h "boxcar" averages. We compare these average-sample types with others: 2-h average, Gaussian, and "brick-wall" low-frequency-pass. Hourly spot measurements provide a statistically unbiased representation of the amplitude range of geomagnetic-field variation, but as a representation of continuous field variation over time, they are significantly affected by aliasing, especially at high latitudes. The 1-h, 2-h, and Gaussian average-samples are affected by a combination of amplitude distortion and aliasing. Brick-wall values are not affected by either amplitude distortion or aliasing, but constructing them is, in an operational setting, relatively more difficult than it is for other average-sample types. It is noteworthy that 1-h average-samples, the present standard for observatory hourly data, have properties similar to Gaussian average-samples that have been optimized for a minimum residual sum of amplitude distortion and aliasing. For 1-h average-samples from medium and low-latitude observatories, the average of the combination of amplitude distortion and aliasing is less than the 5.0 nT accuracy standard established by Intermagnet for modern 1-min data. For medium and low-latitude observatories, average differences between monthly means constructed from 1-min data and monthly means constructed from any of the hourly average-sample types considered here are less than the 1.0 nT resolution of standard databases. We recommend that observatories and World Data Centers continue the standard practice of reporting simple 1-h-average hourly values.