Errors in velocities and displacements deduced from accelerographs: An approach based on the theory of error propagation

Based on the theory of errors, and in particular on the law of error propagation and approximation techniques, we present some simple formulae for random errors of velocities and displacements computed on the basis of numerical integration of accelerometer records. These errors are regarded as function of the characteristic errors of accelerometers and of the duration of the signal for velocities, and of the square of the duration of the signal for displacements. Instabilities in the sampling rate introduce additional noise, which is proportional to the sum of the squares of measurements of acceleration, mostly influenced by high peaks. Because of uneven weighting, however, peaks at early stages of the record are more important than in their later stages.