A transfer function based on Laplace transform for correcting narrow-frequency velocity recording

Affected by the flat response range of the narrow-band seismograph, the narrow-band velocity recording has the problem of low-frequency component distortion, which limits the usable range of the seismic recording. To solve this problem, this paper deduces an improved transfer function based on the Laplace transform and bilinear transform to realize the correction from narrow-band seismic records to broadband ones. And then the Japanese Hi-net velocity records are used as an example for correction, and the corrected velocity records are compared with the KiK-net acceleration integral velocity records from the same station. The results show that the original velocity records are distorted at low frequencies, while the corrected waveforms are consistent with the KiK-net acceleration integral velocity records. The analyse show that the improved transfer function can effectively solve the distortion of the low-frequency components in the original velocity records, which effectively widens the usable range of low-frequency. Moreover, compared with the Nakata-corrected velocity recording method, the velocity recording corrected with the transfer function given in this paper is more accurate in terms of amplitude and waveform.