A transfer function based on bilinear transformation for narrow-band seismic record

Abstract

For a narrow-brand seismograph with a flat response range limited, it cannot precisely record the signal of a ground motion and output the records with the low-frequency components cut down. A transfer function is usually used to spread the spectrum of the narrow-brand seismic records. However, the accuracy of the commonly used transfer function is not high. The authors derive a new transfer function based on the Laplace transform, bilinear transform, and Nyquist sampling theory to solve this problem. And then, the derived transfer function is used to correct the narrow-band velocity records from the Hi-net. The corrected velocity records are compared with the velocities integrated from the synchronously recorded broad-band acceleration at the same station with Hi-net. Meanwhile, the corrected records are compared with those corrected by the Nakata transfer function. The results show that the calculation accuracy of the derived transfer function is higher than the Nakata transfer function. However, when the signal-to-noise ratio is below 24, its accuracy diminishes, and it is unable to recover signals within the 0.05–0.78Hz frequency band.