Ground motions.

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.响应范围受限的窄带地震仪无法精准记录地面运动信号，且输出的记录会滤除低频分量。通常采用传递函数来拓展窄带地震记录的频谱，但现有常用传递函数的计算精度并不理想。为此，本文作者基于拉普拉斯变换（Laplace transform）、双线性变换（bilinear transform）以及奈奎斯特采样定理（Nyquist sampling theory）推导得到一种新型传递函数以解决该问题。随后将该新型传递函数用于校正来自高密度地震观测网（Hi-net）的窄带速度记录。将校正后的速度记录与同站点Hi-net同步记录的宽频带加速度积分得到的速度进行对比，同时将该校正结果与采用中田传递函数（Nakata transfer function）得到的校正结果进行对比。结果表明，本文推导的传递函数的计算精度优于中田传递函数。但当信噪比低于24时，其精度会出现下降，且无法恢复0.05~0.78Hz频段内的信号。