On low-pass digital filters in oceanography

-Two types of filters are widely used to remove semidirunal and diurnal tidal signals and other high frequency noises in oceanography. The first type of filters uses moving average with weights in time domain, and can be easily operated. Some data will be lost at each end of the time series, especially for the low low-pass filters. The second type of filters uses the discrete Fourier transform filter (DFTF) which operates in the frequency domain, and there are no data loss at the ends for the forward transform. However, owing to the Gibbs phenomenon and the discrete sampling (Nyquist effect) , ringing appears in the inverse transformed data, which is especially serious at each end. Thus some data at the ends are also discarded. The present study tries to find out what causes the ringing and then to seek for methods to overcome the ringing. We have found that there are two kinds of ringings, one is the Gibbs phenomenon, as defined before. The other is the 'Nyquist'ringing due to sampling Nyquist critical frequency. The former is due to the abrupt transition in frequency band. The Gibbs and Nyquist effects show the ringing at each end of the filtered time series. Thus, the use of a cosine taper or a linear taper on the window in the frequency domain makes the transition band smooth, so that the Gibbs phenomenon will be minimized. Before applying the Fast Fourier Transform (FFT), the original time series at each end is properly tapered by a split cosine bell that reduces significant ringing since this method limits the energy transfer from outside of the Nyquist frequency. Thus, the DFTF can be a powerful tool to suppress the signals in which we are not interested, with sharp peaks in low frequency variation and less data loss at each end.

Crustal P-and S-Wave Velocity Structure of the North China Craton at 36°N from Active-Source Seismic Data and Its Tectonic Implications

We present crustal models for seismic P-waves(Vp),S-waves(Vs)and the Vp/Vs ratio across the southern North China Craton along latitude 36°N.Our results are based on inverse and forward modeling of long-range wide-angle reflection/refraction data.The crust of the southern Ordos Block has high lower crustal velocity(7.0 km/s)and a Moho depth of~42 km.In contrast,thick sediments and a lower average velocity(compared with the Ordos block)found underneath the Shanxi Graben are likely to be the products of rifting that has occurred since the Cenozoic.Steep Moho dips,exposed basement rock and higher average crustal velocity beneath the Lüliang Mountain and the Taihang Mountain are characteristic of an orogenic belt.The Tanlu fault and the Liaocheng-Lankao fault show sharp crustal velocity variations and a Moho offset.This seismic profile sampled the entire region of the Eastern North China Craton where the cratonic root has been destroyed and the unique crustal structure is correlated with the substantially modified lithosphere.Our crustal seismic velocity model shows a strong correspondence between surface geology,local tectonics and the deep crustal structure.