地震信号瞬时频率的估算

本文比较了四类计算瞬时频率的方法.基于相位差分的方法对噪声敏感；基于零交叉点的方法是针对周期信号提出的，对非周期信号效果不理想，通过插值改善估算结果；基于FIR微分器的方法有三种，基于两点的FIR方法与标准公式较为接近，但会引入半个采样间隔的时移；基于三点的FIR方法可以消除时移，但计算结果会出现负频尖峰；Claerbout方法不仅会引入半个采样间隔的时移，而且估算的频率值可能超过Nyqusit频率.本文在Claerbout公式的基础上导出了一种估算瞬时频率的公式，该公式消除了时移，且负频尖峰也得到抑制；基于时频表示一阶矩的方法的计算结果较为平滑，同时具有一定的抗噪能力.最后用本文导出的公式和时频表示一阶矩两种方法计算了南海东北部一条地震剖面的瞬时频率，并将其结果与Seismic Unix中相关函数的计算结果做了比较，表明本文导出公式的计算结果较为理想.

The estimation of instantaneous frequency of seismic signal

We compare four types of methods for estimating instantaneous frequency. The phase difference estimator is susceptible to noise. The zero-crossing estimator is suitable for periodic signal and is not good enough for non-periodic signal. However, the results of the zero-crossing method can be improved by interpolating the signal. There are three FIR differentiator methods. The instantaneous frequency computed with the two-point FIR differentiator resembles the standard instantaneous frequency, but this method introduces a half-sample time shift. This can be avoided by using a three-point FIR differentiator, but the estimating spikes have a tendency to be negative. The Claerbout′s method not only can introduce a half-sample time shift, but also can produce results greater than Nyquist frequency. We present a new formula based on the Claerbout′s formula. Using this formula, the half-sample time shift can be avoid and the negative spikes can be suppressed. The results calculated with the one-order frequency moment of a time-frequency representation (TFR) are smooth and withstand noise. At last, we calculate the instantaneous frequency section of a seismic post-stack section from the northeastern South China Sea using the new presented formula and the one-order frequency moment of TFR, and compare the results with the instantaneous frequencies which is computed with a related function in Seismic Unix software. The results indicate that the estimations calculated with the new formula are good enough.