Abstract: The pulse response iteration method in acoustical inversion is obtained by using the conception of equaltime-layer-thickness. Generally speaking, signals are inevitably interfered by noise, the frequency band of spectrum of which is much wider than that of signals, and their spectra can be seriously distorted, consequently leading to the poor capability of anti-interference of this method. The signal sampling iteration method has been proposed to avoid the FFT and to improve this capability with remarkable success. From the results of numerical simulations, however, it can be discovered that accumulative effects in inversion error exist in this method. To reduce the accumulative effects, the statistical averaging method is introduced and the sample-averaging iteration method is obtained. The relative error can thus be reduced by 3 times as compared with the sample iteration method when signal to noise ratio is 6.3.