A forward and backward prediction model with higher accuracy based on radial basis functions(RBF) neural networks was proposed and used to model sea bottom reverberation.The one-step prediction error of the prediction models was used as the statistics for weak echoes detection.The results for envelopes of single-frequency reverberation in lake-trails show that

the defined prediction error of the forward and backward prediction model for that is about 10 lower than that of the forward prediction model

and the prediction error of both prediction models can be used as statistics for the detection of weak echoes in reverberation.