Chaotic system detection of weak seismic signals

Abstract

S U M M A R YWhen the signal-to-noise (S/N) ratio is less than −3 dB or even 0 dB, seismic events are generally difficult to identify from a common shot record. To overcome this type of problem we present a method to detect weak seismic signals based on the oscillations described by a chaotic dynamic system in phase space. The basic idea is that a non-linear chaotic oscillator is strongly immune to noise. Such a dynamic system is less influenced by noise, but it is more sensitive to periodic signals, changing from a chaotic state to a large-scale periodic phase state when excited by a weak signal. With the purpose of checking the possible contamination of the signal by noise, we have performed a numerical experiment with an oscillator controlled by the Duffing-Holmes equation, taking a distorted Ricker wavelet sequence as input signal. In doing so, we prove that the oscillator system is able to reach a large-scale periodic phase state in a strong noise environment. In the case of a common shot record with low S/N ratio, the onsets reflected from a same interface are similar to one other and can be put on a single trace with a common reference time and the periodicity of the so-generated signal follows as a consequence of moveout at a particular scanning velocity. This operation, which is called 'horizontal dynamic correction' and leads to a nearly periodic signal, is implemented on synthetic wavelet sequences taking various sampling arrival times and scanning velocities. Thereafter, two tests, both in a noisy ambient of −3.7 dB, are done using a chaotic oscillator: the first demonstrates the capability of the method to really detect a weak seismic signal; the second takes care of the fundamental weakness of the dynamic correction coming from the use of a particular scanning velocity, which is investigated from the effect caused by near-surface lateral velocity variation on the periodicity of the reconstructed seismic signal. Finally, we have developed an application of the method to real data acquired in seismic prospecting and then converted into pseudo-periodic signals, which has allowed us to discriminate fuzzy waveforms as multiples, thus illustrating in practice the performance of our working scheme.

Comparative study of approximate entropy and sample entropy robustness to spikes

“…The complex nature of the explosions appearing in seismic surveys are reflected in the acoustic event and, in some situations, these events exhibit a non-linear chaotic behaviour. 4 The characterization of this chaotic behaviour could also be performed in the frequency domain. However, as previously mentioned, the non-stationarity and the presence of noise make this difficult.…”

Study on detection of small-sized range-spread target by using chaotic Duffing oscillator

“…So the successive target echoes during a short time range are similar to one other. Reference [12] showed that the chaotic Duffing system can detect the desired signals successfully if the periodic signals to be detected include four successive periods or more. Here we found by experiments that the chaotic system by introducing threeperiod signals can work well.…”

Ubiquitous Filtering for Nonlinear Problems

“…However, in the following the dynamic filtering is proposed adopting a different (nonlinear) angle [8,9], namely, using signals from nonlinear chaotic attractors as a model for the desired signals arriving at the filtering structure. The modeling of real phenomena using chaos has been used for more than 50 years, and there is a wide range of scientific and practical applications, such as seismology [10][11][12], statistical theory of communication [13,14], control, geophysics, biomedical telemetry [15,16] under water signal processing [17], and many other areas related to applied physics as well [18].…”