Flow model of active seismic monitoring
© Mostovoi S.V., Gai A.E., Mostovoi V.S., Osadchuk A.E.
In the article the generalisation of an active seismic monitoring model in case of beta distribution of sounding signals starting time is considered. It allows modelling a broad class of the stochastic variables, which are distributed on a closed interval. For such model the algorithm of a signal restoring is created. The medium response to this signal has to characterise its condition. The power of an exploring signal should not be high. At least after exploration the medium should not be essentially changed. The following experimentation corresponds to these conditions, when the weak signals, commensurable with a microseismic background, follow in encoded energy being dispatched strictly periodically in time, and the medium responses are accumulated according to this periodicity. Or at setting experiment all time parameters of experiment are fixed for usage ofthem at description of a medium response. Or at experiment setting all time parameters of experiment are fixed for using them for decoding of the medium response. It is shown, that the instability in time leads to «fading» of a high - frequency component in a medium response function, while the fluctuations of a sounding signal energy are not so essential. And for any high ratio of a medium response to noise it is possible to indicate indispensable number of a sounding signals for implementation of this relation in the case of ideal synchronism of pulsing and their ideal decoding. But it is an ideal case. The real sources ensure stability only in some domain of modification parameters of these signals. In this sense it is possible only to state, that the vector of parameters, which defines the sounding signal, is random with a priori known distribution. This circumstance can be considered as a possibility to research a priori statistic of parameter stability of a source, or it can be considered as a possibility to formally enter the researcher heuristics into the model. In the contribution the active seismic monitoring is modelled by the flow of physically realisable signals with fluctuating amplitude and initiation delay. These models are the natural ones, because the active monitoring is a regime testing of a medium by a sounding signal, by which response one can make a conclusion about its state, and about possible changes in its state. The term «regime» means, first of all, experimentation in time. As are unable to secure the experimentation with absolutely time accuracy it is necessary to model stochastic character of this process. The authors propose a model of a binomial flow (Bernoulli flow) that embodies nonprobability component of sounding process and the stochastic character of parameter instability of this flow. The article is development of the models with a uniform distribution of a start moment which is fragmentarily considered in work .