The ambient passive seismic imaging technique is capable of imaging repetitive passive seismic events. Here we investigate the effect of noise for this method. These repetitive events are the passive seismic sources that emit the seismic energy from a certain subsurface location for a certain amount of time. For example, we assume that drill-bit noise, injection tremors, or long period long duration events occurring during the process of drilling and hydraulic fracturing can be considered to be these kind of the events. Our mathematical analysis provides an understanding of the effectiveness of the imaging in the presence of random and/or coherent noise. We provide synthetic examples to verify our derivation. We conclude first that creating images (averaging) along "long" time windows does not improve the signal-to-noise ratio but does improve the capability to detect repetitive signals by reducing the effects of random noise. Moreover non-random noises such as coherent low velocity surface waves are not reduced by this method, are aliased into the image, and can be misinterpreted as subsurface signal.
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