Signal-to-Noise Ratio Estimation in Passive Correlation-Based Imaging

We consider imaging with passive arrays of sensors using as illumination ambient noise sources. The first step for imaging under such circumstances is the computation of the cross correlations of the recorded signals, which have attracted a lot of attention recently because of their numerous applications in seismic imaging, volcano monitoring, and petroleum prospecting. Here, we use these cross correlations for imaging reflectors with travel-time migration. While the resolution of the image obtained this way has been studied in detail, an analysis of the signal-to-noise ratio (SNR) is presented in this paper along with numerical simulations that support the theoretical results. It is shown that the SNR of the image inherits the SNR of the computed cross correlations and therefore is proportional to the square root of the bandwidth of the noise sources times the recording time. Moreover, the SNR of the image is proportional to the array size. This means that the image can be stabilized by increasing the size of the array when the recorded signals are not of long duration, which is important in applications such as nondestructive testing. 1. Introduction. We consider passive array imaging using as illumination ambient noise sources. We compute the cross correlations of the signals recorded at the array of sensors and form an image by backpropagating or migrating them to a region of interest containing reflectors. In this paper we assess the quality of such images in terms of several parameters that affect it. There are two types of analyses that must be carried out. The first is a resolution analysis of the imaging functional (11), and the second is an analysis of the signal- to-noise ratio (SNR), which is done in this paper. Our main result is that the SNR of the image is proportional NR √ BT for an array of NR sensors placed at a distance of half a central wavelength or more, with B the bandwidth of the noise sources and T the recording time. The analysis and the numerical simulations are carried out in two space dimensions, but the result

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