Compressive sensing imaging of microseismic events constrained by the sign-bit

We have developed a source location algorithm based on compressive sensing (CS) imaging constrained with the sign-bit of the observations. The relationship between sparsity and compression level was exemplified by contrasting synthetic examples of compressed imaging in reflection seismology and microseismic monitoring scenarios. The influence of noise was also illustrated in the microseismic monitoring case. The synthetic and real data examples were used to demonstrate the advantages that the sign-bit constraint provided over a previously proposed CS approach using the adjoint operator. The improvement in the imaging results obtained with and without the sign-bit constraint was quantified by estimating the ratio of the image amplitude at the source position with respect to the background. Images obtained with the sign-bit constraint present larger ratios and more condensed amplitude anomalies, which translate into more confident event detections and smaller location uncertainties.