We address the problem of search-free direction of arrival (DOA) estimation for sensor arrays of arbitrary geometry under the challenging conditions of a single snapshot and coherent sources. We extend a method of searchfree super-resolution beamforming, originally applicable only for uniform linear arrays, to arrays of arbitrary geometry. The infinite dimensional primal atomic norm minimization problem in continuous angle domain is converted to a dual problem. By exploiting periodicity, the dual function is then represented with a trigonometric polynomial using a truncated Fourier series. A linear rule of thumb is derived for selecting the minimum number of Fourier coefficients required for accurate polynomial representation, based on the distance of the farthest sensor from a reference point. The dual problem is then expressed as a semidefinite program and solved efficiently. Finally, the searchfree DOA estimates are obtained through polynomial rooting, and source amplitudes are recovered through least squares. Simulations using circular and random planar arrays show perfect DOA estimation in noise-free cases.
Continuous microseismic monitoring of hydraulic fracturing is commonly used
in many engineering, environmental, mining, and petroleum applications.
Microseismic signals recorded at the surface, suffer from excessive noise that
complicates first-break picking and subsequent data processing and analysis.
This study presents a new first-break picking algorithm that employs concepts
from seismic interferometry and time-frequency (TF) analysis. The algorithm
first uses a TF plot to manually pick a reference first-break and then iterates
the steps of cross-correlation, alignment, and stacking to enhance the
signal-to-noise ratio of the relative first breaks. The reference first-break
is subsequently used to calculate final first breaks from the relative ones.
Testing on synthetic and real data sets at high levels of additive noise shows
that the algorithm enhances the first-break picking considerably. Furthermore,
results show that only two iterations are needed to converge to the true first
breaks. Indeed, iterating more can have detrimental effects on the algorithm
due to increasing correlation of random noise.Comment: 31 pages, 18 Figure
Passive microseismic data are commonly buried in noise, which presents a significant challenge for signal detection and recovery. For recordings from a surface sensor array where each trace contains a time-delayed arrival from the event, we propose an autocorrelation-based stacking method that designs a denoising filter from all the traces, as well as a multi-channel detection scheme. This approach circumvents the issue of time aligning the traces prior to stacking because every trace's autocorrelation is centered at zero in the lag domain. The effect of white noise is concentrated near zero lag, so the filter design requires a predictable adjustment of the zero-lag value. Truncation of the autocorrelation is employed to smooth the impulse response of the denoising filter. In order to extend the applicability of the algorithm, we also propose a noise prewhitening scheme that addresses cases with colored noise. The simplicity and robustness of this method are validated with synthetic and real seismic traces.
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