Review on Speckle-Based Spectrum Analyzer

Accurate spectral measurement and wavelength determination are fundamental and vital for many fields. A compact spectrum analyzer with high performance is expected to meet the growing requirements, and speckle-based spectrum analyzer is a potential solution. The basic principle is based on using the random medium to establish a speckle-to-wavelength mapping relationship for spectrum reconstruction. This article introduces current speckle-based spectrum analyzers with different schemes and reviews recent advances in this field. Besides, some applications by using speckle-based spectrum analyzers are also introduced. Finally, the existing challenges and the future prospects of using speckle for spectrum recovery are discussed.

Inverse spectral decomposition using an lp-norm constraint for the detection of close geological anomalies

An important application of spectral decomposition (SD) is to identify subsurface geological anomalies such as channels and karst caves, which may be buried in full-band seismic data. However, the classical SD methods including the wavelet transform (WT) are often limited by relatively low time–frequency resolution, which is responsible for false high horizon-associated space resolution probably indicating more geological structures, especially when close geological anomalies exist. To address this issue, we impose a constraint of minimizing an lp (0 < p < 1) norm of time–frequency spectral coefficients on the misfit derived by using the inverse WT and apply the generalized iterated shrinkage algorithm to invert for the optimal coefficients. Compared with the WT and inverse SD (ISD) using a typical l1-norm constraint, the modified ISD (MISD) using an lp-norm constraint can yield a more compact spectrum contributing to detect the distributions of close geological features. We design a 3D synthetic dataset involving frequency-close thin geological anomalies and the other 3D non-stationary dataset involving time-close anomalies to demonstrate the effectiveness of MISD. The application of 4D spectrum on a 3D real dataset with an area of approximately 230 km2 illustrates its potential for detecting deep channels and the karst slope fracture zone.

The stable algebra of a Wieler solenoid: inductive limits and -theory

Wieler has shown that every irreducible Smale space with totally disconnected stable sets is a solenoid (i.e., obtained via a stationary inverse limit construction). Using her construction, we show that the associated stable $C^{\ast }$-algebra is the stationary inductive limit of a $C^{\ast }$-stable Fell algebra that has a compact spectrum and trivial Dixmier–Douady invariant. This result applies in particular to Williams solenoids along with other examples. Beyond the structural implications of this inductive limit, one can use this result to, in principle, compute the $K$-theory of the stable $C^{\ast }$-algebra. A specific one-dimensional Smale space (the $aab/ab$-solenoid) is considered as an illustrative running example throughout.