A PSF Approach to Far Field Discretization for Conformal Sources

In this paper we introduce a sampling scheme based on the application of an inverse source problem approach to the far field radiated by a conformal current source. The regularized solution of the problem requires the computation of the Singular Value Decomposition (SVD) of the relevant linear operator, leading to introduce the Point Spread Function in the observation domain, which can be related to the capability of the source to radiate a focusing beam. Then, the application of the Kramer generalized sampling theorem allows introducing a non-uniform discretization of the angular observation domain, tailored to each source geometry. The nearly optimal property of the scheme is compared with the best approximation achievable under a regularized inversion of the pertinent SVD. Numerical results for different two-dimensional curve sources show the effectiveness of the approach with respect to standard sampling approaches with uniform spacing, since it allows to reduce the number of sampling points of the far field.

A PSF Approach to Far Field Discretization for Conformal Sources

In this paper we introduce a sampling scheme based on the application of an inverse source problem approach to the far field radiated by a conformal current source. The regularized solution of the problem requires the computation of the Singular Value Decomposition (SVD) of the relevant linear operator, leading to introduce the Point Spread Function in the observation domain, which can be related to the capability of the source to radiate a focusing beam. Then, the application of the Kramer generalized sampling theorem allows introducing a non-uniform discretization of the angular observation domain, tailored to each source geometry. The nearly optimal property of the scheme is compared with the best approximation achievable under a regularized inversion of the pertinent SVD. Numerical results for different two-dimensional curve sources show the effectiveness of the approach with respect to standard sampling approaches with uniform spacing, since it allows to reduce the number of sampling points of the far field.

A sparsity-based adaptive filtering approach to Shear Wave Splitting

<p>Shear wave splitting analysis is a frequently used tool to study elastic anisotropy from the lower mantle to the crust. Several methods have been developed to evaluate the splitting parameters, Φ (fast axis) and δt (delay time), including the correlation of wave components, minimization of covariance matrix eigenvalues, and minimizing energy on the transverse component. Despite massive progress in introducing sophisticated methods, still fundamental problems, related mainly to noisy data, interfering phases, length of the analyzed waveform, and stability and reliability of results, remain. This study presents a sparsity-based adaptive filtering method to magnify the SKS waveforms and suppress the unwanted noise and interfering phases. The study is an extension of Jurkevics (1988), computing the semi-minor and semi-minor axis of the polarized motion in the time-frequency domain using a regularized inversion-based approach imposing a sparsity constraint. Afterward, the elliptical particle motion caused by the split shear waves and correspond to high semi-minor amplitude is derived in the time-frequency domain. The information is used to design an adaptive filter in the time domain to amplify the SKS phase and suppress the noise and other phases having non-elliptical polarization. The regularized inversion-based approach enables obtaining a sparse time-frequency semi-minor map while handling noise problems in the time-frequency decomposition. Conducting synthetic simulations, we show that the proposed method increases the signal-to-noise ratio of the SKS phase in radial and transverse components, giving a better estimation of anisotropy parameters in the presence of noise and other interfering phases. Future work involves implementing the processing algorithm on real data recorded in São Tomé and Prı́ncipe, Madeira, and Canary islands. This research contributes to the FCT-funded SHAZAM (Ref. PTDC/CTA-GEO/31475/2017) and SIGHT (Ref. PTDC/CTA-GEF/30264/2017) projects.</p>

Three-Dimensional Anisotropic Inversions for Time-Domain Airborne Electromagnetic Data

Rocks and ores in nature usually appear macro-anisotropic, especially in sedimentary areas with strong layering. This anisotropy will lead to false interpretation of electromagnetic (EM) data when inverted under the assumption of an isotropic earth. However, the time-domain (TD) airborne EM (AEM) inversion for an anisotropic model has not attracted much attention. To get reasonable inversion results from TD AEM data, we present in this paper the forward modeling and inversion methods based on a triaxial anisotropic model. We apply three-dimensional (3D) finite-difference on the secondary scattered electric field equation to calculate the frequency-domain (FD) EM responses, then we use the inverse Fourier transform and waveform convolution to obtain TD responses. For the regularized inversion, we calculate directly the sensitivities with respect to three diagonal conductivities and then use the Gauss–Newton (GN) optimization scheme to recover model parameters. To speed up the computation and to reduce the memory requirement, we adopt the moving footprint concept and separate the whole model into a series of small sub-models for the inversion. Finally, we compare our anisotropic inversion scheme with the isotropic one using both synthetic and field data. Numerical experiments show that the anisotropic inversion has inherent advantages over the isotropic ones, we can get more reasonable results for the anisotropic earth structures.

Short-Range Water Temperature Profiling in a Lake with Coastal Acoustic Tomography

Coastal acoustic tomography (CAT), as an innovative technology, can perform water temperature measurements both in horizontal and vertical slices. Investigations on vertical slice observations are significantly fewer in number than horizontal observations due to difficulties in multi-path arrival peak identification. In this study, a two-station sound transmission experiment is carried out in Thousand-Island Lake, Hangzhou, China, to acquire acoustic data for water temperature profiling. Time windows, determined by range-independent ray simulation, are used to identify multi-path arrival peaks and obtain corresponding sound wave travel times. Special attention is paid to travel time correction, whose errors are caused by position drifting by more than 2 m of moored stations. The sound speed and temperature profiling are divided into four layers and are calculated by regularized inversion. Results show a good consistency with conductivity–temperature–depth (CTD) measurements. The root mean square error (RMSE) of water temperature is 0.3494, 0.6838, 1.0236 and 1.0985 °C for layer 1, 2, 3 and 4, respectively. The fluctuations of measurement are further smoothed by the moving average, which decreases the RMSE of water temperature to 0.2858, 0.4742, 0.7719 and 0.9945 °C, respectively. This study illustrates the feasibility and high accuracy of the coastal acoustic tomography method in short-range water temperature measurement. Furthermore, 3D water temperature field profiling can be performed with combined analyzing in horizontal and vertical slices.

A deep resistivity Full Waver survey unravels the 3D structure of the Castelluccio basin in relation to the source of the 2016 Mw 6.5 Norcia earthquake (central Italy)

<p>The Castelluccio basin in the central Apennines (Italy) is a ~20-km<sup>2</sup>-wide intramontane Quaternary depression located in the hangingwall of the NW-trending and SW-dipping Vettore-Bove normal fault system (VBFS). This system is responsible for the 2016-2017 seismic sequence, culminated with the 30 October 2016 Mw 6.5 Norcia earthquake that caused widespread surface faulting affecting also the northern part of the Castelluccio basin. Available borehole and geophysical data are not enough to constrain the basin structure, infill architecture and their relations with the long-term activity of the VBFS. Therefore, we carried out an extensive 3D survey using the innovative Fullwaver (FW) technology, conceived to perform deep electrical resistivity tomography (DERT). We aimed at: a) mapping the geometry of the pre-Quaternary limestone basement and the basin infill thickness down to a depth of ~1 km; b) mapping the subsurface structure of known faults and their extent underneath the alluvial cover; c) mapping possible blind faults splays.</p><p>The 3D survey covered a 23 km<sup>2 </sup>area and it was designed with the aim to map the region as regularly as possible, taking into account the rugged topography and logistic issues. We used a series of independent 2-channels receivers connected each to three grounded steel electrodes, 200 m spaced, to record the electrical field generated by a five kilowatt current regulated Time Domain Induced Polarization transmitter. Data were modelled with ViewLab software via a regularized inversion with smoothness constraints to cope with the expected subsurface strong resistivity changes, and to obtain a robust 3D resistivity model.</p><p>The FW technology allowed us to constrain the geometry of the basin. The infill material is imaged as a wide, N-trending moderately resistive (< 300 Ωm) to conductive  (< 100 Ωm) region, likely made of silty sands and gravels, deepening down to 500 m b.g.l. in the southern sector, suggesting the occurrence of two main depocenters. All over the basin, we identify paired high-resistivity (> 500-1000 Ωm) and low-resistivity (< 400 Ωm) belts related to the limestone basement and to the basin infill, respectively. They display NNE and NNW dominant trends. We interpret the sharp boundaries of NNE-trending belts as related to early extensional faults promoting the basin inception. The NNW-trending belts suggest the occurrence of faults that locally cross-cut the previous ones, and that we interpret as splays of the VBFS buried under the basin sedimentary cover. The recognition of different systems of extensional faults is coherent with results of high-resolution seismic profiling carried out recently in the basin. A high-resolution 2D transect with 15 m-spaced electrodes across the 2016 surface ruptures shows details of the active VBFS splay down to 300 m depth. Moreover, in the eastern sector of the survey area, low-resistivity round-shaped anomalies in the Mesozoic substratum hints for deep Miocene compressional structures. Therefore, our DERT imaging suggests a complex tectonics in the subsurface of the Norcia earthquake fault. In particular, the currently active NNW-trending faults seem to overprint a pre-existing structural framework, promoting fault segmentation at different spatial scales</p>