Linear Inversion Research Articles

Robust linear algebra

We propose a robust optimization (RO) framework that immunizes some of the central linear algebra problems in the presence of data uncertainty. Namely, we formulate linear systems, matrix inversion, eigenvalues–eigenvectors and matrix factorization under uncertainty, as robust optimization problems using appropriate descriptions of uncertainty. The resulting optimization problems are computationally tractable and scalable. We show in theory that RO improves the relative error of the linear system by reducing the condition number of the underlying matrix. Moreover, we provide empirical evidence showing that the proposed approach outperforms state of the art methods for linear systems and matrix inversion, when applied on ill-conditioned matrices. We show that computing eigenvalues–eigenvectors under RO, corresponds to solving linear systems that are better conditioned than the nominal and illustrate with numerical experiments that the proposed approach is more accurate than the nominal, when perturbing ill-conditioned matrices. Finally, we demonstrate empirically the benefit of the robust Cholesky factorization over the nominal.

Gradient optimization method for tunnel resistivity and chargeability joint inversion based on deep learning

The water inrush hazards have become one of the bottleneck problems that constrain tunnel construction. Ahead geological prospecting is the major tool to avoid geo-hazards and ensure safe, economical and efficient tunnelling. This work proposes a novel deep learning-based electrical method, which jointly inverses resistivity and chargeability to estimate water-bearing structures and water volume. Specifically, we design an encoder–decoder network, with one shared encoder to extract features from input data, two encoders to output resistivity and chargeability models, respectively, and an elaborate collinear regularization on the two outputs to reduce solution multiplicity. Moreover, our input is first transformed to the gradient domain to address the spatial incorrespondence issue between observation data and the electrical model. Compared with traditional linear inversion methods, our proposed method demonstrates superiority in locating and delineating anomalous bodies. The ablation study also shows that joint inversion of two parameters could benefit and outperform independent parameter inversion.

Automated workflow for incorporation and evaluation of data uncertainty in ecological networks with autoLIMR

Ecosystems are often modelled as food webs or ecological networks, which map energy flows between species or functional groups. While there are multiple sources of uncertainty in ecological network models, a fundamental difficulty is quantifying the uncertainty of flow magnitudes, even if derived from field data, limiting the degree to which the model captures the inherent uncertainty of the empirical system. Popular techniques of incorporating data uncertainties of flow magnitudes in ecological network models are calculating multiple plausible representations of the food web within data constraints using linear inverse modelling and Markov Chain Monte Carlo (LIM-MCMC) methods. Hurdles in this process include coding input files for data-intense networks and evaluating the quality of the multiple plausible representations. To address these, we present the R package autoLIMR: an open-source automated workflow using LIM-MCMC to incorporate and evaluate data uncertainty in ecological network models. The main objectives are to improve the accessibility of LIM-MCMC, reduce errors, and provide a consistent framework to enhance model output reporting and reproducibility. We display autoLIMR on a small food web time series example and provide guidelines to facilitate the uptake of this robust methodology in the broader ecological systems sciences.

Prediction of acoustic impedance and density porosity using seismic inversion, and geostatistical methods on Krishna Godavari basin, India: A case study

Seismic inversion is a geophysical technique used to estimate subsurface acoustic impedance models from seismic reflection data. The basic concept behind seismic inversion is to establish mathematical assumptions that can relate seismic responses to geological formation properties. This study addresses two types of seismic inversion methods, namely Band-limited inversion (BLI) and Linear programming inversion (LPI) techniques for the delineation of gas reservoirs. The study presents the successful use of the inversion in a real example from a gas sand reservoir in KG-Basin, India. Inversion has led to the removal of ambiguity and revealing clear information about the target area. This work aims to use and compare the results of these two generic seismic post-stack inversion methods for characterizing the reservoir. The inversion reveals the presence of low acoustic impedance around 2320-2440 ms and is inferred as a sandstone layer with a potential hydrocarbon reservoir. One can improve the analysis of the elastic properties for reservoir characterization by using rock physics knowledge to understand better reservoir properties such as water saturation, porosity, and shale volume. This study also uses the Rock Physics Template (RPT) and plots it with elastic properties to aid the efficient interpretation. RPT helps to identify the lithology and fluid content in the area. Results from the seismic study suggest a comparatively better analysis done through the LPI technique over BLI. In the last, the Multi-attribute transform as a part of the Geostatistical method is used to predict porosity away from the borehole. The method shows a very high porosity section and clearly shows the distribution of porosity in and around the region. The interpretation shows that a very high porosity zone (15–25%) is present that is in cross-correlation with a low impedance zone (4000-8000 m/s*g/cc) and confirms the presence of a hydrocarbon zone in-between 2320 and 2440 ms two-way travel time. All seismic inversion and geostatistical methods can retrieve subsurface information with very high-resolution images but the analysis based on linear programming is found slightly better in each step and depicts good prediction results. The study finally gives a flowchart that combines seismic inversion and geostatistical methods to extract petrophysical parameters from seismic data and can help to interpret hydrocarbon-bearing formation in any virgin area.

Crustal structure in the Anyuan Coal Mine and its adjacent areas of Jiangxi Province by P-wave receiver functions

We collected high-quality teleseismic events recorded by 12 broadband seismographs deployed in the Anyuan Coal Mine and its adjacent areas in Pingxiang City, Jiangxi Province for nearly two years. The H-κ-c stacking method was employed to obtain the crustal thickness and Poisson's ratio distribution, then the characteristics of crustal structure below the stations were obtained by using the time-domain linear inversion method. The crustal thickness in the Anyuan Coal Mine and its adjacent areas ranges from approximately 32 ∼ 35 ​km, with an average thickness of 33 ​km, which is consistent with the crustal thickness results in South China from previous studies using the receiver function method. The average Poisson's ratio of the crustal bulk composition in the study area varies between 0.22 and 0.25, which is lower than the global value with a 0.27 average, indicating a predominantly intermediate-acidic or felsic crustal composition. There is a weak negative correlation between Poisson's ratio and crustal thickness estimates in the Anyuan Coal Mine and its adjacent areas, suggesting that the absence of mafic-ultramafic materials in the lower crust is associated with the process of crustal delamination. The velocity inversion results indicate that the crustal structure including three velocity discontinuity interfaces, with the first at a depth of approximately 1.5 ​km, the second at about 10 ∼ 15 ​km, and the third being the Moho. The study also indicates that the results obtained by the H-κ-c stacking method are significantly better than those obtained by the H-κ method, effectively reducing the standard deviation and dispersion of crustal thickness and vP/vS ratio.

Inversion of Late Miocene uplift history from the transient Daxia River landscape, NE Tibetan Plateau

The mechanisms of the upward and outward growth of the Tibetan Plateau are crucial for understanding the geodynamic significance of Cenozoic continental collisions. Northeastern Tibet has been suggested as one of the youngest deforming and uplifting margins surrounding the plateau. The existence of fluvial knickpoints and low-relief topographic surfaces along the Yellow River and its tributaries indicate the transience of the landscape in response to active tectonic uplift. Therefore, the uplift history of the North Eastern Tibetan Plateau (NETP) can be potentially inverted from the disequilibrium channel profiles of the Yellow River and its tributaries. The West Qinling Fault (WQF) is part of the geomorphological and topographic boundaries of the NETP. Its uplift history helps to clarify the deformation history of the Tibetan Plateau. In this study, the focus was on the Daxia River (one of the Yellow River tributaries) to identify the distribution of peneplain surfaces and knickpoints, and to present a linear inversion on the fluvial longitudinal profiles for the relative uplift history of the West Qinling. We obtained a relative uplift history with two pulses of change in the uplift rates at ∼5 and ∼2 Ma. Rates of relative uplift maintained low values during the Late Miocene, then slowly increased from 0.1 to 0.2 mm a −1 after ∼5 Ma and suddenly jumped to 0.3 mm a −1 at ∼2 Ma, consistent with recent findings on the deformation records in the NE Tibetan Plateau. We suggest that (1) the Late Miocene–Pliocene landscape evolution was driven by both tectonics and climate change and (2) inversion of the transient longitudinal channel profiles, if applied, may provide broader insights into the upward and outward growth patterns of the NE Tibetan Plateau. Thematic collection: This article is part of the Mesozoic and Cenozoic tectonics, landscape and climate change collection available at: https://www.lyellcollection.org/topic/collections/mesozoic-and-cenozoic-tectonics-landscape-and-climate-change

Development of a method for the on-line spectral characterization of Bremsstrahlung photons from an electron accelerator

The use of irradiators based on electron accelerator technologies coupled with an electron–photon conversion target requires an accurate and continuous characterization of the Bremsstrahlung spectrum produced. The indirect methods developed so far are either unsuitable for the constraints of on-line measurement or they call for excessively invasive devices. We present here a method for on-line reconstruction of the photon spectrum from the measurement of the energy deposited in a scintillator irradiated on its edge, using a simple, compact and robust device.The approach to reconstructing the Bremsstrahlung spectrum from the measurement of its energy deposited in a scintillator, translates mathematically into the solution of a linear inverse problem. The classical resolution of the problem is disrupted by its very nature and by the presence of noise in the experimental measurement of the deposited energy in the scintillator, but it is possible to apply methods compatible with the on-line constraint. In this paper, a method is implemented on the basis of Tikhonov regularization and, with the use of an effective tool, allows a multi-parametric study to be carried out in order to meet the on-line measurement constraint. In particular, the aim is to optimize the choice of scintillator and the properties of the acquisition system to be used.

Assessing the effectiveness of the shear-tensile-compressive model in earthquake source inversions: synthetic experiments and field application

SUMMARY As an alternative to the moment tensor (MT) model for earthquake sources, the shear-tensile-compressive (STC) model offers a kinematic description of the source mechanism and leads to a more robust inversion problem. However, the premise of the source inversion based on STC is to ensure the accuracy of parameter $\kappa $ defined as the ratio of the Lamé constants, $\kappa $=$\lambda /\mu $, in a fault zone. In this study, we carry out a series of synthetic experiments using P-wave amplitudes in source mechanism inversions based on both the STC and MT models, and consider the influence of noise, the uncertainties in source locations and in the velocity model. We show that the nonlinear STC inversion with an appropriate value of $\kappa $ leads to more accurate result compared to the linear MT inversion. We also propose a new joint-STC inversion method to jointly invert for parameter $\kappa $ and the remaining parameters of the STC model (magnitude and the strike, dip, rake and slope angles). The results indicate that our proposed method yields robust results for both the parameter $\kappa $ and focal mechanisms. We apply our joint-STC inversion method to field microearthquake data observed in the West Bohemia region to validate some of the conclusions drawn from the synthetic experiments.

Reconstructing COVID-19 incidences from positive RT-PCR tests by deconvolution

BackgroundThe emergency of new COVID-19 variants over the past three years posed a serious challenge to the public health. Cities in China implemented mass daily RT-PCR tests by pooling strategies. However, a random delay exists between an infection and its first positive RT-PCR test. It is valuable for disease control to know the delay pattern and daily infection incidences reconstructed from RT-PCR test observations.MethodsWe formulated the convolution model between daily incidences and positive RT-PCR test counts as a linear inverse problem with positivity restrictions. Consequently, the Richard-Lucy deconvolution algorithm was used to reconstruct COVID-19 incidences from daily PCR tests. A real-time deconvolution was further developed based on the same mathematical principle. The method was applied to an Omicron epidemic data set of a bar outbreak in Beijing and another in Wuxi in June 2022. We estimated the delay function by maximizing likelihood via an E-M algorithm.ResultsThe delay function of the bar-outbreak in 2022 differs from that reported in 2020. Its mode was shortened to 4 days by one day. A 95% confidence interval of the mean delay is [4.43,5.55] as evaluated by bootstrap. In addition, the deconvolved infection incidences successfully detected two associated infection events after the bar was closed. The application of the real-time deconvolution to the Wuxi data identified all explosive incidence increases. The results revealed the progression of the two COVID-19 outbreaks and provided new insights for prevention and control strategies, especially for the role of mass daily RT-PCR testing.ConclusionsThe proposed deconvolution method is generally applicable to other infectious diseases if the delay model can be assumed to be approximately valid. To ensure a fair reconstruction of daily infection incidences, the delay function should be estimated in a similar context in terms of virus variant and test protocol. Both the delay estimate from the E-M algorithm and the incidences resulted from deconvolution are valuable for epidemic prevention and control. The real-time feedback is particularly useful during the epidemic’s acute phase because it can help the local disease control authorities modify the control measures more promptly and precisely.

Imaging the Sources of the March 2021 Seismic Sequence in Thessaly Basin (Central Greece) from Kinematic Slip Inversion and Backprojection of Waveform Envelopes

ABSTRACT In March 2021, a series of three moderate events with moment magnitudes Mw 6.3, 6.0, and 5.5 occurred within a span of 10 days in northern Thessaly, Greece, resulting in a stop–start pattern. The moment tensors (MTs) obtained from the events suggested normal faulting along distinct yet adjacent southeast–northwest-trending faults, indicating a sequential triggering process. We applied two methods to investigate the spatial and temporal characteristics of the source process of the triplet. This approach includes linear slip inversion of regional seismic waveforms and static Global Positioning System offsets, along with backprojection of regional waveforms using the Source-Scanning Algorithm technique. The detailed modeling suggests that three adjacent, subparallel (∼300°), and low-angle, detachment-type structures were responsible for the earthquakes. The stress axes orientation was determined by inverting a dataset of recomputed MTs combined with published solutions of the sequence. The results indicated a clockwise rotation of the local extensional axis by ∼25° compared to the regional ∼north–south extension. This rotation is consistent with the orientation of the modeled seismogenic structures. Inversions for both nodal planes and grid-searching fault geometry and orientation showed that for the first-two strongest events, the activated fault planes dipped to the northeast, whereas an antithetic (southwest dipping) fault was activated during the last weaker event. For the Mw 6.3 event, both the independent analyses indicated an overall rupture duration of ∼10 s, energy bursts above and near the hypocenter, up-dip (toward the southwest) rupture propagation in the early stages of the source process, and a bilateral rupture at later stages.

Unsupervised design for broadband multispectral and polarization filter array patterns.

Imaging multiple wavelength and polarization components is problematic due to the complexity of equipment and the increase in the number of imaging shots, so imaging using filter arrays with various patterns has been widely reported from elemental research to practical applications. Most of them use bandpass filters with different center wavelengths for each pixel. Recently, however, filter arrays with multimodal transmission characteristics have been proposed using photonic crystals or Fabry-Perot filters. In any of these methods, the design of the filter array arrangement pattern is important to improve the quality of the captured image, as well as the improvement of the demosaicking algorithm. One way to design a filter array pattern is to minimize the mean squared error (MSE) between the ideal image and the demosaicked image. However, the more multidimensional the imaging components, the more difficult it becomes to collect training data. In such cases, it is necessary to empirically determine candidate transmission characteristics and patterns of filter arrays. In this study, we propose a method for evaluating filter array patterns without using any training data in the design of filter arrays for multispectral and polarization imaging. The proposed method estimates the MSE by approximating the autocorrelation matrix without using image data by expressing the imaging model as a linear forward problem and the demosaicking as a linear inverse problem. Since this method can be applied not only to ideal bandpass filter arrangements, but also to multispectral filter arrays with multimodal spectral transmission characteristics and even multispectral polarization filter arrays with different extinction ratios at different wavelengths, we will show that image quality can be improved over empirical arrangements by evaluating these patterns and by testing examples of optimal designs using genetic algorithms.

Research on Soil Moisture Inversion Method for Canal Slope of the Middle Route Project of the South to North Water Transfer Based on GNSS-R and Deep Learning

The soil moisture from the South-to-North Water Diversion Middle Route Project is assessed in this study. Complex and variable geological conditions complicate the prediction of soil moisture in the study area. To achieve this aim, we carried out research on soil moisture inversion methods for channel slopes in the study area using massive monitoring data from multiple GNSS observatories on channel slopes, incorporating GNSS-R techniques and deep learning algorithms. To address the issue of low accuracy in linear inversion when using a single satellite, this study proposes a multi-satellite and multi-frequency data fusion technique. Furthermore, three soil moisture inversion models, namely, the linear model, BP neural network model, and GA-BP neural network model, are established by incorporating deep learning techniques. In comparison with single-satellite data inversion, with the data fusion technique proposed in this study, the correlation is improved by 12.7%, the root mean square error is reduced by 0.217, the mean square error is decreased by 0.884, and the mean absolute error is decreased by 0.243 with the linear model. With the BP neural network model, the correlation is increased by 15.4%, the root mean square error is decreased by 0.395, the mean square error is decreased by 0.465, and the mean absolute error is reduced by 0.353. Moreover, with the GA-BP neural network model, the correlation is improved by 6.3%, the root mean square error is decreased by 1.207, the mean square error is decreased by 0.196, and the mean absolute error is reduced by 0.155. The results indicate that performing data fusion by using multiple satellites and multi-frequency bands is a feasible approach for improving the accuracy of soil moisture inversion. These research findings provide new technical means for the risk analysis of deformation disasters in the expansive soil channel slopes of the South-to-North Water Diversion Middle Route Project.

3D fictitious wave domain CSEM inversion by adjoint source estimation

Marine controlled-source electromagnetic (CSEM) method has proved its potential in detecting highly resistive hydrocarbon bearing formations. To image the subsurface resistivity, this paper presents the first application of a frequency domain CSEM inversion approach using fictitious wave domain timestepping modelling. Each inversion iteration requires the gradient of the misfit with respect to resistivity computed by the product between the forward and adjoint fields. Simulation of the adjoint field using fictitious time modelling is challenging as it requires the time domain adjoint source functions while only a few discrete frequencies of the data residual are available for the inversion. To overcome this issue, we formulate a regularized linear inverse problem to estimate a long time series from very few frequency samples. It can then be solved using linear optimization technique in matrix-free manner. Instead of computing adjoint source time function one by one at each receiver location, a basis function implementation has been designed, such that the linear inversion can be solved only once and then reused every time to construct all time-domain adjoint sources. The method allows computing all frequencies of the EM fields in one go without heavy memory and computational overhead. Numerical examples are employed to demonstrate the application of our method.

2D magnetotelluric inversion based on ResNet

In this study, a deep learning algorithm was applied to two-dimensional magnetotelluric (MT) data inversion. Compared with the traditional linear iterative inversion methods, the MT inversion method based on convolutional neural networks (CNN) does not rely on the selection of the initial model parameters and does not fall into the local optima. Although the CNN inversion models can provide a clear electrical interface division, their inversion results may remain prone to abrupt electrical interfaces as opposed to the actual underground electrical situation. To solve this issue, a neural network with a residual network architecture (ResNet-50) was constructed in this study. With the apparent resistivity and phase pseudo-section data as the inputs and with the resistivity parameters of the geoelectric model as the training labels, the modified ResNet-50 model was trained end-to-end for producing samples according to the corresponding production strategy of the study area. Through experiments, the training of the ResNet-50 with the dice loss function effectively solved the issue of over-segmentation of the electrical interface by the cross-entropy function, avoided its abrupt inversion, and overcame the computational inefficiency of the traditional iterative methods. The proposed algorithm was validated against MT data measured from a geothermal field prospect in Huanggang, Hubei Province, which showed that the deep learning method has opened up broad prospects in the field of MT data inversion.

Density structure of the upper and middle crust in the northeast Dabie Orogen revealed by terrestrial gravity surveys

Moderate to strong earthquakes have occurred frequently in the northeast Dabie Orogen recently. From 2014 to 2017, the Guanmiao Earthquake Swarm (GES), with a maximum earthquake magnitude of M3.9, and the Quanjun Earthquake Swarm (QES), with a maximum earthquake magnitude of M3.7, occurred successively in the area near southeast Jinzhai County, where two main Mesozoic E–W‐striking boundary faults, including the Xiaotian–Mozitan and Xinyang–Shucheng faults, are cut by the Cenozoic NNE‐/NE‐trending dextral strike‐slip faulting system. These earthquake swarms occurred within areas of human activities and have the potential to cause more violent geological hazards. However, the tectonic geneses of the earthquake swarms are still unknown due to a lack of sufficient geophysical evidence. Based on terrestrial high‐resolution Bouguer gravity anomaly data, the density structure of the northeast Dabie Mountains is inverted using a 3D linear gravity inversion method. As a result, the occurrence and cutting depth of the reactivated faults near the earthquake swarms are defined, suggesting that the Shangloufang–Xialoufang Fault (F11) may be the seismogenic fault of the GES. The genesis of the QES is possibly associated with the fault termination of the Yingshan–Quanjun strike‐slip fault (F10). More broadly, F10 is one of the major synthetic faults of the NNE‐/NE‐trending dextral strike‐slip faulting system between the Tanlu and Shangcheng–Macheng (F2) faults, which bound the East Dabie Block together. The synthetic and antithetic faults fully cover the Beihuaiyang belt and North Dabie unit topography. These intraplate strike‐slip faults formed to accommodate vertical and lateral movements of the Dabie Mountains, driven by the oblique subduction of the Pacific Plate, were likely responsible for generating earthquakes in both Huoshan and Jinzhai.

The Cenozoic spatiotemporal exhumation of the SE Tibetan Plateau: insight from the data mining and modeling of low-temperature thermochronology

Introduction: The SE Tibetan Plateau is distinct from other margins due to its high elevation, long wavelength, and low relief. A clear understanding of the Cenozoic exhumation history of this region is the key to understanding the special geomorphological process and the associated mechanisms. Previous thermochronological studies have either focused on vertical sections or horizontal variations in the local regions. However, the spatiotemporal exhumation pattern of the entire SE Tibetan Plateau is enigmatic.Methods: In this article, we have compiled 1,202 thermochronological data using joint kernel density estimation (KDE) and linear inversion approaches to address the exhumation process.Results: The results reveal that at least six episodes of rapid cooling have occurred since the Cenozoic, which include ∼61–58 Ma, 38–35 Ma, 32–23 Ma, 18–13 Ma, 11–6 Ma, and 4–3 Ma. Furthermore, the entire SE Tibetan Plateau underwent spatially inhomogeneous exhumation throughout the main episodes.Discussion: We infer that all cooling episodes may be attributed to the lateral extrusion and continuous convergence between the Indian and Eurasian continents. Meanwhile, climate changes (e.g., intensified Asian summer monsoon and glacial processes) have also played a non-negligible role in shaping the landscape since the Miocene. Our results will provide new insights into geodynamic mechanisms of the exhumation processes throughout the whole SE Tibetan Plateau since the Cenozoic.

Linear Maps Preserving Inverses of Tensor Products of Hermite Matrices

Let C be a complex field, H_{m_1m_2} be a linear space of tensor products of Hermite matrices H_{m_1}⊗H_{m_2} over C , and suppose m_{1}, m_2≥2 are positive integers. A linear map f :H_{m_1m_2} → H_n is called a linear inverse preserver if f( X_{1} ⊗X_{2} )^{-1}= f( X_{1}⊗X_{2}) ^{-1} ) for arbitrary invertible matrix X_{1} ⊗ X_{2}∈ H_{m_{1}m_{2}} .The aim of this paper is to characterize the linear maps preserving inverses of tensor products of Hermite matrices.

An inversion for asymmetric hydraulic fracture growth and fracture opening distribution from tilt measurements

The eigenstrain tensor is defined in terms of the unit vector normal to the fracture plane and the dislocation vector to characterize the fracture geometry and to determine the fracture induced deformation field. Compared to the conventional nonlinear fracture model, the forward fracture model provides a linear relationship between fracture geometry parameters (eigenstrain) and the induced deformation. Therefore, a linear inverse problem needs to be tackled in mapping the fracture geometry by inversion of tilt observations. The fracture orientation and opening distribution of a tensile-dominated hydraulic fracture can be mapped iteratively in a coupled way by using the forward model defined in terms of the dislocation vector. The proposed analysis method is applied to field tilt data collected for monitoring the growth of a hydraulic fracture placed in the preconditioning of a roof rock over a coal longwall panel at a test site. Inversion of the tilt data produces a low fracture dip angle of 6.8°, which agrees with a nearly horizontal fracture orientation confirmed by intersection data collected in offset monitoring boreholes. Tikhonov regularization technique is applied to stabilize the discrete ill-posed inverse problem. The regularized solution provides information on the fracture opening distribution and asymmetric fracture growth. The inversion shows that the fracture grows uniformly and roughly in a radial pattern at early injection times, but grows asymmetrically, preferentially, and consistently to the northwest during later times. The predicted fracture growth agrees with the temperature logging to measure fracture intersections with the offset monitoring boreholes.

The Sub‐Ice Structure of Mt. Melbourne Volcanic Field (Northern Victoria Land, Antarctica) Uncovered by High‐Resolution Aeromagnetic Data

AbstractThe Mt. Melbourne Volcanic Field is a quiescent volcanic complex located in Northern Victoria Land, Antarctica, mostly covered by ice. Its inner structure has remained largely unknown, due to the paucity of outcrops and the lack of detailed multi‐disciplinary investigations. Here we present a novel high‐resolution aeromagnetic dataset, revealing strong long‐wavelength negative anomalies superimposed by short‐wavelength positive ones forming characteristic radial patterns. Automatic lineament detection, through the Hough transform technique applied to the tilt derivative of our magnetic dataset, shows prevailing NW‐SE‐to NNE‐SSW‐trending structural features, which combined with the few structural field observations contribute to define the deformation pattern. Pre‐existing and novel magnetic property measurements, coupled with available geochronological data, are used to constrain a two‐step 3D magnetic inversion. A layer‐structured Oldenburg‐Parker's inversion was utilized to model the deep and long‐wavelength components of the magnetic field, whereas a linear inversion based on a set of shallower prisms was used to model the short‐wavelength components. The final 3D model shows widespread reversely‐polarized volcanics, which are locally intruded and superimposed, respectively by swarms of normally‐polarized dikes and radial lava flows along paleo‐valleys. These results support the onset of volcanic activity in the entire field at least in the Matuyama magnetic epoch, that is, between 2.58 and 0.78 Ma.

Efficient line shape estimation by ghost spectroscopy.

Recovering the original spectral line shapes from data obtained by instruments with extended transmission profiles is a basic tenet in spectroscopy. By using the moments of the measured lines as basic variables, we turn the problem into a linear inversion. However, when only a finite number of these moments are relevant, the rest of them act as nuisance parameters. These can be taken into account with a semiparametric model, which allows us to establish the ultimate bounds on the precision attainable in the estimation of the moments of interest. We experimentally confirm these limits with a simple ghost spectroscopy demonstration.