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Research on linear inversion of SIP using the Debye decomposition method

JOURNAL OF APPLIED GEOPHYSICS 2023年第1期212卷

作者： Wang, Shu Yang, Jin Su, Peng China Univ Geosci Sch Geophys & Informat Technol Beijing 100083 Peoples R China

Spectral-induced polarization data can provide information regarding the polarization properties of underground media. The characteristic relaxation time of polarized media is related in part to the composition of rocks and minerals and porosity. Therefore, the spectral-induced polarization method is widely used to obtain underground lithology/structure, hydrogeology, and geochemical data. Because the Debye decomposition method can flexibly fit the spectrum shape, it is being increasingly used to analyze the relaxation time distribution of spectral-induced polarization (SIP) signals. In this study, the Debye decomposition method was used to directly invert the relaxation time distribution curve from SIP data to extract the characteristic relaxation time of the target. First, we discuss the Debye decomposition method in terms of its physical principle and show the relationship between the multi-Cole-Cole model and Debye decomposition through a numerical simulation. We then used the linear inversion method to invert the synthetic and measured data based on the Debye decomposition parameterization and verify the effectiveness of the inversion. Compared with the numerical simulations of several models, we proved that the parameters of the Cole-Cole model are strongly correlated. Additionally, the inversion results show that the linear inversion method is suitable for inverting the Debye decomposition and that expanding the range of the relaxation time in the Debye decomposition can effectively alleviate the influence of the truncation error on inversion.

关键词： Spectral induced polarization Laboratory data Debye decomposition linear inversion

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Evaluation of a linear inversion Method for retrieval of directional wave spectra from SAR look cross spectra

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REMOTE SENSING OF ENVIRONMENT 2022年 282卷

作者： Brasil-Correa, Yuri O. Violante-Carvalho, Nelson Santos, Felipe M. Carvalho, Luiz Mariano Santos, Andre L. C. Costa, Leonardo P. F. Portilla-Yandun, Jesus Romeiser, Roland Rio De Janeiro Fed Univ Ocean Engn Program COPPE UFRJ Rio De Janeiro Brazil Rio De Janeiro State Univ UERJ Rio De Janeiro Brazil Fed Ctr Technol Educ Rio De Janeiro CEFET RJ Rio De Janeiro Brazil Escuela Politec Nacl Quito Ecuador Univ Miami Rosenstiel Sch Marine & Atmospher Sci Coral Gables FL USA

The feasibility of a linear inversion Method applied to Synthetic Aperture Radar cross spectra to retrieve wave directional spectra is investigated. The proposed method is computationally efficient and does not require any a priori information from wave or atmospheric models, as is usually the case with other approaches. It is also comparatively less sensitive to low signal-to-noise ratio image spectra, which in general hinders the disambig-uation of the retrieved directional wave spectrum. Several test cases were computed employing a simulator of complex SAR image spectra considering a broad range of values of steepness for the Envisat and Sentinel-1 satellite configurations. The results of the simulated cases were employed as lookup tables to correct biases while retrieving directional wave spectra from Level 1 cross spectra. As the nonlinearities, not accounted for when applying a linear inversion, are dependent on satellite configuration and on the relative position of the peak wave spectrum in relation to the azimuth cut-off, it is possible to quantify them through numerical sim-ulations. The SAR wave spectra retrieved with the linear inversion Method from an Envisat ground track were evaluated against the ECMWF reanalysis ERA5 and compared to the results of ESA Level 2 WVW wave mode spectra. The SAR-inverted wave spectra, retrieved with both methods, presented similar results in terms of root -mean-square error (RMSE) and scatter index (SI) for significant wave height, peak wavelength and peak prop-agation direction. Specifically for significant wave height, the linear inversion Method yielded a bias of-0.14 m, a SI of 0.34 and a RMSE of 0.44 m for a segment of ground track over the Pacific Ocean employed in our val-idations. The directional wave spectra retrieved with the linear inversion Method presented better similarity with the ERA5 spectra, in comparison with the WVW spectra. Moreover, in around one third of the cases, the ESA method did not resolve the

关键词： SAR Synthetic Aperture Radar Wave spectra linear inversion Hasselmann SAR-wave mapping relation Image spectra

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Pulsed uplift of the South Tianshan since the Late Miocene indicated by the linear inversion on river longitudinal profiles

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GEOMORPHOLOGY 2024年 466卷

作者： Li, Jiangang Liang, Wentian Wang, Yizhou Song, Shida Shen, Qi Yuan, Sihua Northwest Univ State Key Lab Continental Dynam Xian Peoples R China China Earthquake Adm Inst Geol State Key Lab Earthquake Dynam Beijing Peoples R China Inst Disaster Prevent Sch Earth Sci Sanhe Peoples R China

The early Cenozoic collision and subsequent continuous convergence between the Indian and Eurasian plates reactivated the Tianshan orogen in the Central Asia and caused multistage uplift of the mountain range. The modern Tianshan, with high mountain peaks of >7000 m, forms very prominent topography that profoundly affects the regional tectonics and climate. However, the late Cenozoic uplift process and topography growth of the South Tianshan remain controversial. River longitudinal profile inversion provides a distinctive way to reveal rock uplift history since the late Cenozoic. In this study, we presented linear inversion on river longitudinal profiles of four drainage basins originating from high mountains in the South Tianshan. The inversion results from two basins in the northern flank show fast and continuous increases in the uplift rates from about 0.1-0.2 mm/a to 0.6-1.0 mm/a since 4 Ma. While in the southern flank, the uplift rates of the two basins increased gradually from about 0.1 mm/a to 0.2 mm/a before 10 Ma and from 0.2 mm/a to 0.4 mm/a around 10 Ma and 6 Ma, respectively. Our results combined with recently published chronological data in this region indicate that the South Tianshan experienced a pulsed tectonic uplift process since the Late Miocene. Moreover, the pulsed tectonic uplift should lead to an elevated South Tianshan during 6-4 Ma, coinciding well with the similar to 5.3 Ma extreme aridification in the Tarim Basin, thus supporting that the rain shadow effect caused by high topography of South Tianshan is a critical reason for aridification.

关键词： linear inversion Tectonic uplift Extreme aridification South Tianshan Tarim Basin

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River linear inversion to assess drainage base-level fall history in North-western Apennines and implications on the Alessandria Basin tectonic activity

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GEOMORPHOLOGY 2024年 462卷

作者： Tebar, Victor Buleo Bonasera, Mauro Racano, Simone Fubelli, Giandomenico Univ Turin Dept Earth Sci Turin Italy Italian Inst Environm Protect & Res ISPRA Geol Survey Italy Rome Italy Univ Potsdam Inst Geosci Potsdam Germany

Drainage network systems are responsive elements to recent active tectonics from among all the topographic features. In geodynamically active areas, fluvial landscapes can record different processes through the formation and current presence of features related to spatial-temporal variation in base-level fall and vertical incision of stream channels. This study focuses on the tectonic evolution of the Alessandria Basin, a synorogenic tectonic basin located at the junction between the Alps and the Apennines, that experienced progressive subsidence during the overthrusting of the Monferrato Thrust Front (the westernmost outer arc of the Apennine belt) onto the Po Foreland Basin. Even though several studies have assessed the Neogene tectonic evolution at a regional scale, rates and timing of the Quaternary activity are still poorly understood in terms of both Alps/Apennines uplift and activity of the compressive front of the Monferrato Arc. In this paper, we applied the method of the river profile linear inversions to reconstruct the base-level fall history of 6 catchments that drain into the Alessandria Basin. We used nine Be-10-derived basin-average denudation rates to constrain the erodibility parameter needed to infer base-level fall rates from chi-transformed river profiles. The results describe the tectonic history of the area in the last similar to 5 Ma, documenting increases in base-level fall rate with an initial peak between 3 and 2.5 Ma, and a second between 2 and 1.5 Ma. While the first peak is coeval with the uplift phase that involved most of the northern-central Apennine, the second one suggests an acceleration in subsidence of the Alessandria Basin concurrently with the uplift of the Monferrato Thrust Front.

关键词： Drainage network systems Active tectonics linear inversion Base-level fall history Alessandria Basin Quaternary activity

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linear geophysical inversion via the discrete cosine pseudo-inverse: application to potential fields

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GEOPHYSICAL PROSPECTING 2017年第Sup1期65卷 94-111页

作者： Fernandez-Martinez, J. L. Fernandez-Muniz, Z. Pallero, J. L. G. Bonvalot, S. Univ Oviedo Grp Problemas Inversos Optimizac & Aprendizaje Au Dept Matemat Oviedo 33007 Spain Univ Politecn Madrid ETSI Topog Geodesia & Cartog E-28040 Madrid Spain Univ Toulouse Lab GET CNRS IRDCNESBGI F-31401 Toulouse France

In this paper, we present a methodology to perform geophysical inversion of large-scale linear systems via a covariance-free orthogonal transformation: the discrete cosine transform. The methodology consists of compressing the matrix of the linear system as a digital image and using the interesting properties of orthogonal transformations to define an approximation of the Moore-Penrose pseudo-inverse. This methodology is also highly scalable since the model reduction achieved by these techniques increases with the number of parameters of the linear system involved due to the high correlation needed for these parameters to accomplish very detailed forward predictions and allows for a very fast computation of the inverse problem solution. We show the application of this methodology to a simple synthetic two-dimensional gravimetric problem for different dimensionalities and different levels of white Gaussian noise and to a synthetic linear system whose system matrix has been generated via geostatistical simulation to produce a random field with a given spatial correlation. The numerical results show that the discrete cosine transform pseudo-inverse outperforms the classical least-squares techniques, mainly in the presence of noise, since the solutions that are obtained are more stable and fit the observed data with the lowest root-mean-square error. Besides, we show that model reduction is a very effective way of parameter regularisation when the conditioning of the reduced discrete cosine transform matrix is taken into account. We finally show its application to the inversion of a real gravity profile in the Atacama Desert (north Chile) obtaining very successful results in this non-linear inverse problem. The methodology presented here has a general character and can be applied to solve any linear and non-linear inverse problems (through linearisation) arising in technology and, particularly, in geophysics, independently of the geophysical model discretisation and dim

关键词： linear inversion Model reduction Discrete cosine transform (DCT) Pseudo-inverse

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Obtaining electron attachment cross sections by means of linear inversion of swarm parameters

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JOURNAL OF PHYSICS D-APPLIED PHYSICS 2015年第7期48卷 075201-075201页

作者： Rabie, M. Haefliger, P. Chachereau, A. Franck, C. M. ETH Power Syst & High Voltage Labs CH-8092 Zurich Switzerland

We investigate electron attachment to strongly attaching gases as a function of the electron energy. The total electron attachment cross section of this electronegative sample gas is determined from the effective ionization rate ***/ N measured in a swarm experiment using the buffer gases N2 and CO2 with minor proportions (. 0.8%) of the sample gas SF6, and C3F8 respectively. The measured rate ***/ N for varying reduced electric field strengths E/ N are unfolded from the electron energy distribution of the buffer gases. Different unfolding routines for so- called ill- posed problems are tested to find robust solutions for the attachment cross section. Finally, we propose Tikhonov regularization, which is a well defined algorithm for discrete linear inversion problems, as most efficient. Our method gives rise to an approximate and clearly defined solution for the attachment cross section, and it is described in detail.

关键词： swarm parameters attachment cross sections linear inversion

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Tectonics from fluvial topography using formal linear inversion: Theory and applications to the Inyo Mountains, California

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JOURNAL OF GEOPHYSICAL RESEARCH-EARTH SURFACE 2014年第8期119卷 1651-1681页

作者： Goren, L. Fox, Matthew Willett, Sean D. Ben Gurion Univ Negev Dept Geog & Environm Sci IL-84105 Beer Sheva Israel ETH Dept Earth Sci Zurich Switzerland Univ Calif Berkeley Dept Earth & Planetary Sci Berkeley CA 94720 USA Berkeley Geochronol Ctr Berkeley CA USA

Tectonic activity generates topography, and the variability of tectonic forcing is responsible for topographic patterns and variability of relief in fluvial landscapes. Despite this basic relation, the inverse problem, by which features of the topography are used for inferring tectonic uplift rates, has proven challenging. Here we develop formal linear inversion schemes to infer a record of the rate of relative uplift as a function of space and time from the long profiles of rivers. The relative uplift rate is the difference between the rates of rock uplift and of the base level change. The inversion schemes are based on a closed-form analytic solution to the transient linear stream power model, and to increase model resolution they make use of the multiplicity of information made available by multiple rivers and their tributaries. The distribution of the fluvial response time to tectonic perturbations is a key component of the inversion scheme, as this determines which tectonic events are preserved in the topography. We develop two inversion parameterizations that differ in their assumptions about the tectonic forcing: space-invariant and time-space variability with an assumed spatial distribution. The inversion schemes are applied to the Inyo Mountains, an uplifted block along the western boundary of the Basin and Range Province in California. inversion results indicate that the range has been experiencing an acceleration of the relative uplift in the past similar to 2-3 Ma. We use the inversion results to constrain the paleotopography and paleo-erosion rate along the range and to recover the throw rate history along the fault that bounds the Inyo range.

关键词： fluvial geomorphology linear inversion tectonic uplift rate river long profile tectonics from topography Inyo Mountains

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linear quadrature method of moments for solving the transported probability density function model for turbulent combustion

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COMBUSTION THEORY AND MODELLING 2025年第2期29卷 145-176页

作者： Wang, Yunchu Wang, Yize Yuan, Li Chinese Acad Sci ICMSEC Beijing Peoples R China Chinese Acad Sci Acad Math & Syst Sci LSEC Beijing Peoples R China Univ Chinese Acad Sci Sch Math Sci Beijing Peoples R China

Large eddy simulation (LES) coupled with the transported probability density function (PDF) model has become a promising strategy for modelling turbulent combustion. For solving the high-dimensional PDF transport equation numerically, deterministic quadrature-based moment methods have arisen as an alternative choice besides stochastic particle and stochastic field methods. In this work, we propose a new quadrature-based moment method called linear Quadrature Method Of Moments (LQMOM) for the univariate PDF case. This method assumes that the underlying PDF distribution is smooth and it uses a set of predefined quadrature nodes and weights in the sample space to establish a linear system of equations for the PDF values at the quadrature nodes from the moments. The LQMOM is more efficient than the original QMOM which needs to solve a nonlinear system of equations for the moment inversion. However, it may generate negative PDF values for non-smooth PDF distributions. To remedy this flaw, we construct the LQMOM-QMOM hybrid algorithm by using detectors to detect single- and two-peak distributions. Furthermore, we extend the LQMOM to the multivariate PDF case by utilizing the main idea of the conditional QMOM (CQMOM) to obtain the linear CQMOM (LCQMOM), and then reduce it to the simplified version (LCQMOM-S) to gain efficiency. The LQMOM-QMOM hybrid algorithm for univariate PDFs is tested in a typical example and the LCQMOM-S-CQMOM hybrid algorithm for multivariate PDFs is checked in compressible turbulent reactive 2D shear layer flow and 3D air/H2 jet. It is shown that the hybrid algorithms can reduce 20-35% simulation time and produce similar results compared with the respective QMOM and CQMOM.

关键词： turbulent combustion large eddy simulation probability density function quadrature-based moment method linear inversion hybrid algorithm

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Understanding tectonics from fluvial topography by using the stochastic-threshold incision model: Theory and application to the Dadu River basin, eastern Tibetan Plateau

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EARTH SURFACE PROCESSES AND LANDFORMS 2024年第5期49卷 1653-1666页

作者： Wang, Yizhou Zheng, Dewen Zhang, Huiping China Earthquake Adm Inst Geol State Key Lab Earthquake Dynam Beijing 100029 Peoples R China

The flood distribution and bedrock incision threshold exert important influences on the erosion efficiency, which can result into a nonlinear scaling between channel steepness (normalized channel gradients for the downstream increases in drainage area) and erosion rates. Here, we explore the incorporation of both river incision threshold and discharge probability distribution into erosion efficiency to construct a stochastic-threshold incision model equation to simulate river power incision and the evolution of fluvial topography. Assuming time-dependent tectonic uplift, we develop a closed-form analytical solution to the model equation and derive a linear inverse procedure to retrieve relative uplift rate history from river longitudinal profiles. Application of the inverse scheme to the Dadu River basin in the eastern Tibetan Plateau produces a history with three-phase increases in the uplift/incision rates during the Cenozoic. We use the inversion results to forward the time-changed river long profile, which indicates the existence of paleo relief before the Oligocene and significant contributions of the late Miocene regional uplift and early Pleistocene river capture on the present topography. Assuming timely dependent tectonic uplift, we develop an analytic solution to the stochastic-threshold incision model equation. The analytical solution yields a linear inverse scheme to infer tectonic uplift history from river longitudinal profiles. linear inversion on the Dadu River basin in the eastern Tibetan Plateau produces a history with three-stage increases in the relative uplift/incision rates during the Cenozoic. image

关键词： analytical solution linear inversion stochastic-threshold incision model the Dadu River time-dependent tectonic uplift

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Realistic FDTD GPR Antenna Models Optimized Using a Novel linear/Nonlinear Full-Waveform inversion

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IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING 2019年第3期57卷 1768-1778页

作者： Giannakis, Iraklis Giannopoulos, Antonios Warren, Craig Univ Edinburgh Sch Engn Edinburgh EH9 3FG Midlothian Scotland Univ West London London W5 5RF England Northumbria Univ Dept Mech & Construct Engn Newcastle NE1 8ST England

Finite-difference time-domain forward modeling of ground-penetrating radar (GPR) is becoming regularly used in model-based interpretation methods, such as full-waveform inversion (FWI) and machine learning schemes. Oversimplifications in such forward models can compromise the accuracy and realism with which real GPR responses can be simulated, which degrades the overall performance of interpretation techniques. A forward model must be able to accurately simulate every part of the GPR problem that affects the resulting scattered field. A key element, especially for near-field applications, is the antenna system. Therefore, the model must contain a complete description of the antenna, including the excitation source and waveform, the geometry, and the dielectric properties of any materials in the antenna. The challenge is that some of these parameters are not known or cannot be easily measured, especially for commercial GPR antennas that are used in practice. We present a novel hybrid linear/nonlinear FWI approach that can be used, with only knowledge of the basic antenna geometry, to simultaneously optimize the dielectric properties and excitation waveform of the antenna and minimize the error between real and synthetic data. The accuracy and stability of our proposed methodology are demonstrated by successfully modeling a 1.5-GHz commercial antenna from Geophysical Survey Systems, Inc. Our framework allows accurate models of GPR antennas to be developed without requiring detailed knowledge of every component of the antenna. This is significant because it allows commercial GPR antennas, regularly used in GPR surveys, to be more readily simulated.

关键词： Antennas commercial finite-difference time-domain (FDTD) full-waveform inversion (FWI) ground-penetrating radar (GPR) hybrid optimization linear inversion nonlinear inversion

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