Top PDF Duality Methods for Waveform Inversion

Duality Methods for Waveform Inversion

Duality Methods for Waveform Inversion

Unit´e de recherche INRIA Lorraine, Technopˆole de Nancy-Brabois, Campus scientifique, 615 rue du Jardin Botanique, BP 101, 54600 VILLERS LES NANCY Unit´e de recherche INRIA Rennes, Iris[r]

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Asymptotic waveform inversion for unbiased velocity and attenuation measurements: numerical tests and application for Vesuvius lava sample analysis

Asymptotic waveform inversion for unbiased velocity and attenuation measurements: numerical tests and application for Vesuvius lava sample analysis

and scattering in addition to intrinsic damping (Sheriff 1975). It is important that these latter effects are accounted for in order to obtain the true intrinsic attenuation. Different techniques are used in laboratory and field experiments to study the attenuation of acoustic waves propagating through rocks. Toks¨oz & Johnston (1981) mainly focused on laboratory measurements of field samples. Methods generally used to measure attenuation in the laboratory may be classified into the following categories: (i) free vibration, (ii) forced vibration, (iii) wave propagation and (iv) observation of stress–strain curves (see Toks¨oz & Johnston 1981, for a review). Laboratory wave propagation techniques for estimation of sample attenuation within the lower ultrasonic frequency range are of particular interest since these techniques can be extended for use with data from field experiments. A migration/inversion method adapted to acquisition of multichannel seismic reflections was developed for 2-D and 3-D acoustic and 2-D elastic media (Jin et al. 1992; Lambar´e et al. 1992; Forgues 1996; Thierry et al. 1999a,b). Extensions of the method to the viscoacoustic and viscoelastic cases were developed by Ribodetti et al. (1995) and Ribodetti & Virieux (1998) to retrieve the attenuation factor in addition to velocities and density. The viscoacoustic method was finally adapted to laboratory experiments for the characterization of rock properties (Ribodetti et al. 2000).
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Full Waveform Inversion and the truncated Newton method

Full Waveform Inversion and the truncated Newton method

METHOD L. M´ ETIVIER ∗ , R. BROSSIER ∗ , J. VIRIEUX ∗ , AND S. OPERTO † Abstract. Full Waveform Inversion (FWI) is a powerful method for reconstructing subsurface parameters from local measurements of the seismic wavefield. This method consists in minimizing a distance between predicted and recorded data. The predicted data is computed as the solution of a wave propagation problem. Conventional numerical methods for the resolution of FWI problems are gradient-based methods, such as the preconditioned steepest-descent, or more recently the l-BFGS quasi-Newton algorithm. In this study, we investigate the interest of applying a truncated Newton method to FWI. The inverse Hessian operator plays a crucial role in the parameter reconstruction. The truncated Newton method allows one to better account for this operator. This method is based on the computation of the Newton descent direction by solving the corresponding linear system through an iterative procedure such as the conjugate gradient method. The large-scale nature of FWI problems requires however to carefully implement this method to avoid prohibitive computational costs. First, this requires to work in a matrix-free formalism, and the capability of computing efficiently Hessian-vector products. To this purpose, we propose general second-order adjoint state formulas. Second, special attention must be payed to define the stopping criterion for the inner linear iterations associated with the computation of the Newton descent direction. We propose several possibilities and establish a theoretical link between the Steihaug-Toint method, based on trust-regions, and the Eisenstat stopping criterion, designed for method globalized by linesearch. We investigate the application of the truncated Newton method to two test cases: the first is a standard test case in seismic imaging based on the Marmousi II model. The second one is inspired by a near- surface imaging problem for the reconstruction of high velocity structures. In the latter case, we demonstrate that the presence of large amplitude multi-scattered waves prevents standard methods from converging while the truncated Newton method provides more reliable results.
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Full Waveform Inversion by Proximal Newton Method using Adaptive Regularization

Full Waveform Inversion by Proximal Newton Method using Adaptive Regularization

Denoising as the simplest inverse problem (Section 2.1) has contributed to enormous progress in developing sophisticated adap- tive and non-adaptive priors for complicated signal recovery from noisy signals (Milanfar 2012). Some recently proposed excellent denoising methods include nonlocal means filters (Milanfar 2012; Goyal et al. 2020) and block matching and 3D filtering (BM3D) (Dabov et al. 2007) and its variants (Goyal et al. 2020). These patch-based methods use both local and nonlocal redundancy of information in the input signal to preserve structures in the solution by yielding locally adaptive filters via similarity kernels. Specify- ing the kernel function in these methods is essentially equivalent to estimating a particular type of empirical prior from the input sig- nal (Milanfar 2012). This somehow contrasts with the traditional non-adaptive regularization methods, for which the prior is fixed and independent from the input signal (Tarantola 2005). Such an adaptive regularization has been applied to linear inverse problems in, e.g., Danielyan et al. (2011) and Venkatakrishnan et al. (2013). We refer the reader to Appendix A for a more detailed review of the BM3D method that will be used in this study.
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Two-dimensional near-surface seismic imaging with surface waves : alternative methodology for waveform inversion

Two-dimensional near-surface seismic imaging with surface waves : alternative methodology for waveform inversion

4.1 Introduction The characterisation of the near surface (the first hundreds of meters) is essential for improving seismic imaging of both shallow and deeper exploration targets. Conven- tional seismic characterisation is done by analysing body waves. For example, first-arrival traveltime tomography is used to reconstruct the long wavelength velocity model ( Tail- landier et al. , 2009 ). Moreover, near-surface characterisation based on common-depth- point (CDP) reflection profiling requires ultra high-frequency seismic data acquisition (a few hundred Hz) ( Knapp and Steeples , 1986 ). In these imaging methods, surface waves are considered to be coherent noise that should be eliminated from the seismograms to enhance body waves. However, surface waves commonly represent more than half the seismic energy recorded in shot gathers and carry useful information. Surface waves are dispersive in heterogeneous media ( Thomson , 1950 ). Such property can be used to retrieve model parameters and characterise the near surface ( Nazarian and Stokoe II , 1984 ; Park et al. , 1999 ). Our objective is to use surface waves for reconstructing 2D high-resolution near-surface velocity models. We propose a surface-wave inversion approach based on a combination of the properties of two classical techniques: Surface Wave Analysis (SWA) and Full Waveform Inversion (FWI).
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Validation of ground penetrating radar full-waveform inversion for field scale soil moisture mapping

Validation of ground penetrating radar full-waveform inversion for field scale soil moisture mapping

Abstract Ground penetrating radar (GPR) is an efficient method for soil moisture mapping at the field scale, bridging the scale gap between small-scale invasive sensors and large-scale remote sensing instruments. Nevertheless, commonly-used GPR approaches for soil moisture characterization suffer from several limitations and the determination of the uncertain- ties in GPR soil moisture sensing has been poorly addressed. Herein, we used an advanced proximal GPR method based on full-waveform inversion of ultra-wideband radar data for mapping soil mois- ture and uncertainties in the soil moisture maps were evaluated by three different methods. First, GPR- derived soil moisture uncertainties were computed from the GPR data inversion, according to measure- ments and modeling errors and to the sensitivity of the electromagnetic model to soil moisture. Sec- ond, the reproducibility of the soil moisture map- ping was evaluated. Third, GPR-derived soil mois- ture was compared with ground-truth measurements (soil core sampling). The proposed GPR method ap- peared to be highly precise and accurate, with spa- tially averaged GPR inversion uncertainty of 0.0039 m 3 m −3 , a repetition uncertainty of 0.0169 m 3 m −3
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Multiscale seismic imaging of the eastern Nankai trough by full waveform inversion

Multiscale seismic imaging of the eastern Nankai trough by full waveform inversion

Received 6 May 2004; revised 26 July 2004; accepted 17 August 2004; published 23 September 2004. [ 1 ] Classical active seismic methods fail to sharply image the earth’s deep crust. We present the first crustal-scale application of 2-D full waveform inversion based on dense ocean bottom seismic data to investigate the Eastern Nankai subduction system (Japan). This approach allows to quantify seismic velocities up to an unprecedented degree of resolution. Results reveal compressive tectonic features within both the subducting oceanic crust and the backstop. At depth, velocity anomalies along major faults and structural discontinuities bring evidence for the presence of fluids and weakened material and also for a possible co- seismic slip partitioning structure. I NDEX T ERMS : 0902 Exploration Geophysics: Computational methods, seismic; 3025 Marine Geology and Geophysics: Marine seismics (0935); 8010 Structural Geology: Fractures and faults; 8105 Tectonophysics: Continental margins and sedimentary basins (1212). Citation: Dessa, J.-X., S. Operto, S. Kodaira, A. Nakanishi, G. Pascal, J. Virieux, and Y. Kaneda (2004), Multiscale seismic imaging of the eastern Nankai trough by full waveform inversion, Geophys. Res. Lett., 31, L18606, doi:10.1029/2004GL020453.
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The potential of time-lapse GPR full-waveform inversion as high resolution imaging technique for salt and ethanol transport

The potential of time-lapse GPR full-waveform inversion as high resolution imaging technique for salt and ethanol transport

content. Thus, tracers of different geophysical properties, which change (a) only electrical conductivity (e.g., salt [3]), and, (b) both electrical conductivity and permittivity (e.g., heat [4], ethanol [5]) are promising for GPR techniques. In this regard, this abstract shows first a synthetic ethanol tracer test monitored by GPR FWI. As first step in the methodology, the synthetic tracer test is simulated and monitored by time-lapse crosshole GPR FWI, mimicking an experiment in typical aquifer conditions using a realistic aquifer model of the Krauthausen test site in Germany [6, 7]. Scenarios of different tracer types and magnitude of geophysical parameter changes are investigated. Thereby, different FWI starting models (SM) and two time-lapse FWI strategies are investigated to estimate the limitations of the techniques. The gained knowledge is used to perform real time-lapse GPR field measurements for several tracer tests. Field results, using for example heat as tracer (conducted at Krauthausen alluvial aquifer. site description in [6]), are preliminary interpreted in time-lapse by ray-based inversion and crosshole zero-offset (ZOP) attenuation analysis. In the next step, FWI will be applied on the GPR data with perspective whether it improves transport imaging resolution compared to other geophysical methods.
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Compound Regularization of Full-Waveform Inversion for Imaging Piecewise Media

Compound Regularization of Full-Waveform Inversion for Imaging Piecewise Media

I. I NTRODUCTION F ULL waveform inversion (FWI) seeks to estimate consti- tutive parameters by nonlinear minimization of a distance between recorded and simulated wavefield measurements. This technology was originally developed in geophysical imaging [1], and has spread more recently into other fields of imaging sciences such as medical imaging [2] and oceanography [3]. This partial-differential equation (PDE)-constrained nonlinear inverse problem is classically solved with local reduced-space optimization methods [4]. In this linearized framework, a challenging source of non linearity is the so-called cycle skipping pathology which occurs when the initial model does not allow to match the data with a kinematic error smaller than half a period [5], [6]. Other sources of error are noise,
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Waveform inversion based on wavefield decomposition

Waveform inversion based on wavefield decomposition

The short wavelengths provide the ine structure of the subsurface model, allowing to lo- calize relectors in depth. The short wavelengths can be obtained by migration techniques, assuming the background velocity is correct. There are two major categories of migration methods: ray-based methods [ Beylkin, 1985 , Bleistein, 1987 ], which are based on the high frequency assumption, and wave-equation based methods [ Baysal et al., 1983 , Whitmore et al., 1983 ]. [ Etgen et al., 2009 ] gives a comparison of diferent migration methods. The principle of migration is formulated by [ Claerbout, 1971 ], and it consists of propagating the source signal and the recorded data into to the medium and cross correlate these two wave- ields. The zero-lag cross correlation gives the locations of relectors. There exist other imaging conditions, such as deconvolution-based imaging condition [ Valenciano et al., 2003 ], source/receiver-normalized imaging condition [ Kaelin et al., 2006 ], extended imag- ing condition [ Sava and Fomel, 2006 ]. [ Chattopadhyay and McMechan, 2008 ] and [ Sava and Hill, 2009 ] give a summary of the imaging conditions. The classical correlation-based migration is qualitative, as it only provides a relectivity image. Alternately, quantitative migration [ Lambaré et al., 1992 , Jin et al., 1992 , Lameloise et al., 2015 , Symes, 2015 ] al- lows imaging the values of the physical parameters. Recent developments have shown that for migration-based velocity analysis, quantitative migration is preferable as it provides a more accurate migration image.
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Increasing the robustness and applicability of full-waveform inversion: An optimal transport distance strategy

Increasing the robustness and applicability of full-waveform inversion: An optimal transport distance strategy

The main reason for the limitation in the applicability of FWI is related to what is usually referred to as cycle skipping, or phase ambiguity. In standard FWI, the oscillatory seismic data is matched in the least-squares sense where each observed sample is compared to the synthetic sample at the same position in time and/or in space. This choice is problematic: if the initial model predicts the signal with a shift larger than half a period, minimizing the least-squares distance between observed and calculated data amounts to match the observed data up to one or several phase shifts. This yields an incorrect estimation of the subsurface model which cannot be overcome through iterations: the optimization is locked into a local minimum. An illustration of this phenomenon, where the seismic data is considered schematically as a sinusoidal temporal signal, is presented in Figure 1. Overcoming this difficulty has been a recurrent objective since the introduction of FWI by Lailly (1983) and Tarantola (1984). Increasing the accuracy of the initial model through high resolution tomography methods, as well as designing hierarchical workflows focusing first on low frequency components of the data, early-arrivals, and/or short offsets, have been initial strategies proposed to challenge this issue (Kolb et al., 1986; Bunks et al., 1995; Pratt, 1999; Shipp and Singh, 2002; Sirgue and Pratt, 2004; Wang and Rao, 2009). They are still the ones implemented for real data applications to guarantee the success of FWI. This careful tuning is case-dependent, therefore, it reduces the flexibility of FWI, and requires an expert usage of FWI and pre-processing tools.
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Two-dimensional elastic full waveform inversion using Born and Rytov formulations in the frequency domain

Two-dimensional elastic full waveform inversion using Born and Rytov formulations in the frequency domain

Key words: Born and Rytov formulations, diffraction tomography, finite difference methods, medium wavenumber illumination, seismic imaging, waveform inversion. 1 I N T R O D U C T I O N Quantitative imaging using full wave equation has been achieved through the use of the adjoint formulation problem for seismic data in the last 20 yr. Both formulations in time domain (Lailly 1984; Tarantola 1984; Gauthier et al. 1986) and in frequency domain (Pratt et al. 1996; Pratt 1999; Ravaut et al. 2004) have been implemented and applied to various synthetic and real data examples with specific advantages on both sides. Easier seismic traces processing in time domain will allow progressive introduction of phases by increasing the time domain window in both observed and synthetic data (Kolb et al. 1986; Shipp & Singh 2002; Sheng 2004). Efficient ways of solving the forward problem in the frequency domain make the frequency formulation appealing (Stekl & Pratt 1998). Moreover, the progressive introduction of higher frequencies allows both to introduce and mitigate the non-linearity and recover shorter and shorter heterogeneities (Pratt 1999; Sirgue 2003). Furthermore, for wide-angle data acquisitions, this frequency approach efficiently takes benefit of the wavenumber redundancy by limiting the number of inverted frequencies (Pratt 1990; Sirgue & Pratt 2004). The attenuation may be introduced, which has been applied to real data examples (Hicks & Pratt 2001).
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Two-dimensional elastic full waveform inversion using Born and Rytov formulations in the frequency domain

Two-dimensional elastic full waveform inversion using Born and Rytov formulations in the frequency domain

Key words: Born and Rytov formulations, diffraction tomography, finite difference methods, medium wavenumber illumination, seismic imaging, waveform inversion. 1 I N T R O D U C T I O N Quantitative imaging using full wave equation has been achieved through the use of the adjoint formulation problem for seismic data in the last 20 yr. Both formulations in time domain (Lailly 1984; Tarantola 1984; Gauthier et al. 1986) and in frequency domain (Pratt et al. 1996; Pratt 1999; Ravaut et al. 2004) have been implemented and applied to various synthetic and real data examples with specific advantages on both sides. Easier seismic traces processing in time domain will allow progressive introduction of phases by increasing the time domain window in both observed and synthetic data (Kolb et al. 1986; Shipp & Singh 2002; Sheng 2004). Efficient ways of solving the forward problem in the frequency domain make the frequency formulation appealing (Stekl & Pratt 1998). Moreover, the progressive introduction of higher frequencies allows both to introduce and mitigate the non-linearity and recover shorter and shorter heterogeneities (Pratt 1999; Sirgue 2003). Furthermore, for wide-angle data acquisitions, this frequency approach efficiently takes benefit of the wavenumber redundancy by limiting the number of inverted frequencies (Pratt 1990; Sirgue & Pratt 2004). The attenuation may be introduced, which has been applied to real data examples (Hicks & Pratt 2001).
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Carbon sequestration monitoring with acoustic double-difference waveform inversion: A case study on SACROC walkaway VSP data

Carbon sequestration monitoring with acoustic double-difference waveform inversion: A case study on SACROC walkaway VSP data

form inversions of time-lapse seismic data. The conventional approach for analysis using waveform tomography is to take the difference of the images obtained using baseline and sub- sequent time-lapse datasets that are inverted independently. By contrast, double-difference waveform inversion uses time- lapse seismic datasets to jointly invert for reservoir changes. We apply conventional and double difference methods to a field time-lapse walkaway VSP data set acquired in 2008 and 2009 for monitoring CO 2 injection at an enhanced oil recov-

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Soil surface water content estimation by full-waveform GPR signal inversion in the presence of thin layers

Soil surface water content estimation by full-waveform GPR signal inversion in the presence of thin layers

1 Introduction At the eld scale, evaluating the soil water content spatial variability is an important issue for many research and engineering applications [1]. For in- stance, in catchment hydrology, as the soil surface water content determines the partitioning of precipitation into run-o and inltration under specic weather conditions, disregarding the spatial variability of the soil water content can lead to erroneous predictions in eld run-o and, further, in discharge estimation of the whole catchment [2]. Usual soil water content measurement techniques at the eld scale are invasive methods, like gravimetric sampling or time domain reectometry (TDR). Although the TDR technology has been automated to some extent, the method remains problematic for mapping large areas due to the local measuring support of the TDR probe [3]. On the other hand, airborne and spaceborne remote sensing methods have been proven to be eective tools for estimating soil surface water content over larger areas, with either passive microwave radiometry or active radar instruments [4]. However, major limi- tations with current remote sensing techniques are the unknown within-pixel heterogeneity and the usually resulting poor agreement with calibrating and gravimetric sampling [59]. Hence, no absolute relation between the backscat- tered signals from synthetic aperture radar (SAR) and the soil water content exist, necessitating site-specic calibrations [10]. In particular, remote sensing radar systems are highly aected by soil roughness, due to the relatively high frequencies used in SAR systems, such that many studies have also addressed that problem [11]. Radar sensing is also aected by high apparent electrical conductivity values when not taken into account [12].
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Local full-waveform inversion using distant data

Local full-waveform inversion using distant data

Imaging remote objects in the deep Earth, such as, subducting slabs, mantle plumes, or large low shear velocity provinces and ultra low velocity zones is key for understanding Earth’s structure and the geodynamical processes involved as it cools. In order to image these structures, we developed a strategy for performing regional-scale full-waveform inversions at arbitrary location inside the Earth [1]. Our approach is to confine wave propagation computations inside the region to be imaged. This local wavefield modeling is used in combination with wavefield extrapolation techniques in order to obtain synthetic seismograms at the surface of the Earth [2]. This allows us to evaluate a misfit functional and sensitivity kernels can then be computed locally using the adjoint state method [3]. The Green’s functions needed for extrapolating the wavefield are computed once for all in a 3D reference Earth model using the spectral element software Specfem/3DGLOBE. We will present benchmark tests demonstrating that the proposed method allows us to image 3D localized structures - this without having to model wave propagation in the entire Earth at each iteration, which is prohibitively costly, thus improving the feasibility of accurate imaging of regional structures anywhere in the Earth using numerical methods. We will show that our method permits to account for additional data in regional inversions, that is to account for distant earthquakes that are located outside the region of the study - preliminary results for the tomography of the north American continent will be presented.
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A Parallel Evolution Strategy for Acoustic Full-Waveform Inversion

A Parallel Evolution Strategy for Acoustic Full-Waveform Inversion

Motivated by the recent growth of high performance computing HPC, we will try to tackle the high non-linearity of the problem to minimize, using global optimization methods which are eas[r]

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The truncated Newton method for Full Waveform Inversion

The truncated Newton method for Full Waveform Inversion

Darse, B.P. 48, 06235 Villefranche sur Mer CEDEX, France E-mail: ludovic.metivier@ujf-grenoble.fr Abstract. Full Waveform Inversion (FWI) is a promising seismic imaging method. It aims at computing quantitative estimates of the subsurface parameters (bulk wave velocity, shear wave velocity, rock density) from local measurements of the seismic wavefield. Based on a particular wave propagation engine for wavefield estimation, it consists in minimizing iteratively the distance between the predicted wavefield at the receivers and the recorded data. This amounts to solving a strongly nonlinear large scale inverse problem. This minimization is generally performed using gradient-based methods. We investigate the possibility of applying the truncated Newton (TrN) method to this problem. This is done through the development of general second-order adjoint state formulas that yield an efficient algorithm to compute Hessian- vector products, and the design of an adaptive stopping criterion for the inner conjugate gradient (CG) iterations. Numerical results demonstrate the interest of using the TrN method when multi-scattered waves dominate the recorded data.
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Multilevel preconditioning techniques for Schwarz waveform relaxation domain decomposition methods for real-and imaginary-time nonlinear Schrödinger equations

Multilevel preconditioning techniques for Schwarz waveform relaxation domain decomposition methods for real-and imaginary-time nonlinear Schrödinger equations

Keywords: Domain decomposition method, Schwarz waveform relaxation algorithm, multilevel preconditioning, nonlinear Schr¨ odinger equation, dynamics, stationary states 1. Introduction This paper is devoted to the derivation of a multilevel Schwarz Waveform Relaxation (SWR) method for computing both in real- and imaginary-time the solution to the NonLinear Schr¨ odinger Equation (NLSE) [4, 5, 6, 10, 11]. Domain decomposition SWR methods for solving wave equations have a long history from the classical SWR method with overlapping zones to optimized version without overlap (see e.g. [7, 9, 12, 15, 16, 17, 18, 19, 22, 8] as well as http://www.ddm.org, for a complete review and references about this method). Basically in SWR methods, the transmission conditions at the subdomain interfaces are derived from the solution to the corresponding wave equation, usually using Dirichlet boundary conditions (Classical SWR), Robin boundary conditions, transparent or high-order Absorbing Boundary Conditions (ABCs) including Dirichlet-to-Neumann (DtN) transmitting conditions (Optimized SWR), or Perfectly Matched Layers [1, 9, 21]. We also refer to [1, 2, 20, 23] for some reviews on truncation techniques for quantum wave equations in infinite domains. SWR methods can be a priori applied to any type of wave equation [13, 14, 15].
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K-duality for stratified pseudomanifolds

K-duality for stratified pseudomanifolds

with inverses given respectively by · ⊗ A α and · ⊗ B α. Example 1 A basic example is A = C(V) and B = C 0 (T ∗ V) where V is a closed smooth manifold ([ 21 , 8 ], see also [ 13 ] for a description of the Dirac element in terms of groupoids). This duality allows to recover that the usual quantification and principal symbol maps are mutually inverse isomorphisms in K -theory:

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