Global Inversion Research Articles

Thermal expansivity, heat capacity and bulk modulus of the mantle

SUMMARYWe derive exact expressions for the thermal expansivity, heat capacity and bulk modulus for assemblages with arbitrarily large numbers of components and phases, including the influence of phase transformations and chemical exchange. We illustrate results in simple two-component, two-phase systems, including Mg–Fe olivine-wadsleyite and Ca–Mg clinopyroxene-orthopyroxene and for a multicompontent model of mantle composition in the form of pyrolite. For the latter we show results for the thermal expansivity and heat capacity over the entire mantle pressure–temperature regime to 40 GPa, or a depth of 1000 km. From the thermal expansivity, we derive a new expression for the phase buoyancy parameter that is valid for arbitrarily large numbers of phases and components and which is defined at every point in pressure–temperature space. Results reveal regions of the mantle where the magnitude of the phase buoyancy parameter is larger in magnitude than for those phase transitions that are most commonly included in mantle convection simulations. These regions include the wadsleyite to garnet and ferropericlase transition, which is encountered along hot isentropes (e.g. 2000 K potential temperature) in the transition zone, and the ferropericlase and stishovite to bridgmanite transition, which is encountered along cold isentropes (e.g. 1000 K potential temperature) in the shallow lower mantle. We also show the bulk modulus along a typical mantle isentrope and relate it to the Bullen inhomogeneity parameter. All results are computed with our code HeFESTo, updates and improvements to which we discuss, including the implementation of the exact expressions for the thermal expansivity, heat capacity and bulk modulus, generalization to allow for pressure dependence of non-ideal solution parameters and an improved numerical scheme for minimizing the Gibbs free energy. Finally, we present the results of a new global inversion of parameters updated to incorporate more recent results from experiment and first principles theory, as well as a new phase (nal phase), and new species: Na-majorite and the NaAlO2 end-member of ferropericlase.

Global distribution of methane emissions: a comparative inverse analysis of observations from the TROPOMI and GOSAT satellite instruments

Abstract. We evaluate the global atmospheric methane column retrievals from the new TROPOMI satellite instrument and apply them to a global inversion of methane sources for 2019 at 2∘ × 2.5∘ horizontal resolution. We compare the results to an inversion using the sparser but more mature GOSAT satellite retrievals and to a joint inversion using both TROPOMI and GOSAT. Validation of TROPOMI and GOSAT with TCCON ground-based measurements of methane columns, after correcting for retrieval differences in prior vertical profiles and averaging kernels using the GEOS-Chem chemical transport model, shows global biases of −2.7 ppbv for TROPOMI and −1.0 ppbv for GOSAT and regional biases of 6.7 ppbv for TROPOMI and 2.9 ppbv for GOSAT. Intercomparison of TROPOMI and GOSAT shows larger regional discrepancies exceeding 20 ppbv, mostly over regions with low surface albedo in the shortwave infrared where the TROPOMI retrieval may be biased. Our inversion uses an analytical solution to the Bayesian inference of methane sources, thus providing an explicit characterization of error statistics and information content together with the solution. TROPOMI has ∼ 100 times more observations than GOSAT, but error correlation on the 2∘ × 2.5∘ scale of the inversion and large spatial inhomogeneity in the number of observations make it less useful than GOSAT for quantifying emissions at that scale. Finer-scale regional inversions would take better advantage of the TROPOMI data density. The TROPOMI and GOSAT inversions show consistent downward adjustments of global oil–gas emissions relative to a prior estimate based on national inventory reports to the United Nations Framework Convention on Climate Change but consistent increases in the south-central US and in Venezuela. Global emissions from livestock (the largest anthropogenic source) are adjusted upward by TROPOMI and GOSAT relative to the EDGAR v4.3.2 prior estimate. We find large artifacts in the TROPOMI inversion over southeast China, where seasonal rice emissions are particularly high but in phase with extensive cloudiness and where coal emissions may be misallocated. Future advances in the TROPOMI retrieval together with finer-scale inversions and improved accounting of error correlations should enable improved exploitation of TROPOMI observations to quantify and attribute methane emissions on the global scale.

Observation of Spin-Momentum-Layer Locking in a Centrosymmetric Crystal.

The spin polarization in nonmagnetic materials is conventionally attributed to the outcome of spin-orbit coupling when the global inversion symmetry is broken. The recently discovered hidden spin polarization indicates that a specific atomic site asymmetry could also induce measurable spin polarization, leading to a paradigm shift in research on centrosymmetric crystals for potential spintronic applications. Here, combining spin- and angle-resolved photoemission spectroscopy and theoretical calculations, we report distinct spin-momentum-layer locking phenomena in a centrosymmetric, layered material, BiOI. Themeasured spin is highly polarized along the Brillouin zone boundary, while the same effect almost vanishes around the zone center due to its nonsymmorphic crystal structure. Our work demonstrates the existence of momentum-dependent hidden spin polarization and uncovers the microscopic mechanism of spin, momentum, and layer locking to each other, thus shedding light on the design metrics for future spintronic materials.

Global stochastic seismic inversion using turning bands simulation and co-simulation

Global stochastic seismic inversion using turning bands simulation and co-simulation

Evaluation of CarbonTracker's Inverse Estimates of North American Net Ecosystem Exchange of CO2 From Different Observing Systems Using ACT‐America Airborne Observations

AbstractQuantification of regional terrestrial carbon dioxide (CO2) fluxes is critical to our understanding of the carbon cycle. We evaluate inverse estimates of net ecosystem exchange (NEE) of CO2 fluxes in temperate North America, and their sensitivity to the observational data used to drive the inversions. Specifically, we consider the state‐of‐the‐science CarbonTracker global inversion system, which assimilates (a) in situ measurements (IS), (b) the Orbiting Carbon Observatory‐2 (OCO‐2) v9 column CO2 (XCO2) retrievals over land (LNLG), (c) OCO‐2 v9 XCO2 retrievals ocean‐glint (OG), and (d) a combination of all these observational constraints (LNLGOGIS). We use independent CO2 observations from the Atmospheric Carbon and Transport (ACT)—America aircraft mission to evaluate the inversions. We diagnose errors in the flux estimates using the differences between modeled and observed biogenic CO2 mole fractions, influence functions from a Lagrangian transport model, Bayesian inference, and root‐mean‐square error (RMSE) and bias metrics. The IS fluxes have the smallest RMSE among the four products, followed by LNLG. Both IS and LNLG outperform the OG and LNLGOGIS inversions with regard to RMSE. Regional errors do not differ markedly across the four sets of posterior fluxes. The CarbonTracker inversions appear to overestimate the seasonal cycle of NEE in the Midwest and Western Canada, and overestimate dormant season NEE across the Central and Eastern US. The CarbonTracker inversions may overestimate annual NEE in the Central and Eastern US. The success of the LNLG inversion with respect to independent observations bodes well for satellite‐based inversions in regions with more limited in situ observing networks.

Far-field biogenic and anthropogenic emissions as a dominant source of variability in local urban carbon budgets: A global high-resolution model study with implications for satellite remote sensing

With the launch of the Observing Carbon Observatories (OCO-2 and OCO-3), we have entered a new era of greenhouse gas (GHG) data collection where sub-city scale data can be collected at varying times across the entire globe. An increasing focus on quantifying urban emissions of GHGs from policy makers has begun to spur new research into how best to use this unique and very high resolution data set. While, historically, this line of research has been the domain of limited domain mesoscale and regional models, an increasing understanding and respect for boundary inflow uncertainty and bias has led people to search for an alternative modeling framework that both characterizes high frequency variability of CO2 in space and time as well as honor mass conservation requirements globally and be seamless with respect to boundaries. To monitor local anthropogenic emissions from space, the influence of atmospheric signals originating from outside the local area of interest needs to be quantified. In our first step towards building a comprehensive multi-scale CO2 inversion system, we use free running simulations of the Ocean Land Atmosphere Model (OLAM), a variable-resolution general circulation model, to explore the signal-to-noise statistics of anthropogenic urban emissions of CO2 versus the background inflow for approximately 40 of the largest cities across the globe. We show that signal-to-noise levels are much better in winter time than summer but also that the winter biological inflow is far from negligible, suggesting that the commonly held assumption that biology can be ignored in winter time urban emission estimates is probably incorrect. Simulated pressure-weighted column average CO2 (XCO2) is also used to evaluate the ability of fixed location XCO2 measurements to provide background inflow estimates. Results show why Los Angeles, a heavily instrumented and studied urban center, is likely one of the easiest cities to observe globally from space, despite its relatively complex meteorology. Lastly, we discuss challenges and possible research paths forward to continue to advance the notion of multi-scale global CO2 flux inversion systems capable of simultaneously optimizing local urban emissions and large-scale CO2 transport patterns.

Assessing Global Present‐Day Surface Mass Transport and Glacial Isostatic Adjustment From Inversion of Geodetic Observations

AbstractLong‐term monitoring of global mass transport within the Earth system improves our ability to mitigate natural hazards and better understand their relations to climate change. Satellite gravity is widely used to monitor surface mass variations for its unprecedented spatial and temporal coverage. However, the gravity data contain signals from visco‐elastic deformation in response to past ice sheet melting, preventing us from extracting signals of present‐day surface mass trend (PDMT) directly. Here we present a global inversion scheme that separates PDMT and visco‐elastic glacial isostatic adjustment (GIA) signatures by combining satellite gravimetry with satellite altimetry and ground observations. Our inversion provides global dual data coverage that enables a robust separation of PDMT and GIA spherical harmonic coefficients. It has the advantage of providing estimates of Earth's long wavelength deformation signatures and their uncertainties. Our GIA result, along with its uncertainty estimates, can be used in future GRACE processing to better assess the impact of GIA on surface mass change. Our GIA estimates include a rapid GIA uplift in the Southeast Alaska and the Amundsen Sea Embayment, due to the visco‐elastic response to recent glacial unloading. We estimate the average surface mass change rate from 2002–2010 to be −203 ± 3 GT·a−1 in Greenland, −126 ± 18 GT·a−1 in Antarctica and, −62 ± 5 GT·a−1 in Alaska. The GIA low degree spherical harmonic coefficients are sensitive to rheological properties in Earth's deep interior. Our low‐degree GIA estimates include geocenter motion and which provide unique constraints to understand Earth's lower mantle and ice history.

Valley filtering in strain-induced α−T3 quantum dots

We test the valley-filtering capabilities of a quantum dot inscribed by locally straining an $\alpha$-$\mathcal{T}_3$ lattice. Specifically, we consider an out-of-plane Gaussian bump in the center of a four-terminal configuration and calculate the generated pseudomagnetic field having an opposite direction for electrons originating from different valleys, the resulting valley-polarized currents, and the conductance between the injector and collector situated opposite one another. Depending on the quantum dot's width and width-to-height ratio, we detect different transport regimes with and without valley filtering for both the $\alpha$-$\mathcal{T}_3$ and dice lattice structures. In addition, we analyze the essence of the conductance resonances with a high valley polarization in terms of related (pseudo-) Landau levels, the spatial distribution of the local density of states, and the local current densities. The observed local charge and current density patterns reflect the local inversion symmetry breaking by the strain, besides the global inversion symmetry breaking due to the scaling parameter $\alpha$. By this way we can also filter out different sublattices.

A new integrated geophysical-petrological global 3-D model of upper-mantle electrical conductivity validated by the Swarm M2 tidal magnetic field

SUMMARY A new global model of the present-day thermochemical state of the lithosphere and upper mantle based on global waveform inversion, satellite gravity and gradiometry measurements, surface elevation and heat flow data has been recently presented: WINTERC-G (Fullea et al. 2021). WINTERC-G is built within an integrated geophysical-petrological framework where the mantle seismic velocity and density fields are computed in a thermodynamically self-consistent framework, allowing for a direct parametrization in terms of the temperature, pressure and composition of the subsurface rocks. In this paper, we combine WINTERC-G thermal and compositional fields along with laboratory experiments constraining the electrical conductivity of mantle minerals, melt and water, and derive a set of new global three dimensional electrical conductivity models of the upper mantle. The new conductivity models, WINTERC-e, consist of two end-members corresponding to minimum and maximum conductivity of the in situ rock aggregate accounting for mantle melting, mineral water content and the individual conductivities of the main stable mantle mineral phases. The end-member models are validated over oceans by simulating the magnetic field induced by the ocean M2 tidal currents and comparing the predicted fields with the M2 tidal magnetic field estimated from 6-yr Swarm satellite observations. Our new conductivity model, derived independently from any surface or satellite magnetic data sets, is however able to predict tidal magnetic fields that are in good agreement with the Swarm M2 tidal magnetic field models estimated by Sabaka et al. and Grayver & Olsen. Our predicted M2 tidal magnetic fields differ in amplitudes by about 5–20 per cent from the Swarm M2 tidal magnetic field, with the high conductivity WINTERC-e end-member model accounting for mantle melt and water content capturing the structure of Swarm data better than the low conductivity end-member model. Spherically symmetric conductivity models derived by averaging new WINTERC-e conductivities over oceanic areas are slightly more conductive than the recent global conductivity models AA17 by Grayver et al. derived from Swarm and CHAMP satellite data in the 60–140 km depth range, while they are less conductive deeper in the mantle. The conductivities in WINTERC-e are about three to four times smaller than the AA17 conductivities at a depth of 400 km. Despite the differences in electrical conductivity, our spherically symmetric high conductivity end-member model WINTERC-e captures the structure of Swarm M2 tidal magnetic field almost the same as a state of the art 1-D conductivity models derived entirely from magnetic data (AA17, Grayver et al.). Moreover, we show that realistic lateral electrical conductivity inhomogeneities of the oceanic upper mantle derived from the temperature, melt and water distributions in WINTERC-e contribute to the M2 tidal magnetic field up to ±0.3 nT at 430 km altitude.

Global methane budget and trend, 2010–2017: complementarity of inverse analyses using in situ (GLOBALVIEWplus CH<sub>4</sub> ObsPack) and satellite (GOSAT) observations

Abstract. We use satellite (GOSAT) and in situ (GLOBALVIEWplus CH4 ObsPack) observations of atmospheric methane in a joint global inversion of methane sources, sinks, and trends for the 2010–2017 period. The inversion is done by analytical solution to the Bayesian optimization problem, yielding closed-form estimates of information content to assess the consistency and complementarity (or redundancy) of the satellite and in situ data sets. We find that GOSAT and in situ observations are to a large extent complementary, with GOSAT providing a stronger overall constraint on the global methane distributions, but in situ observations being more important for northern midlatitudes and for relaxing global error correlations between methane emissions and the main methane sink (oxidation by OH radicals). The in-situ-only and the GOSAT-only inversions alone achieve 113 and 212 respective independent pieces of information (DOFS) for quantifying mean 2010–2017 anthropogenic emissions on 1009 global model grid elements, and respective DOFS of 67 and 122 for 2010–2017 emission trends. The joint GOSAT+ in situ inversion achieves DOFS of 262 and 161 for mean emissions and trends, respectively. Thus, the in situ data increase the global information content from the GOSAT-only inversion by 20 %–30 %. The in-situ-only and GOSAT-only inversions show consistent corrections to regional methane emissions but are less consistent in optimizing the global methane budget. The joint inversion finds that oil and gas emissions in the US and Canada are underestimated relative to the values reported by these countries to the United Nations Framework Convention on Climate Change (UNFCCC) and used here as prior estimates, whereas coal emissions in China are overestimated. Wetland emissions in North America are much lower than in the mean WetCHARTs inventory used as a prior estimate. Oil and gas emissions in the US increase over the 2010–2017 period but decrease in Canada and Europe. The joint inversion yields a global methane emission of 551 Tg a−1 averaged over 2010–2017 and a methane lifetime of 11.2 years against oxidation by tropospheric OH (86 % of the methane sink).

Characterization of carbonate reservoir using post-stack global geostatistical acoustic inversion approach: A case study from a mature gas field, onshore Pakistan

Seismic characterization of carbonate reservoir is a challenging undertaking for geo-scientists due to their complex depositional settings, internal structure, and pervasive diagenetic history. Results from post-stack deterministic inversion are band limited due to missing low and high frequencies in the wavelet, which generally poorly resolve thin beds which are of prime interest in reservoir characterization of a mature gas field and help locate prolific infill drilling locations. In this paper, we employed and compare performance of Post-stack Global Geostatistical Acoustic Inversion (PGGAI) with the Post-stack deterministic inversion to better characterize thin beds and maximize reservoir potential of Eocene (S1) carbonate reservoir from a mature gas field lying in the Middle Indus Basin, onshore Pakistan. We discovered that both the inversion methods derive a broad-band acoustic impedance from the band-limited post-stack seismic data. The results show that PGGAI produced high resolution (thin bedding) p-impedance attribute and mapped spatial distribution variations along with uncertainty quantification hitherto not possible from standard deterministic inversion approach and therefore result in possible increasing confidence in the interpretation. Furthermore, high resolution p-impedance attribute from PGGAI served as input for porosity prediction using probabilistic neural networking (PNN). Stepwise validation of PNN provided high precision porosity estimation which showed significant amount of correlation between the input attribute property. In addition, high resolution volumes offered optimistic scenarios of the distribution of impedance and porosity lateral extent and helpful in determining perspective zones and proved useful in designing the subsequent reservoir management plan and proposing future infill drilling locations.

Symmetry and control of spin-scattering processes in two-dimensional transition metal dichalcogenides

Transition metal dichalcogenides (TMDs) combine interesting optical and spintronic properties in an atomically thin material, where the light polarization can be used to control the spin and valley degrees of freedom for the development of novel optospintronic devices. These promising properties emerge due to their large spin-orbit coupling in combination with their crystal symmetries. Here, we provide simple symmetry arguments in a group-theory approach to unveil the symmetry-allowed spin-scattering mechanisms, and indicate how one can use these concepts towards an external control of the spin lifetime. We perform this analysis for both monolayer (inversion asymmetric) and bilayer (inversion symmetric) crystals, indicating the different mechanisms that play a role in these systems. We show that in monolayer TMDs, electrons and holes transform fundamentally differently----leading to distinct spin-scattering processes. We find that one of the electronic states in the conduction band is partially protected by time-reversal symmetry, indicating a longer spin lifetime for that state. In bilayer and bulk TMDs, a hidden spin polarization can exist within each layer despite the presence of global inversion symmetry. We show that this feature enables control of the interlayer spin-flipping scattering processes via an out-of-plane electric field, providing a mechanism for electrical control of the spin lifetime.

Inversion of IP-Affected TEM Responses and Its Application in High Polarization Area

The transient electromagnetic (TEM) responses measured in areas with highly polarizable media commonly show induced polarization (IP) effects, which poses difficulties to the TEM data interpretation and inversion with conventional methods. When present, the IP effects break the monotony in TEM decay curves and can even cause sign reversals, and lead to the singularity and non-monotony of inversion method. It is therefore important to take the IP effects into account when processing those TEM data. In this paper, a new inversion method is developed to invert TEM data with IP effects. The Cole-Cole model was introduced to the forward modeling solver so that the IP effects can be accurately calculated. The regularization terms were adapted to the objective function and a global optimization method, the particle swarm optimization algorithm, was used to solve the optimization problem, which weakened the singularity and non-monotony of the inversion greatly. Field data were collected in Wulong gold mine where IP effects were detected. The data were inverted using the method developed in this paper, and the inversion results were able to identify the depth extension of NO. 163 ore-bearing quartz veins and their associated fine-grained diorite veins. The global inversion method in this paper primarily solved the inversion problem of IP-affected TEM responses, and recovered the polarization parameters, which can be used as an aid to the geological interpretation.

Global Inversion of Grounded Electric Source Time-domain Electromagnetic Data Using Particle Swarm Optimization

Global optimization inversion of grounded wire time-domain electromagnetic (TDEM) data was implemented through application of the particle swarm optimization (PSO) algorithm. This probabilistic approach is an alternative to the widely used deterministic local-optimization approach. In the PSO algorithm, each particle that constitutes the swarm epitomizes a probable geophysical model comprised by subsurface resistivity values at several layers and layer thicknesses. The forward formulation of the TDEM problem for calculating the vertical component of the induced magnetic field is first expressed in the Laplace domain. Transformation of the magnetic field from the Laplace domain into the time domain is performed by applying the Gaver-Stehfest numerical method. The implementation of PSO inversion to the TDEM problem is straightforward. It only requires adjustment of a few inversion parameters such as inertia, acceleration coefficients and numbers of iteration and particles. The PSO inversion scheme was tested on synthetic noise-free data and noisy synthetic data as well as to field data recorded in a volcanic-geothermal area. The results suggest that the PSO inversion scheme can effectively solve the TDEM 1D stratified earth problem.

Chiral Spin Textures in Amorphous Iron-Germanium Thick Films.

Topological solitary fields, such as magnetic and polar skyrmions, are envisioned to revolutionize microelectronics. These configurations have been stabilized in solid-state materials with a global inversion symmetry breaking, which translates in magnetic materials into a vector spin exchange known as the Dzyaloshinskii-Moriya interaction (DMI), as well as spin chirality selection and isotropic solitons. This work reports experimental evidence of 3D chiral spin textures, such as helical spins and skyrmions with different chirality and topological charge, stabilized in amorphous Fe-Ge thick films. These results demonstrate that structurally and chemically disordered materials with a random DMI can resemble inversion symmetry broken systems with similar magnetic properties, moments, and states. Disordered systems are distinguished from systems with global inversion symmetry breaking by their degenerate spin chirality that allows for forming isotropic and anisotropic topological spin textures at remanence, while offering greater flexibility in materials synthesis, voltage, and strainmanipulation.

Global inversion for metrically regular mappings between Banach spaces

Global inversion for metrically regular mappings between Banach spaces

Concentrated Slip and Low Rupture Velocity for the May 20, 2012, MW 5.8, Po Plain (Northern Italy) Earthquake Revealed From the Analysis of Source Time Functions

AbstractWe analyse the rupture properties of the May 20, 2012, MW 5.8, Po Plain (Northern Italy) earthquake by using two different modeling procedures based on the source time functions: a forward modeling and a global inversion Bayesian method. While the forward modeling allows to retrieve general information on the source characteristics, the global inversion allows to explore a substantially larger number of possible solutions, with more parameters, providing a quantitative estimate of the misfit. We invert for the spatial slip distribution and for the rupture velocity on a planar fault model. The unknown slip is given at the nodes of the subfaults (control points) and then given at the elementary subfaults through a bilinear interpolation. The number of control points is progressively increased to move from a high‐ to low‐wavelength description of final slip on the fault plane. The optimal model parameter set is chosen according to the Akaike Information Criterion. The uncertainty on the slip distribution and rupture velocity has been estimated by a statistical analysis of the model ensemble and, in particular, through the weighted mean model and the standard deviation. We find that the most earthquake slip occurred in the regions located northeast and southwest of the hypocenter, consistent with the forward modeling. Moreover, we find a low rupture propagation velocity (0.4 compressional Mach number) similarly to what has been observed for the close 29 May, MW 5.6, and radiation efficiency suggesting that half of the strain energy was used to create new fracture.

On Global Solvability of Nonlinear Equations with Parameters

We consider smooth mappings acting from one Banach space to another and depending on a parameter belonging to a topological space. Under various regularity assumptions, sufficient conditions for the existence of global and semilocal continuous inverse and implicit functions are obtained. We consider applications of these results to the problem of continuous extension of implicit functions and to the problem of coincidence points of smooth and continuous compact mappings.

Pulmonary Embolism and Global T-Wave Inversion as the Concomitant Presentation of IgA Vasculitis

Pulmonary Embolism and Global T-Wave Inversion as the Concomitant Presentation of IgA Vasculitis

NQR and NMR spectra in the odd-parity multipole material CeCoSi

We theoretically study NQR and NMR spectra in the presence of odd-parity multipoles originating from staggered antiferromagnetic and antiferroquadrupole orderings. For the $f$-electron metal, CeCoSi, which is a candidate hosting odd-parity multipoles, we derive an effective hyperfine field acting on Co nucleus generated from electronic origin multipole moments at Ce ion under zero and nonzero magnetic fields. We elucidate that emergent odd-parity multipoles give rise to sublattice-dependent spectral splittings in NQR and NMR through the effective hyperfine coupling in the absence of the global inversion symmetry. We mainly examine behaviors of the NQR and NMR spectra in three odd-parity multipole ordered states: a $y$-type magnetic toroidal dipole order with a staggered $x$-type antiferromagnetic structure, an $xy$-type electric toroidal quadrupole order with a staggered $x^2-y^2$-type antiferroquadrupole structure, and a $z$-type electric dipole order with a staggered $3z^2-r^2$-type antiferroquadrupole structure. We show that different odd-parity multipole orders lead to different field-dependent spectral splittings in NMR, while only the $xy$-type electric toroidal quadrupole order exhibits the NQR spectral splitting. We also present possible sublattice-dependent spectral splittings for all the odd-parity multipole orders potentially activated in low-energy crystal-field levels, which will be useful to identify odd-parity order parameters in CeCoSi by NQR and NMR measurements.