Survey Geometry Research Articles

Anisotropic effective redshift and evolving clustering amplitude

A typical galaxy survey geometry results in galaxy pairs of different separation and angle to the line-of-sight having different distributions in redshift and consequently a different effective redshift. However, clustering measurements are analysed assuming that the clustering is representative of that at a single effective redshift. We investigate the impact of variations in the galaxy-pair effective redshift on the large-scale clustering measured in galaxy surveys. We find that galaxy surveys spanning a large redshift range have different effective redshifts as a function of both pair separation and angle. Furthermore, when considering tracers whose clustering amplitude evolves strongly with redshift, this combination can result in an additional scale-dependent clustering anisotropy. We demonstrate the size of this effect on the eBOSS DR16 Quasar sample and show that, while the impact on monopole is negligible, neglecting this effect can result in a tilt of ∼ 4% and ∼40% in quadrupole and hexadecapole, respectively, on scales ∼1 h -1Gpc. We discuss strategies to mitigate this effect when making measurements.

Cosmic Flow Measurement and Mock Sampling Algorithm of Cosmicflows-4 Tully−Fisher Catalog

Abstract Measurements of cosmic flows enable us to test whether cosmological models can accurately describe the evolution of the density field in the nearby universe. In this paper, we measure the low-order kinematic moments of the cosmic flow field, namely bulk flow and shear moments, using the Cosmicflows-4 Tully−Fisher catalog (CF4TF). To make accurate cosmological inferences with the CF4TF sample, it is important to make realistic mock catalogs. We present the mock sampling algorithm of CF4TF. These mocks can accurately realize the survey geometry and luminosity selection function, enabling researchers to explore how these systematics affect the measurements. These mocks can also be further used to estimate the covariance matrix and errors of the power spectrum and two-point correlation function in future work. In this paper, we use the mocks to test the cosmic flow estimator and find that the measurements are unbiased. The measured bulk flow in the local universe is 376 ± 23 (error) ± 183 (cosmic variance) km s−1 at depth d MLE = 35 Mpc h −1, to the Galactic direction of (l, b) = (298° ± 3°, −6° ± 3°). Both the measured bulk and shear moments are consistent with the concordance Λ Cold Dark Matter cosmological model predictions.

Encore: an O (Ng2) estimator for galaxy N-point correlation functions

ABSTRACT We present a new algorithm for efficiently computing the N-point correlation functions (NPCFs) of a 3D density field for arbitrary N. This can be applied both to a discrete spectroscopic galaxy survey and a continuous field. By expanding the statistics in a separable basis of isotropic functions built from spherical harmonics, the NPCFs can be estimated by counting pairs of particles in space, leading to an algorithm with complexity $\mathcal {O}(N_\mathrm{g}^2)$ for Ng particles, or $\mathcal {O}(N_\mathrm{FFT}\log N_\mathrm{FFT})$ when using a Fast Fourier Transform with NFFT grid-points. In practice, the rate-limiting step for N > 3 will often be the summation of the histogrammed spherical harmonic coefficients, particularly if the number of radial and angular bins is large. In this case, the algorithm scales linearly with Ng. The approach is implemented in the encore code, which can compute the 3PCF, 4PCF, 5PCF, and 6PCF of a BOSS-like galaxy survey in ${\sim}100$ CPU-hours, including the corrections necessary for non-uniform survey geometries. We discuss the implementation in depth, along with its GPU acceleration, and provide practical demonstration on realistic galaxy catalogues. Our approach can be straightforwardly applied to current and future data sets to unlock the potential of constraining cosmology from the higher point functions.

Dark Energy Survey year 3 results: covariance modelling and its impact on parameter estimation and quality of fit

ABSTRACT We describe and test the fiducial covariance matrix model for the combined two-point function analysis of the Dark Energy Survey Year 3 (DES-Y3) data set. Using a variety of new ansatzes for covariance modelling and testing, we validate the assumptions and approximations of this model. These include the assumption of Gaussian likelihood, the trispectrum contribution to the covariance, the impact of evaluating the model at a wrong set of parameters, the impact of masking and survey geometry, deviations from Poissonian shot noise, galaxy weighting schemes, and other sub-dominant effects. We find that our covariance model is robust and that its approximations have little impact on goodness of fit and parameter estimation. The largest impact on best-fitting figure-of-merit arises from the so-called fsky approximation for dealing with finite survey area, which on average increases the χ2 between maximum posterior model and measurement by $3.7{{\ \rm per\ cent}}$ (Δχ2 ≈ 18.9). Standard methods to go beyond this approximation fail for DES-Y3, but we derive an approximate scheme to deal with these features. For parameter estimation, our ignorance of the exact parameters at which to evaluate our covariance model causes the dominant effect. We find that it increases the scatter of maximum posterior values for Ωm and σ8 by about $3{{\ \rm per\ cent}}$ and for the dark energy equation-of-state parameter by about $5{{\ \rm per\ cent}}$.

Evaluation of three approaches for simulating 3-D time-domain electromagnetic data

SUMMARY We implemented and compared the implicit Euler time-stepping approach, the inverse Fourier transform-based approach and the Rational Arnoldi method for simulating 3-D transient electromagnetic data. We utilize the finite-element method with unstructured tetrahedral meshes for the spatial discretization supporting irregular survey geometries and anisotropic material parameters. Both, switch-on and switch-off current waveforms, can be used in combination with direct current solutions of Poisson problems as initial conditions. Moreover, we address important topics such as the incorporation of source currents and opportunities to simulate impulse as well as step response magnetic field data with all approaches for supporting a great variety of applications. Three examples ranging from simple to complex real-world geometries and validations against external codes provide insight into the numerical accuracy, computational performance and unique characteristics of the three applied methods. We further present an application of logarithmic Fourier transforms to convert transient data into the frequency domain. We made all approaches available in the open-source Python toolbox custEM, which previously supported only frequency-domain electromagnetic data. The object-oriented software implementation is suited for further elaboration on distinct modelling topics and the presented examples can serve for benchmarking other codes.

Does jackknife scale really matter for accurate large-scale structure covariances?

ABSTRACT The jackknife method gives an internal covariance estimate for large-scale structure surveys and allows model-independent errors on cosmological parameters. Using the SDSS-III BOSS CMASS sample, we study how the jackknife size and number of resamplings impact the precision of the covariance estimate on the correlation function multipoles and the error on the inferred baryon acoustic scale. We compare the measurement with the MultiDark Patchy mock galaxy catalogues, and we also validate it against a set of lognormal mocks with the same survey geometry. We build several jackknife configurations that vary in size and number of resamplings. We introduce the Hartlap factor in the covariance estimate that depends on the number of jackknife resamplings. We also find that it is useful to apply the tapering scheme to estimate the precision matrix from a limited number of resamplings. The results from CMASS and mock catalogues show that the error estimate of the baryon acoustic scale does not depend on the jackknife scale. For the shift parameter α, we find an average error of 1.6 per cent, 2.2 per cent and 1.2 per cent, respectively, from CMASS, Patchy, and lognormal jackknife covariances. Despite these uncertainties fluctuate significantly due to some structural limitations of the jackknife method, our α estimates are in reasonable agreement with published pre-reconstruction analyses. Jackknife methods will provide valuable and complementary covariance estimates for future large-scale structure surveys.

Practical data acquisition strategy for time-lapse experiments using crosshole GPR and full-waveform inversion

Crosshole ground penetrating radar (GPR) methods are increasingly used in time-lapse studies of flow in the uppermost near subsurface with important implications for our understanding of e.g., water infiltration in the unsaturated zone, and fluid flow in the saturated zone. A particular challenge in such time-lapse crosshole studies is the trade-off between collecting sufficient data to be able to resolve how a tracer moves, and, minimizing the data acquisition time such that the data approximates a static state. We test how dense recording geometries are needed for resolving a gas bubble injected in a highly heterogeneous chalk reservoir analogue using a full-waveform inversion (FWI) approach for modelling the crosshole GPR data. We show that even relatively sparse geometries provide sufficient resolution of the permittivity contrast caused by the gas bubble, provided that the detailed background permittivity structure is known from prior (before gas injection) FWI analysis of densely recorded high-resolution data. The conductivity contrast caused by the gas is more challenging to recover and the resolution suffers to a higher degree when reducing the survey geometry or at higher noise levels. As long as the permittivity change during the time-lapse experiment is the main target, a significant reduction in acquisition time is therefore possible as compared to the time needed to record the background permittivity structure. This reduced acquisition time has important practical implications for time-lapse experiments under realistic conditions. Our results are based on synthetic analysis based on a realistic subsurface scenario closely linked to characterization of heterogeneous chalk reservoirs. However, our findings also have important implications for planning of future time-lapse studies in other settings.

Constraining M ν with the bispectrum. Part II. The information content of the galaxy bispectrum monopole

Massive neutrinos suppress the growth of structure on small scales and leave an imprint on large-scale structure that can be measured to constrain their total mass, M ν. With standard analyses of two-point clustering statistics, M ν constraints are severely limited by parameter degeneracies. Ref. [1] demonstrated that the bispectrum, the next higher-order statistic, can break these degeneracies and dramatically improve constraints on M ν and other cosmological parameters. In this paper, we present the constraining power of the redshift-space galaxy bispectrum monopole, Bg 0. We construct the Molino suite of 75,000 mock galaxy catalogs from the Quijote N-body simulations using the halo occupation distribution (HOD) model, which provides a galaxy bias framework well-suited for simulation-based approaches. Using these mocks, we present Fisher matrix forecasts for {Ωm, Ωb, h, ns , σ8, M ν} and quantify, for the first time, the information content of the Bg 0 down to nonlinear scales. For k max = 0.5 h/Mpc, Bg 0 improves constraints on Ωm, Ωb, h, ns , σ8, and M ν by 2.8, 3.1, 3.8, 4.2, 4.2, and 4.6× over the power spectrum, after marginalizing over HOD parameters. Even with priors from Planck, Bg 0 improves all of the cosmological constraints by ≳ 2×. In fact, for Pg 0+Pg 2 and Bg 0 out to k max = 0.5 h/Mpc with Planck priors, we achieve a 1σ M ν constraint of 0.048 eV, which is tighter than the current best cosmological constraint. While effects such as survey geometry and assembly bias will have an impact, these constraints are derived for (1 h-1 Gpc)3, a substantially smaller volume than upcoming surveys. Therefore, we conclude that the galaxy bispectrum will significantly improve cosmological constraints for upcoming galaxy surveys — especially for M ν.

Cosmic shear power spectra in practice

Cosmic shear is one of the most powerful probes of Dark Energy, targeted by several current and future galaxy surveys. Lensing shear, however, is only sampled at the positions of galaxies with measured shapes in the catalog, making its associated sky window function one of the most complicated amongst all projected cosmological probes of inhomogeneities, as well as giving rise to inhomogeneous noise. Partly for this reason, cosmic shear analyses have been mostly carried out in real-space, making use of correlation functions, as opposed to Fourier-space power spectra. Since the use of power spectra can yield complementary information and has numerical advantages over real-space pipelines, it is important to develop a complete formalism describing the standard unbiased power spectrum estimators as well as their associated uncertainties. Building on previous work, this paper contains a study of the main complications associated with estimating and interpreting shear power spectra, and presents fast and accurate methods to estimate two key quantities needed for their practical usage: the noise bias and the Gaussian covariance matrix, fully accounting for survey geometry, with some of these results also applicable to other cosmological probes. We demonstrate the performance of these methods by applying them to the latest public data releases of the Hyper Suprime-Cam and the Dark Energy Survey collaborations, quantifying the presence of systematics in our measurements and the validity of the covariance matrix estimate. We make the resulting power spectra, covariance matrices, null tests and all associated data necessary for a full cosmological analysis publicly available.

Fast analytical calculation of the random pair counts for realistic survey geometry

Galaxy clustering is a standard cosmological probe that is commonly analysed through two-point statistics. In observations, the estimation of the two-point correlation function crucially relies on counting pairs in a random catalogue. The latter contains a large number of randomly distributed points, which accounts for the survey window function. Random pair counts can also be advantageously used for modelling the window function in the observed power spectrum. Since pair counting scales as 𝒪(N2), where N is the number of points, the computational time to measure random pair counts can be very expensive for large surveys. In this work, we present an alternative approach for estimating those counts that does not rely on the use of a random catalogue. We derived an analytical expression for the anisotropic random-random pair counts that accounts for the galaxy radial distance distribution, survey geometry, and possible galaxy weights. We show that a prerequisite is the estimation of the two-point correlation function of the angular selection function, which can be obtained efficiently using pixelated angular maps. Considering the cases of the VIPERS and SDSS-BOSS redshift surveys, we find that the analytical calculation is in excellent agreement with the pair counts obtained from random catalogues. The main advantage of this approach is that the primary calculation only takes a few minutes on a single CPU and it does not depend on the number of random points. Furthermore, it allows for an accuracy on the monopole equivalent to what we would otherwise obtain when using a random catalogue with about 1500 times more points than in the data at hand. We also describe and test an approximate expression for data-random pair counts that is less accurate than for random-random counts, but still provides subpercent accuracy on the monopole. The presented formalism should be very useful in accounting for the window function in next-generation surveys, which will necessitate accurate two-point window function estimates over huge observed cosmological volumes.

KiDS-1000 methodology: Modelling and inference for joint weak gravitational lensing and spectroscopic galaxy clustering analysis

We present the methodology for a joint cosmological analysis of weak gravitational lensing from the fourth data release of the ESO Kilo-Degree Survey (KiDS-1000) and galaxy clustering from the partially overlapping Baryon Oscillation Spectroscopic Survey (BOSS) and the 2-degree Field Lensing Survey (2dFLenS). Cross-correlations between BOSS and 2dFLenS galaxy positions and source galaxy ellipticities have been incorporated into the analysis, necessitating the development of a hybrid model of non-linear scales that blends perturbative and non-perturbative approaches, and an assessment of signal contributions by astrophysical effects. All weak lensing signals were measured consistently via Fourier-space statistics that are insensitive to the survey mask and display low levels of mode mixing. The calibration of photometric redshift distributions and multiplicative gravitational shear bias has been updated, and a more complete tally of residual calibration uncertainties was propagated into the likelihood. A dedicated suite of more than 20 000 mocks was used to assess the performance of covariance models and to quantify the impact of survey geometry and spatial variations of survey depth on signals and their errors. The sampling distributions for the likelihood and the χ2 goodness-of-fit statistic have been validated, with proposed changes for calculating the effective number of degrees of freedom. The prior volume was explicitly mapped, and a more conservative, wide top-hat prior on the key structure growth parameter S8 = σ8 (Ωm/0.3)1/2 was introduced. The prevalent custom of reporting S8 weak lensing constraints via point estimates derived from its marginal posterior is highlighted to be easily misinterpreted as yielding systematically low values of S8, and an alternative estimator and associated credible interval are proposed. Known systematic effects pertaining to weak lensing modelling and inference are shown to bias S8 by no more than 0.1 standard deviations, with the caveat that no conclusive validation data exist for models of intrinsic galaxy alignments. Compared to the previous KiDS analyses, S8 constraints are expected to improve by 20% for weak lensing alone and by 29% for the joint analysis.

Observing relativistic features in large-scale structure surveys – I. Multipoles of the power spectrum

ABSTRACT Planned efforts to probe the largest observable distance scales in future cosmological surveys are motivated by a desire to detect relic correlations left over from inflation and the possibility of constraining novel gravitational phenomena beyond general relativity (GR). On such large scales, the usual Newtonian approaches to modelling summary statistics like the power spectrum and bispectrum are insufficient, and we must consider a fully relativistic and gauge-independent treatment of observables such as galaxy number counts in order to avoid subtle biases, e.g. in the determination of the fNL parameter.In this work, we present an initial application of an analysis pipeline capable of accurately modelling and recovering relativistic spectra and correlation functions. As a proof of concept, we focus on the non-zero dipole of the redshift-space power spectrum that arises in the cross-correlation of different mass bins of dark matter haloes, using strictly gauge-independent observable quantities evaluated on the past light cone of a fully relativistic N-body simulation in a redshift bin 1.7 ≤ z ≤ 2.9. We pay particular attention to the correct estimation of power spectrum multipoles, comparing different methods of accounting for complications such as the survey geometry (window function) and evolution/bias effects on the past light cone, and discuss how our results compare with previous attempts at extracting novel GR signatures from relativistic simulations.

The clustering of DESI-like luminous red galaxies using photometric redshifts

ABSTRACT We present measurements of the redshift-dependent clustering of a DESI-like luminous red galaxy (LRG) sample selected from the Legacy Survey imaging data set, and use the halo occupation distribution (HOD) framework to fit the clustering signal. The photometric LRG sample in this study contains 2.7 million objects over the redshift range of 0.4 < z < 0.9 over 5655 deg2. We have developed new photometric redshift (photo-z) estimates using the Legacy Survey DECam and WISE photometry, with σNMAD = 0.02 precision for LRGs. We compute the projected correlation function using new methods that maximize signal-to-noise ratio while incorporating redshift uncertainties. We present a novel algorithm for dividing irregular survey geometries into equal-area patches for jackknife resampling. For a five-parameter HOD model fit using the MultiDark halo catalogue, we find that there is little evolution in HOD parameters except at the highest redshifts. The inferred large-scale structure bias is largely consistent with constant clustering amplitude over time. In an appendix, we explore limitations of Markov chain Monte Carlo fitting using stochastic likelihood estimates resulting from applying HOD methods to N-body catalogues, and present a new technique for finding best-fitting parameters in this situation. Accompanying this paper, we have released the Photometric Redshifts for the Legacy Surveys catalogue of photo-z’s obtained by applying the methods used in this work to the full Legacy Survey Data Release 8 data set. This catalogue provides accurate photometric redshifts for objects with z < 21 over more than 16 000 deg2 of sky.

Galaxy power spectrum multipoles covariance in perturbation theory

We compute the covariance of the galaxy power spectrum multipoles in perturbation theory, including the effects of nonlinear evolution, nonlinear and nonlocal bias, radial redshift-space distortions, arbitrary survey window and shot noise. We rewrite the power spectrum FKP estimator in terms of the usual windowed galaxy fluctuations and the fluctuations in the number of galaxies inside the survey volume. We show that this leads to a stronger super-sample covariance than assumed in the literature and causes a substantial leakage of Gaussian information. We decompose the covariance matrix into several contributions that provide an insight into its behavior for different biased tracers. We show that for realistic surveys, the covariance of power spectrum multipoles is already dominated by shot noise and super survey mode coupling in the weakly non-linear regime. Both these effects can be accurately modeled analytically, making a perturbative treatment of the covariance very compelling. Our method allows for the covariance to be varied as a function of cosmology and bias parameters very efficiently, with survey geometry entering as fixed kernels that can be computed separately using fast fourier transforms (FFTs). We find excellent agreement between our analytic covariance and that estimated from BOSS DR12 Patchy mock catalogs in the whole range we tested, up to $k=0.6$ h/Mpc. This bodes well for application to future surveys such as DESI and Euclid. The CovaPT code that accompanies this paper is available at https://github.com/JayWadekar/CovaPT

New-generation simultaneous shooting sparse OBN survey and FWI delineate deep subsalt structures in the Greater Mars-Ursa area

The U.S. Gulf of Mexico (GoM) geology is well known for prolific structural hydrocarbon traps created by salt tectonics. In many areas, these structures lie below salt overhangs or thick canopies, requiring advanced seismic imaging to identify prospects and plan exploration wells. Ever-evolving geophysical technologies, such as 3D seismic, wide azimuth, multiwide azimuth, coil, and ocean-bottom node (OBN) acquisition designs, have unlocked the image for some of these structures over the past three decades. Recently, automatic velocity model building methods, particularly full-waveform inversion (FWI), introduced another step change in the subsalt image quality and refocused the acquisition methods on the need to acquire long-offset data. To make such a long-offset program affordable, a new survey geometry was set up with sparse OBN nodes and simultaneous shooting. The actual survey was acquired in 2019 and fully processed within 15 months from the end of the acquisition. Offsets up to 65 km were recorded, enabling FWI velocity updates down to 15 km depth. To provide the reader with a glimpse of the geologic insight that the new technology enabled, we report a few examples of deep geology revealed by this survey in a hydrocarbon- and seismic-data-rich area of the GoM — the Greater Mars-Ursa Basin.

Galaxy power spectrum in general relativity

We present the galaxy power spectrum in general relativity. Using a novel approach, we derive the galaxy power spectrum taking into account all the relativistic effects in observations. In particular, we show independently of survey geometry that relativistic effects yield no divergent terms (proportional to k−4Pm(k) or k−2Pm(k) on all scales) that would mimic the signal of primordial non-Gaussianity. This cancellation of such divergent terms is indeed expected from the equivalence principle, meaning that any perturbation acting as a uniform gravity on the scale of the experiment cannot be measured. We find that the unphysical infrared divergence obtained in previous calculations occurred only due to not considering all general relativistic contributions consistently. Despite the absence of divergent terms, general relativistic effects represented by non-divergent terms alter the galaxy power spectrum at large scales (smaller than the horizon scale). In our numerical computation of the full galaxy power spectrum, we show the deviations from the standard redshift-space power spectrum due to these non-divergent corrections. We conclude that, as relativistic effects significantly alter the galaxy power spectrum at k≲ keq, they need to be taken into account in the analysis of large-scale data.

Cosmological homogeneity scale estimates are dressed

We investigate number count statistics as measures for transition to homogeneity of the matter distribution in the Universe and analyse how such statistics might be 'dressed' by the assumed survey selection function. Since the estimated survey selection function—which ideally accounts for selection bias in the observed distribution—is partially degenerate with the estimated underlying distribution of galaxies, the ability to identify the correct survey selection function is of importance for obtaining reliable estimates for clustering statistics. Selection functions of existing galaxy catalogues are modelled from data to resemble the redshift distribution and mean density of the observed galaxies. Proposed estimates of the selection function for upcoming surveys in addition use the angular distribution of galaxies to generate the angular selection function instead of using angular completeness estimates. We argue that such modelling of the selection function could potentially underestimate the deviance from homogeneity at scales probed by existing catalogues. We investigate the impact of conventionally applied methods for estimation of the survey selection function on number count in sphere statistics in a toy model setting. The example density distribution is asymptotically homogeneous, while non-linear density fluctuations are present regionally. We find that density oscillations with period comparable to characteristic scales of the survey are suppressed when conventional estimates of the survey selection function are invoked, resulting in number count statistics that are biased towards homogeneity. For our concrete toy model with maximum density contrasts of 1 and period of the density oscillation comparable in size to the survey radius, we find that the homogeneity scale is underestimated by ∼ 40%, however this quantitative result is dependent on the model setup including the form of the simplistic density field considered and the survey geometry.

The completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: GLAM-QPM mock galaxy catalogues for the emission line galaxy sample

ABSTRACT We present 2000 mock galaxy catalogues for the analysis of baryon acoustic oscillations (BAOs) in the Emission Line Galaxy (ELG) sample of the extended Baryon Oscillation Spectroscopic Survey Data Release 16 (eBOSS DR16). Each mock catalogue has a number density of $6.7 \times 10^{-4} h^3 \rm Mpc^{-3}$, covering a redshift range from 0.6 to 1.1. The mocks are calibrated to small-scale eBOSS ELG clustering measurements at scales of $\lesssim 30\, h^{-1}$Mpc. The mock catalogues are generated using a combination of GaLAxy Mocks (GLAM) simulations and the quick particle-mesh (QPM) method. GLAM simulations are used to generate the density field, which is then assigned dark matter haloes using the QPM method. Haloes are populated with galaxies using a halo occupation distribution. The resulting mocks match the survey geometry and selection function of the data, and have slightly higher number density that allows room for systematic analysis. The large-scale clustering of mocks at the BAO scale is consistent with data and we present the correlation matrix of the mocks.

The cosmic web through the lens of graph entropy

ABSTRACT We explore the information theory entropy of a graph as a scalar to quantify the cosmic web. We find entropy values in the range between 1.5 and 3.2 bits. We argue that this entropy can be used as a discrete analogue of scalars used to quantify the connectivity in continuous density fields. After showing that the entropy clearly distinguishes between clustred and random points, we use simulations to gauge the influence of survey geometry, cosmic variance, redshift space distortions, redshift evolution, cosmological parameters, and spatial number density. Cosmic variance shows the least important influence while changes from the survey geometry, redshift space distortions, cosmological parameters, and redshift evolution produce larger changes of the order of 10−2 bits. The largest influence on the graph entropy comes from changes in the number density of clustred points. As the number density decreases, and the cosmic web is less pronounced, the entropy can diminish up to 0.2 bits. The graph entropy is simple to compute and can be applied both to simulations and observational data from large galaxy redshift surveys; it is a new statistic that can be used in a complementary way to other kinds of topological or clustering measurements.

Full moment tensor inversion constrained by double-couple focal mechanism for induced seismicity*

In this study, we propose a new method to determine full moment tensor solution for induced seismicity. This method generalizes the full waveform matching algorithm we have developed to determine the double-couple (DC) focal mechanism based on the neighbourhood algorithm. One major difference between the new method and the former one is that we adopt a new misfit function to constrain the candidate moment tensor solutions with respect to a reference DC solution in addition to other misfit terms characterizing the waveform matching. Through synthetic tests using a real passive seismic survey geometry, the results show the new constraint can help better recover the DC components of inverted moment tensors. We further investigate how errors in the velocity model and source location affect the moment tensor solution. The synthetic test results indicate that the constrained inversion is robust in recovering both the DC and non-DC components. We also test the proposed method on several real induced events in an oil/gas field in Oman using the same observation system as synthetic tests. While it is found that the full moment tensor solutions without using the DC constraints have much larger non-DC components than solutions with the DC constraints, both solutions are able to fit the observed waveforms at similar levels. The synthetic and real test results suggest the proposed DC constrained inversion method can reliably retrieve full moment tensor solutions for the induced seismicity.