Accurate Waveform Research Articles

Waveforms and fluxes: Towards a self-consistent effective one body waveform model for nonprecessing, coalescing black-hole binaries for third generation detectors

We present a comprehensive comparison between numerical relativity (NR) angular momentum fluxes at infinity and the corresponding quantity entering the radiation reaction in TEOBResumS, an Effective-One-Body (EOB) waveform model for nonprecessing coalescing black hole binaries on quasi-circular orbits. This comparison prompted us to implement two changes in the model: (i) including Next-to-Quasi-Circular corrections in the $\ell=m$, $\ell\leq 5$ multipoles entering the radiation reaction and (ii) consequently updating the NR-informed spin-orbital sector of the model. This yields a new waveform model that presents a higher self-consistency between waveform and dynamics and an improved agreement with NR simulations. We test the model computing the EOB/NR unfaithfulness $\bar{F}_{\rm EOB/NR}$ over all 534 spin-aligned configurations available through the Simulating eXtreme Spacetime catalog, notably using the noise spectral density of Advanced LIGO, Einstein Telescope and Cosmic Explorer, for total mass up to $500M_\odot$. We find that the maximum unfaithfulness $\bar{F}^{\rm max}_{\rm EOB/NR}$ is mostly between $10^{-4}$ and $10^{-3}$, and the performance progressively worsens up to $\sim 5\times 10^{-3}$ as the effective spin of the system is increased. We perform similar analyses on the \SEOB{} model, that delivers $\bar{F}^{\rm max}_{\rm EOB/NR}$ values uniformly distributed versus effective spin and mostly between $10^{-3}$ and $10^{-2}$. We conclude that the improved TEOBResumS model already represents a reliable and robust first step towards the development of highly accurate waveform templates for third generation detectors.

Releasing the Time Step Upper Bound of CFL Stability Condition for the Acoustic Wave Simulation With Model-Order Reduction

The maximum time step size for the explicit finite-difference scheme complies with the Courant–Friedrichs–Lewy (CFL) stability condition, which essentially restricts the optimization and tuning of the communication-intensive massive seismic wave simulation in a parallel manner. This study brings forward the model-order reduction (MOR) method to simulate acoustic wave propagation. It briefly takes advantage of the update matrix’s eigenvalues and the expansion coefficients of the variables for the time in the semi-discrete scheme of the wave equation, reducing the computational complexity and enhancing its computing efficiency. Moreover, we introduced the eigenvalue abandonment and eigenvalue perturbation methods to stabilize the unstable oscillations when the time step size breaks the CFL stability upper bound. We then introduced the time-dispersion transform method to eliminate the time-dispersion error caused by the large time step and secure the high accuracy. Numerical experiments exhibit that the MOR method, in conjunction with eigenvalue abandonment (and the eigenvalue perturbation) and the time-dispersion transform method, can capture highly accurate waveforms even when the time step size exceeds the CFL stability condition. The eigenvalue perturbation method is suitable for strongly heterogenous media and can maintain the numerical accuracy and stability even when the time step size is toward the upper bound of the Nyquist sampling.

Blind interpolation for multi-frequency blade tip timing signals

Blade tip timing (BTT) is a promising non-contact on-line monitoring technique for rotor blades. Although various analytical methods for BTT signals have been developed, their accuracy and stability still need to be improved for subsequent blade damage detection. This paper derives and validates a blind interpolation method for multi-frequency BTT signals (BIMF). It is an integration of two novel algorithms proposed by this paper: (1) the multi-band interpolation (MBI) algorithm breaks the single-band limitation of established interpolation methods, and is capable of accurate and stable spectrum identification and waveform reconstruction when the approximate frequency distribution is known; (2) the real signal-based multiple signal classification (RSMUSIC) algorithm provides reliable prior knowledge of frequency for MBI. Simulation results verify the accuracy of the proposed methods and the advantages of BIMF over the BTT-based compressed sensing algorithms. Experimental results also validate the accuracy and stability of BIMF in spectrum identification.

On the Robustness and Efficiency of the Plane-Wave-Enriched FEM with Variable q-Approach on the 2D Room Acoustics Problem

Partition of unity finite element method with plane wave enrichment (PW-FEM) uses a shape function with a set of plane waves propagating in various directions. For room acoustic simulations in a frequency domain, PW-FEM can be an efficient wave-based prediction method, but its practical applications and especially its robustness must be studied further. This study elucidates PW-FEM robustness via 2D real-scale office room problems including rib-type acoustic diffusers. We also demonstrate PW-FEM performance using a sparse direct solver and a high-order Gauss–Legendre rule with a recently developed rule for ascertaining the number of integration points against the classical linear and quadratic FEMs. Numerical experiments investigating mesh size and room geometrical complexity effects on the robustness of PW-FEM demonstrated that PW-FEM becomes more robust at wide bands when using a mesh in which the maximum element size maintains a comparable value to the wavelength of the upper-limit frequency. Moreover, PW-FEM becomes unstable with lower spatial resolution mesh, especially for rooms with complex shape. Comparisons of accuracies and computational costs of linear and quadratic FEM revealed that PW-FEM requires twice the computational time of the quadratic FEM with a mesh having spatial resolution of six elements per wavelength, but it is highly accurate at wide bands with lower memory and with markedly fewer degrees of freedom. As an additional benefit of PW-FEM, the impulse response waveform of quadratic FEM in a time domain was found to deteriorate over time, but the PW-FEM waveform can maintain accurate waveforms over a long time.

Cartesian Meshing Spherical Earth (CMSE): A Code Package to Incorporate the Spherical Earth in SPECFEM3D Cartesian Simulations

AbstractThe SPECFEM3D_Cartesian code package is widely used in simulating seismic wave propagation on local and regional scales due to its computational efficiency compared with the one-chunk version of the SPECFEM3D_Globe code. In SPECFEM3D_Cartesian, the built-in meshing tool maps a spherically curved cube to a rectangular cube using the Universal Transverse Mercator projection (UTM). Meanwhile, the geodetic east, north, and up directions are assigned as the local x–y–z directions. This causes coordinate orientation issues in simulating waveform propagation in regions larger than 6° × 6° or near the Earth’s polar regions. In this study, we introduce a new code package, named Cartesian Meshing Spherical Earth (CMSE), that can accurately mesh the 3D geometry of the Earth’s surface under the Cartesian coordinate frame, while retaining the geodetic directions. To benchmark our new package, we calculate the residual amplitude of the CMSE synthetics with respect to the reference synthetics calculated by SPECFEM3D_Globe. In the regional scale simulations with an area of 1300 km × 1300 km, we find a maximum of 5% amplitude residual for the SPECFEM3D_Cartesian synthetics using the mesh generated by the CMSE, much smaller than the maximum amplitude residual of 100% for the synthetics based on its built-in meshing tool. Therefore, our new meshing tool CMSE overcomes the limitations of the internal mesher used by SPECFEM3D_Cartesian and can be used for more accurate waveform simulations in larger regions beyond one UTM zone. Furthermore, CMSE can deal with regions at the south and north poles that cannot be handled by the UTM projection. Although other external code packages can be used to mesh the curvature of the Earth, the advantage of the CMSE code is that it is open-source, easy to use, and fully integrated with SPECFEM3D_Cartesian.

Intense, wideband optical waveform generation by self-balanced amplification of fiber electro-optical sideband modulation

We demonstrate a simple method to obtain accurate optical waveforms with a gigahertz-level programmable modulation bandwidth and a watt-level output power for wideband optical control of free atoms and molecules. Arbitrary amplitude and phase modulations are transferred from microwave to light with a low-power fiber electro-optical modulator. The sub-milliwatt optical sideband is co-amplified with the optical carrier in a power-balanced fashion through a tapered semiconductor amplifier (TSA). By automatically keeping TSA near saturation in a quasi-continuous manner, typical noise channels associated with pulsed high-gain amplifications are efficiently suppressed. As an example application, we demonstrate interleaved cooling and trapping of two rubidium isotopes with coherent nanosecond pulses.

Multichannel Interconnection Decomposition for Hyperspectral LiDAR Waveforms Detected From Over 500 m

The full-waveform hyperspectral light detection and ranging (FWHSL) data have been widely used in surface topography, vegetation detection, and 3-D urban terrain modeling, capable of revealing the spatial distribution of a target and more detailed spectral information in the vertical direction. However, the echo signals of a target would significantly vary between different spectral channels due to the reflectance characteristics and the uneven energy distribution of supercontinuum laser source. Especially, band channels with weak reflectance over a long distance would affect the extraction accuracy of waveform parameters, which are essential for retrieving the spatial and spectral information of targets. This article proposes a multichannel interconnection decomposition method to improve the extraction accuracy of distance and spectral information at each pulse using hyperspectral waveform data. Two experiments were conducted to verify the performance of long-distance detection of targets using FWHSL. The first experiment detected a standard whiteboard, a green leaf, and a yellow leaf at roughly 518 m. Results demonstrated a considerable improvement in ranging precision and spectral detection using the proposed method compared with using the optimal channel with the best data quality. The second experiment simultaneously detected two adjacent targets at a distance of approximately 518 m. Results presented clear superiority of adding waveform channels in terms of discovering overlapping components and retrieving accurate waveform parameters. The success rate of extracting two targets 60 cm apart was greatly increased from 47% to 73% through the multichannel interconnection waveform decomposition (MIWD) method.

Testing gravitational waveform models using angular momentum

The anticipated enhancements in detector sensitivity and the corresponding increase in the number of gravitational wave detections will make it possible to estimate parameters of compact binaries with greater accuracy assuming general relativity(GR), and also to carry out sharper tests of GR itself. Crucial to these procedures are accurate gravitational waveform models. The systematic errors of the models must stay below statistical errors to prevent biases in parameter estimation and to carry out meaningful tests of GR. Comparisons of the models against numerical relativity (NR) waveforms provide an excellent measure of systematic errors. A complementary approach is to use balance laws provided by Einstein's equations to measure faithfulness of a candidate waveform against exact GR. Each balance law focuses on a physical observable and measures the accuracy of the candidate waveform vis a vis that observable. Therefore, this analysis can provide new physical insights into sources of errors. In this paper we focus on the angular momentum balance law, using post-Newtonian theory to calculate the initial angular momentum, surrogate fits to obtain the remnant spin and waveforms from models to calculate the flux. The consistency check provided by the angular momentum balance law brings out the marked improvement in the passage from \texttt{IMRPhenomPv2} to \texttt{IMRPhenomXPHM} and from \texttt{SEOBNRv3} to \texttt{SEOBNRv4PHM} and shows that the most recent versions agree quite well with exact GR. For precessing systems, on the other hand, we find that there is room for further improvement, especially for the Phenom models.

Gravitational spin-orbit dynamics at the fifth-and-a-half post-Newtonian order

Accurate waveform models are crucial for gravitational-wave data analysis, and since spin has a significant effect on the binary dynamics, it is important to improve the spin description in these models. In this paper, we derive the spin-orbit (SO) coupling at the fifth-and-a-half post-Newtonian (5.5PN) order. The method we use splits the conservative dynamics into local and nonlocal-in-time parts, and then relates the local-in-time part to gravitational self-force results by exploiting the simple mass-ratio dependence of the post-Minkowskian expansion of the scattering angle. We calculate the nonlocal contribution to the 5.5PN SO dynamics to eighth order in the small-eccentricity expansion for bound orbits, and to leading order in the large-eccentricity expansion for unbound orbits. For the local contribution, we obtain all of the 5.5PN SO coefficients from first-order self-force results for the redshift and spin-precession invariants, except for one unknown that could be fixed in the future by second-order self-force results. However, by incorporating our 5.5PN results in the effective-one-body formalism and comparing its binding energy to numerical relativity, we find that the remaining unknown has a small effect on the SO dynamics, demonstrating an improvement in accuracy at that order.

Method for detecting highly eccentric binaries with a gravitational wave burst search

Detection of gravitational waves (GW) from highly eccentric binary black hole (BBH) systems can provide insight into their dynamics and formation. To date, all of the LIGO-Virgo BBH detections have been made using quasi-circular templates in their initial discovery. However, recent studies have found some of these systems to be compatible with high eccentricity in the LIGO band, $e_{10 \textrm{Hz}} > 0.1$, possibly pointing to a population of sources that are challenging to detect. Current low-latency search methods used with ground-based GW detector data are not well equipped to detect highly eccentric sources. Template-based, matched-filter searches require accurate eccentric waveform models that are computational expensive. Unmodeled burst searches are designed to detected localized excess power and are unable to identify multiple isolated bursts, as would originate from a single highly eccentric BBH. Therefore, we propose a signal-based prior that can be incorporated into an existing GW burst search to target highly eccentric BBHs. Our eccentric burst prior is based on the Newtonian burst model described by Loutrel & Yunes (2017). As a proof of concept, we test our method on simulated data and find that for intermediate SNR $\sim3-6$ signals using the eccentric burst prior more effectively localizes GW bursts when compared to a uniform prior.

Resonant self-force effects in extreme-mass-ratio binaries: A scalar model

Extreme-mass ratio inspirals (EMRIs), compact binaries with small mass ratios $\epsilon\ll 1$, will be important sources for low-frequency gravitational wave detectors. Almost all EMRIs will evolve through important transient orbital $r\theta$ resonances, which will enhance or diminish their gravitational wave flux, thereby affecting the phase evolution of the waveforms at $O(\epsilon^{1/2})$ relative to leading order. While modeling the local gravitational self-force (GSF) during resonances is essential for generating accurate EMRI waveforms, so far the full GSF has not been calculated for an $r\theta$-resonant orbit owing to computational demands of the problem. As a first step we employ a simpler model, calculating the scalar self-force (SSF) along $r\theta$-resonant geodesics in Kerr spacetime. We demonstrate two ways of calculating the $r\theta$-resonant SSF (and likely GSF), with one method leaving the radial and polar motions initially independent as if the geodesic is nonresonant. We illustrate results by calculating the SSF along geodesics defined by three $r\theta$-resonant ratios (1:3, 1:2, 2:3). We show how the SSF and averaged evolution of the orbital constants vary with the initial phase at which an EMRI enters resonance. We then use our SSF data to test a previously proposed integrability conjecture, which argues that conservative effects vanish at adiabatic order during resonances. We find prominent contributions from the conservative SSF to the secular evolution of the Carter constant, $\langle \dot{\mathcal{Q}}\rangle$, but these nonvanishing contributions are on the order of, or less than, the estimated uncertainties of our self-force results. The uncertainties come from residual, incomplete removal of the singular field in the regularization process. Higher order regularization parameters, once available, will allow definitive tests of the integrability conjecture.

Fast extreme-mass-ratio-inspiral waveforms: New tools for millihertz gravitational-wave data analysis

We present the FastEMRIWaveforms (FEW) package, a collection of tools to build and analyze extreme mass ratio inspiral (EMRI) waveforms. Here, we expand on the Physical Review Letter that introduced the first fast and accurate fully-relativistic EMRI waveform template model. We discuss the construction of the overall framework; constituent modules; and the general methods used to accelerate EMRI waveforms. Because the fully relativistic FEW model waveforms are for now limited to eccentric orbits in the Schwarzschild spacetime, we also introduce an improved Augmented Analytic Kludge (AAK) model that describes generic Kerr inspirals. Both waveform models can be accelerated using graphics processing unit (GPU) hardware. With the GPU-accelerated waveforms in hand, a variety of studies are performed including an analysis of EMRI mode content, template mismatch, and fully Bayesian Markov Chain Monte Carlo-based EMRI parameter estimation. We find relativistic EMRI waveform templates can be generated with fewer harmonic modes ($\sim10-100$) without biasing signal extraction. However, we show for the first time that extraction of a relativistic injection with semi-relativistic amplitudes can lead to strong bias and anomalous structure in the posterior distribution for certain regions of parameter space.

Accurate Deep CNN-Based Waveform Recognition for Intelligent Radar Systems

Nowadays radar systems have been facing with the disordered electromagnetic spectrum access and utilization in shared spectrum environments with radio communication systems. Numerous waveform recognition methods have been studied with feature engineering and conventional machine learning (ML) for intelligent radar systems, but they are critically challenged by practical problems of scalability and reliability. Deep learning (DL) with the ability to automatically learn the representational features is leveraged to handle the aforementioned obstacles effectively. In this work, we proposed a high-accurate waveform recognition method for intelligent radar systems by developing a novel residual-attention multiscale-accumulation convolutional network (RamNet). By deliberately incorporating the residual connection and attention connection in selective-feature improvement blocks, RamNet can enrich high-impact features without vanishing gradient. Moreover, a structural multiscale-accumulation connection is deployed to improve feature utilization by gathering the high-relevant features at multiple signal resolutions. Experimental results from exhaustive simulation demonstrate that RamNet recognizes waveform robustly under rigorous channel impairments and presents superior performance compared to traditional ML and state-of-the-art DL models.

Assessing the readiness of numerical relativity for LISA and 3G detectors

Future detectors such as LISA promise signal-to-noise ratios potentially in the thousands and data containing simultaneous signals. Accurate numerical relativity waveforms will be essential to maximize the science return. A question of interest to the broad gravitational wave community is: Are the numerical relativity codes ready to face this challenge? Towards answering this question, we provide a new criteria to identify the minimum resolution a simulation must have as a function of signal-to-noise ratio in order for the numerical relativity waveform to be indistinguishable from a true signal. This criteria can be applied to any finite-differencing numerical relativity code with multiple simulations of differing resolutions for the desired binary parameters and waveform length. We apply this criteria to binary systems of interest with the fourth-order MAYA code to obtain the first estimate of the minimum resolution a simulation must have to be prepared for next generation detectors.

A new tightly coupled method for high-rate seismogeodesy: a shake table experiment and application to the 2016 Mw 6.6 central Italy earthquake

SUMMARY High-rate global navigation satellite system (GNSS) has emerged as an effective method to recover seismic waveforms without saturation and drifts, but it has the limitation of relatively lower sampling rate and higher noise level compared to seismic instruments. In this study, we present a new seismogeodetic method by integrating GNSS and accelerometer data to obtain optimal real-time seismic waveforms. Unlike traditional integration methods based on GNSS techniques of relative positioning or precise point positioning, the new method uses a GNSS time difference technique and inherits its unique advantage in real-time and high-accuracy velocity solutions. Furthermore, by incorporating the tightly coupled structure, it can overcome the cascading problem and provide more accurate and robust waveforms compared to its loosely coupled counterpart. The performance of this method is first compared with the traditional loosely coupled approach in challenging environments through a set of shake table experiments. With three GNSS satellites, this approach method can improve the accuracy of velocities and displacements by 42 and 87 per cent, respectively. With four or more GNSS satellites, the average improvements of the method reach 25 and 41 per cent for the velocities and displacements, respectively. We then validate the full performances of the method through simulated shake table experiments and collocated GNSS and accelerometer data during the 2016 Mw 6.6 central Italy earthquake. The simulated and real-event analyses demonstrate that the new integration method can take full advantage of the complementary characteristics of GNSS and accelerometer sensors. By providing more accurate and broad-band velocity and displacement waveforms in a real-time or near-real-time manner, this method is quite promising in earthquake early warning and rapid source inversion.

Accurate LPI Radar Waveform Recognition With CWD-TFA for Deep Convolutional Network

Automotive radars, with a widespread emergence in the last decade, have faced various jamming attacks. Utilizing low probability of intercept (LPI) radar waveforms, as one of the essential solutions, demands an accurate waveform recognizer at the intercept receiver. Numerous conventional approaches have been studied for LPI radar waveform recognition, but their performance is inadequate under channel condition deterioration. In this letter, by exploiting deep learning (DL) to capture intrinsic radio characteristics, we propose a convolutional neural network (CNN), namely LPI-Net, for automatic radar waveform recognition. In particular, radar signals are first analyzed by a time-frequency analysis using the Choi-Williams distribution. Subsequently, LPI-Net, primarily consisting of three sophisticated modules, is built to learn the representational features of time-frequency images, in which each module is constructed with a preceding maps collection to gain feature diversity and a skip-connection to maintain informative identity. Simulation results show that LPI-Net achieves the 13-waveform recognition accuracy of over 98% at 0 dB SNR and further performs better than other deep models.

New public code for initial data of unequal-mass, spinning compact-object binaries

The construction of constraint-satisfying initial data is an essential element for the numerical exploration of the dynamics of compact-object binaries. While several codes have been developed over the years to compute generic quasi-equilibrium configurations of binaries comprising either two black holes, or two neutron stars, or a black hole and a neutron star, these codes are often not publicly available or they provide only a limited capability in terms of mass ratios and spins of the components in the binary. We here present a new open-source collection of spectral elliptic solvers that are capable of exploring the major parameter space of binary black holes (BBHs), binary neutron stars (BNSs), and mixed binaries of black holes and neutron stars (BHNSs). Particularly important is the ability of the spectral-solver library to handle neutron stars that are either irrotational or with an intrinsic spin angular momentum that is parallel to the orbital one. By supporting both analytic and tabulated equations of state at zero or finite temperature, the new infrastructure is particularly geared towards allowing for the construction of BHNS and BNS binaries. For the latter, we show that the new solvers are able to reach the most extreme corners in the physically plausible space of parameters, including extreme mass ratios and spin asymmetries, thus representing the most extreme BNS computed to date. Through a systematic series of examples, we demonstrate that the solvers are able to construct quasi-equilibrium and eccentricity-reduced initial data for BBHs, BNSs, and BHNSs, achieving spectral convergence in all cases. Furthermore, using such initial data, we have carried out evolutions of these systems from the inspiral to after the merger, obtaining evolutions with eccentricities $\lesssim 10^{-4}-10^{-3}$, and accurate gravitational waveforms.

Geometrized effective-one-body formalism for extreme-mass-ratio limits: Generic orbits

Compact objects inspiraling into supermassive black holes, known as extreme-mass-ratio inspirals, are an important source for future space-borne gravitational-wave detectors. When constructing waveform templates, usually the adiabatic approximation is employed to treat the compact object as a test particle for a short duration, and the radiation reaction is reflected in the changes of the constants of motion. However, the mass of the compact object should have contributions to the background. In the present paper, employing the effective-one-body formalism, we analytically calculate the trajectories of a compact object around a massive Kerr black hole with generally three-dimensional orbits and express the fundamental orbital frequencies in explicit forms. In addition, by constructing an approximate "constant" similar to the Carter constant, we transfer the dynamical quantities such as energy, angular momentum, and the "Carter constant" to the semilatus rectum, eccentricity, and orbital inclination with mass-ratio corrections. The linear mass-ratio terms in the formalism may not be sufficient for accurate waveforms, but our analytical method for solving the equations of motion could be useful in various approaches to building waveform models.

Identification of Lensed Gravitational Waves with Deep Learning

Abstract Similar to light, gravitational waves (GWs) can be lensed. Such lensing phenomena can magnify the waves, create multiple images observable as repeated events, and superpose several waveforms together, inducing potentially discernible patterns on the waves. In particular, when the lens is small, ≲105 M ⊙, it can produce lensed images with time delays shorter than the typical gravitational-wave signal length that conspire together to form “beating patterns.” We present a proof-of-principle study utilizing deep learning for identification of such a lensing signature. We bring the excellence of state-of-the-art deep learning models at recognizing foreground objects from background noise to identifying lensed GWs from noisy spectrograms. We assume the lens mass is around 103–105 M ⊙, which can produce time delays of the order of milliseconds between two images of lensed GWs. We discuss the feasibility of distinguishing lensed GWs from unlensed ones and estimating physical and lensing parameters. The suggested method may be of interest to the study of more complicated lensing configurations for which we do not have accurate waveform templates.

Testing general relativity with gravitational-wave catalogs: The insidious nature of waveform systematics

SummaryGravitational-wave observations of binary black holes allow new tests of general relativity (GR) to be performed on strong, dynamical gravitational fields. These tests require accurate waveform models of the gravitational-wave signal; otherwise waveform errors can erroneously suggest evidence for new physics. Existing waveforms are generally thought to be accurate enough for current observations, and each of the events observed to date appears to be individually consistent with GR. In the near future, with larger gravitational-wave catalogs, it will be possible to perform more stringent tests of gravity by analyzing large numbers of events together. However, there is a danger that waveform errors can accumulate among events: even if the waveform model is accurate enough for each individual event, it can still yield erroneous evidence for new physics when applied to a large catalog. This paper presents a simple linearized analysis, in the style of a Fisher matrix calculation that reveals the conditions under which the apparent evidence for new physics due to waveform errors grows as the catalog size increases. We estimate that, in the worst-case scenario, evidence for a deviation from GR might appear in some tests using a catalog containing as few as events above a signal-to-noise ratio of 20. This is close to the size of current catalogs and highlights the need for caution when performing these sorts of experiments.