Elastic Finite-difference Research Articles

Quality Control of DAS VSP Data in Desert Environment Using Simulations and Matching Filters.

The unconsolidated near surface and large, daily temperature variations in the desert environment degrade the vertical seismic profiling (VSP) data, posing the need for rigorous quality control. Distributed acoustic sensing (DAS) VSP data are often benchmarked using geophone surveys as a gold standard. This study showcases a new simulation-based way to assess the quality of DAS VSP acquired in the desert without geophone data. The depth uncertainty of the DAS channels in the wellbore is assessed by calibrating against formation depth based on the concept of conservation of the energy flux. Using the 1D velocity model derived from checkshot data, we simulate both DAS and geophone VSP data via an elastic pseudo-spectral finite difference method, and estimate the source and receiver signatures using matching filters. These field geophone data show high amplitude variations between channels that cannot be replicated in the simulation. In contrast, the DAS simulation shows a high visual similarity with the field DAS first arrival waveforms. The simulated source and receiver signatures are visually indistinguishable from the field DAS data in this study. Since under perfect conditions, the receiver signatures should be invariant with depth, we propose a new DAS data quality control metric based on local variations of the receiver signatures which does not require geophone measurements.

Effect of inconsistency of irradiation conditions of acoustic radiation force caused by tissue structure on shear wave velocity evaluation

Previous studies have shown that shear wave elastography of liver tissue can be unstable due to factors such as uncertainties in the acoustic radiation force (ARF) irradiation due to the influence of tissues near the surface and the complexity of the liver’s structure and its physical properties. This study aims to verify the influence of near-surface tissues on ARF and the effect of tissue structure on shear wave propagation and shear wave velocity (SWV) evaluation using wave propagation simulations by the elastic finite-difference time domain method. It is found that the ARF becomes weakly focused on multiple locations due to refraction of longitudinal waves by near-surface tissues, and multiple shear waves of small amplitude are propagated. However, a macroscopic SWV assessment, as in clinical practice, reduces the influence of near-surface tissues because the microscopic assessment results are averaged over the near-surface tissues.

Quantifying the Surface Strain Field Induced by Active Sources with Distributed Acoustic Sensing: Theory and Practice.

Quantitative dynamic strain measurements of the ground would be useful for engineering scale problems such as monitoring for natural hazards, soil-structure interaction studies, and non-invasive site investigation using full waveform inversion (FWI). Distributed acoustic sensing (DAS), a promising technology for these purposes, needs to be better understood in terms of its directional sensitivity, spatial position, and amplitude for application to engineering-scale problems. This study investigates whether the physical measurements made using DAS are consistent with the theoretical transfer function, reception patterns, and experimental measurements of ground strain made by geophones. Results show that DAS and geophone measurements are consistent in both phase and amplitude for broadband (10 s of Hz), high amplitude (10 s of microstrain), and complex wavefields originating from different positions around the array when: (1) the DAS channels and geophone locations are properly aligned, (2) the DAS cable provides good deformation coupling to the internal optical fiber, (3) the cable is coupled to the ground through direct burial and compaction, and (4) laser frequency drift is mitigated in the DAS measurements. The transfer function of DAS arrays is presented considering the gauge length, pulse shape, and cable design. The theoretical relationship between DAS-measured and pointwise strain for vertical and horizontal active sources is introduced using 3D elastic finite-difference simulations. The implications of using DAS strain measurements are discussed including directionality and magnitude differences between the actual and DAS-measured strain fields. Estimating measurement quality based on the wavelength-to-gauge length ratio for field data is demonstrated. A method for spatially aligning the DAS channels with the geophone locations at tolerances less than the spatial resolution of a DAS system is proposed.

Improving accuracy and efficiency in elastic finite difference modelling

Multicomponent technology has known to have a better imaging quality as compared to P-wave imaging. However, the cost of acquiring and processing the multicomponent data is more costly than P-wave imaging. Although P-wave imaging may have poorer imaging capability as compared to shear wave imaging, a good P-wave imaging can still be obtained if a good seismic modelling technique is used. Thus, this paper aims to enhance seismic modelling technique, in terms of accuracy, suppression of grid dispersion, and reduction in computation time. The finite difference (FD) technique is used as the modelling scheme, and the elastic modelling approach is used in this paper. The new method is applied on homogeneous model and synthetic data, and then compared to conventional FD modelling (4th order), higher order FD modelling (14th order), optimization of staggered grid coefficients such as least squares method and Wang & Liang’s method. The comparison will then be shown and discussed.

Tensorial elastodynamics for coupled acoustic/elastic anisotropic media: incorporating bathymetry

SUMMARYCorrectly implementing the fluid/solid boundary conditions at the seafloor is important for accurate full-wavefield imaging and inversion of marine seismic data. Because bathymetric profiles are rarely flat, the associated undulations influence wave modes interacting with the seafloor and, therefore, the ensuing imaging and inversion results. The conventional method of using single-domain elastic finite-difference (FD) solutions assumes that the fluid/solid contact is welded, which leads to incorrect handling of the boundary conditions and introduces modelling errors. We present a mimetic finite-difference (MFD) approach to solve the equations of anisotropic elastodynamics in a non-orthogonal coordinate system conformal to the bathymetric interface. The vertically deformed coordinate mapping transforms the irregular Cartesian (physical) domain into a regularly sampled generalized computational domain. We partition the medium into the acoustic and elastic subdomains and explicitly satisfy the fluid/solid boundary conditions with a split-node approach involving high-order one-sided MFD operators that achieve uniform spatial accuracy throughout the computational domain. Fully staggered grids (FSGs) are used to solve the velocity–pressure and velocity–stress formulations of the acoustic and anisotropic elastic wave equations, respectively. Numerical examples demonstrate that the proposed MFD+FSG algorithm accurately simulates wavefields even for strongly undulating bathymetric surfaces overlying structurally complex anisotropic media, and produces no spurious numerical artefacts (e.g. staircasing) or unphysical wave modes often caused by improper handling of the strong-contrast bathymetric interface. The wavefields generated by the tensorial MFD scheme closely match those from the more computationally expensive spectral-element method used to validate our implementation. The developed MFD+FSG technique can be effectively employed as the modelling kernel in a variety of coupled acoustic/elastic imaging and inversion applications.

Low-frequency ambient distributed acoustic sensing (DAS): case study from Perth, Australia

SUMMARYAmbient wavefield data acquired on existing (so-called ‘dark fibre’) optical fibre networks using distributed acoustic sensing (DAS) interrogators allow users to conduct a wide range of subsurface imaging and inversion experiments. In particular, recorded low-frequency (<2 Hz) surface-wave information holds the promise of providing constraints on the shear-wave velocity (VS) to depths exceeding 0.5 km. However, surface-wave analysis can be made challenging by a number of acquisition factors that affect the amplitudes of measured DAS waveforms. To illustrate these sensitivity challenges, we present a low-frequency ambient wavefield investigation using a DAS data set acquired on a crooked-line optical fibre array deployed in suburban Perth, Western Australia. We record storm-induced microseism energy generated at the nearby Indian Ocean shelf break and/or coastline in a low-frequency band (0.04−1.80 Hz) and generate high-quality virtual shot gathers (VSGs) through cross-correlation and cross-coherence interferometric analyses. The resulting VSG volumes clearly exhibit surface wave energy, though with significant along-line amplitude variations that are due to the combined effects of ambient source directivity, crooked-line acquisition geometry and the applied gauge length, fibre coupling, among other factors. We transform the observed VSGs into dispersion images using two different methods: phase shift and high-resolution linear Radon transform. These dispersion images are then used to estimate 1-D near-surface VS models using multichannel analysis of surface waves (MASW), which involves picking and inverting the estimated Rayleigh-wave dispersion curves using the particle-swarm optimization global optimization algorithm. The MASW inversion results, combined with nearby deep borehole information and 2-D elastic finite-difference modeling, show that low-frequency ambient DAS data constrain the VS model, including a low-velocity channel, to at least 0.5 km depth. Thus, this case study illustrates the potential of using DAS technology as a tool for undertaking large-scale surface wave analysis in urban geophysical and geotechnical investigations to depths exceeding 0.5 km.

Reduced memory implementation of a local elastic finite-difference solver

The recovery of elastic properties from seismic data often requires the iterative use of seismic modeling. Finite-difference (FD) simulation is a common component in seismic modeling, and it is usually the most computationally expensive step in methodologies such as inversion or reverse time migration. Local solvers attempt to reduce the cost of FD simulations by reducing the computational domain to small areas, updating the model within these areas without recomputing throughout the full domain. We have implemented a local elastic solver that allows us to propagate the elastic wavefield within a subvolume after local alterations of the model. We determine how the scattered wavefield due to the alterations can be extrapolated from the local domain to surface receivers. We extend existing works by using the method of multiple point sources to recompute the wavefield within the local domain. This method is memory efficient because it only requires the global wavefield to be recorded along the local domain boundary. By injecting these recordings as point sources, the global wavefield is emulated within the local domain. Thus, the method requires no modifications of standard FD solvers, merely the ability to record and inject data. We evaluate the capability of the local elastic solver to reconstruct the wavefield in a subvolume of the elastic SEAM model.

Anisotropic elastic finite-difference modeling of sources and receivers on Lebedev grids

The Lebedev grid finite-difference (FD) method allows modeling of anisotropic elastic-wave propagation. On Lebedev grids, erroneous point-source excitations can create spurious (nonphysical) waves. The only known remedy for such artifacts in the literature is the Lisitsa-Vishnevsky method. This method uses a distributed array to create point sources and point receivers on the FD grid. However, the Lisitsa-Vishnevsky method does not fully eliminate spurious artifacts. A novel approach is found in the FD-consistent point source, which suppresses spurious artifacts entirely. The method requires no array recording to create point receivers. The advantage of this method over the Lisitsa-Vishnevsky method is determined with two anisotropic modeling examples.

Mimetic finite-difference coupled-domain solver for anisotropic media

Accurately modeling full-wavefield solutions at and near the seafloor is challenging for conventional single-domain elastic finite-difference (FD) methods. Because they treat the fluid layer as a solid with zero shear-wave velocity, the energy partitioning for body and surface waves at the seafloor is distorted. This results in incorrect fluid/solid boundary conditions, which has significant implications for imaging and inversion applications that use amplitude information for model building. To address these issues, here we use mimetic FD (MFD) operators to develop and test a numerical approach for accurately implementing the boundary conditions at a fluid/solid interface. Instead of employing a single “global” model domain, we partition the full grid into two subdomains that represent the acoustic and elastic (possibly anisotropic) media. A novel split-node approach based on one-sided MFD operators is introduced to distribute grid points at the fluid/solid interface and satisfy the wave equation and the boundary conditions. Numerical examples demonstrate that such MFD operators achieve stable implementation of the boundary conditions with the same (fourth) order of spatial accuracy as that inside the split-domain interiors. We compare the wavefields produced by the MFD scheme with those from a more computationally expensive spectral-element method to validate our algorithm. The modeling results help analyze the events associated with the fluid/solid (seafloor) interface and provide valuable insights into the horizontal displacement or velocity components (e.g., recorded in ocean-bottom-node data sets). The developed MFD approach can be efficiently used in elastic anisotropic imaging and inversion applications involving ocean-bottom seismic data.

Anisotropic elastic finite-difference modeling of sources and receivers on Lebedev grids

Anisotropic elastic finite-difference modeling of sources and receivers on Lebedev grids

Cross-profile seismic data acquisition, imaging, and modeling of iron-oxide deposits: A case study from Blötberget, south-central Sweden

Two 2D reflection seismic profiles were acquired in Blötberget, south-central Sweden, for deep targeting and delineation of sheet-like iron-oxide deposits, known to dip toward the southeast and extend down to at least 0.8 km depth from core drilling observations. The two perpendicular profiles recorded shots at every receiver station along the main and cross profiles. To obtain more information on the lateral extent of the mineralized horizons, data from the two profiles, including the cross-profile records, were binned together in a 3D grid and further processed as a 3D data set. Processing results suggest that more information is retrieved when 3D processing is used and the mineralization lateral extent can be inferred for at least 0.3 km. The seismic response of the mineralization was further studied through forward reflection traveltime modeling, using a 3D ray-tracing approach; thus, the 3D geometry of several planar reflectors was validated. Additionally, 2D elastic finite-difference modeling work showed that the observed reflection pattern in the seismic data may originate from several mineralized horizons, suggesting potential resources in the footwall of the known deposits and large-scale geologic structures. The results encourage the use of seismic methods for direct delineation of mineral deposits even from 2D profiles and prompted a 3D survey in the area.

Amplitude variation with offset inversion using acoustic-elastic local solver

Conventional amplitude variation with offset (AVO) inversion analysis uses the Zoeppritz equations, which are based on a plane-wave approximation. However, because real seismic data are created by point sources, wave reflections are better modeled by spherical waves than by plane waves. Indeed, spherical reflection coefficients deviate from planar reflection coefficients near the critical and postcritical angles, which implies that the Zoeppritz equations are not applicable for angles close to critical reflection in AVO analysis. Elastic finite-difference simulations provide a solution to the limitations of the Zoeppritz approximation because they can handle near- and postcritical reflections. We have used a coupled acoustic-elastic local solver that approximates the wavefield with high accuracy within a locally perturbed elastic subdomain of the acoustic full domain. Using this acoustic-elastic local solver, the local wavefield generation and inversion are much faster than performing a full-domain elastic inversion. We use this technique to model wavefields and to demonstrate that the amplitude from within the local domain can be used as a constraint in the inversion to recover elastic material properties. Then, we focus on understanding how much the amplitude and phase contribute to the reconstruction accuracy of the elastic material parameters ([Formula: see text], [Formula: see text], and [Formula: see text]). Our results suggest that the combination of amplitude and phase in the inversion helps with the convergence. Finally, we analyze elastic parameter trade-offs in AVO inversion, from which we find that to recover accurate P-wave velocities we should invert for [Formula: see text] and [Formula: see text] simultaneously with fixed density.

Acoustic and elastic finite-difference modeling by optimal variable-length spatial operators

Time-space domain finite-difference modeling has always had the problem of spatial and temporal dispersion. High-order finite-difference methods are commonly used to suppress spatial dispersion. Recently developed time-dispersion transforms can effectively eliminate temporal dispersion from seismograms produced by the conventional modeling of high-order spatial and second-order temporal finite differences. To improve the efficiency of the conventional modeling, I have developed optimal variable-length spatial finite differences to efficiently compute spatial derivatives involved in acoustic and elastic wave equations. First, considering that temporal dispersion can be removed, I prove that minimizing the relative error of the phase velocity can be approximately implemented by minimizing that of the spatial dispersion. Considering that the latter minimization depends on the wavelength that is dependent on the velocity, in this sense, this minimization is indirectly related to the velocity, and thus leads to variation of the spatial finite-difference operator with velocity for a heterogeneous model. Second, I use the Remez exchange algorithm to obtain finite-difference coefficients with the lowest spatial dispersion error over the largest possible wavenumber range. Then, dispersion analysis indicates the validity of the approximation and the algorithm. Finally, I use modeling examples to determine that the optimal variable-length spatial finite difference can greatly increase the modeling efficiency, compared to the conventional fixed-length one. Stability analysis and modeling experiments also indicate that the variable-length finite difference can adopt a larger time step to perform stable modeling than the fixed-length one for inhomogeneous models.

Two-grid full-waveform Rayleigh-wave inversion via a genetic algorithm — Part 2: Application to two actual data sets

We have applied our two-grid genetic-algorithm Rayleigh-wave full-waveform inversion (FWI) to two actual data sets acquired in Luni (Italy) and Grenoble (France), respectively. Because our technique used 2D elastic finite-difference modeling for solving the forward problem, the observed data were 3D to 2D corrected prior to the inversion. To limit the computing time, both inversions focused on predicting low-resolution, smooth models by using quite coarse inversion grids. The wavelets for FWI were estimated directly from the observed data by using the Wiener method. In the Luni case, due to the strong dispersion effects on the data, to strengthen the inversion, envelopes and waveforms were considered in the objective function and an offset-marching strategy was applied. Though no a priori information was exploited, the outcomes of the Luni and Grenoble data inversion were fair. The predicted Luni [Formula: see text] model indicates a strong velocity increase from approximately 3 to 6 m, and velocity inversions have been detected at approximately 2 and 9 m depths. Analyzing the dispersion spectra, it results that the predicted Luni data reasonably reproduced the waveforms related to the fundamental mode and, likely, a small part of those related to the first higher mode. Concerning the Grenoble example, the predicted [Formula: see text] model coincides reasonably well with the long-wavelength structures presented in the [Formula: see text] profiles obtained from nearby boreholes. The data reconstruction is generally satisfactory, and when mismatches occur between the predicted and observed traces, the phase differences are always within half-periods. The fair inversion outcomes suggest that the predicted Luni and Grenoble models would likely be adequate initial models for local FWI, which could further increase the resolution and the details of the estimated [Formula: see text] models.

Stress-dependent permeability of coal fracture networks: A numerical study with Lattice Boltzmann method

Since coal permeability is sensitive to stress, fundamental understanding of gas flow in coal fracture networks and permeability change with varying effective stress are necessary in the processes of CBM production. Based on the rock elastic theory and finite difference method, the stress-strain model of reconstructed coal fracture networks is established. It has provided a more accurate geometry model under stress condition. For comparison purposes, gas permeability and porosity of coal sample with artificially generated fracture are measured under varying effective stress. Based on the experimental results and the Walsh model, fracture width and roughness are estimated. Lattice Boltzmann methods are implemented to model the flows in a single rough fracture under stress condition and the stress-dependent permeability is predicted. Compared with laboratory measurement, the maximum relative error is 25%. Furthermore, applications and case studies are performed for the flows in the 2D and 3D fracture networks. The effects of stress, fracture density, surface roughness and aperture on the associated permeability are discussed. The present study provides an alternative to investigate the microcosmic stress sensitivity mechanism of coal permeability.

Sub-basalt Imaging of Hydrocarbon-Bearing Mesozoic Sediments Using Ray-Trace Inversion of First-Arrival Seismic Data and Elastic Finite-Difference Full-Wave Modeling Along Sinor\u2013Valod Profile of Deccan Syneclise, India

Imaging below the basalt for hydrocarbon exploration is a global problem because of poor penetration and significant loss of seismic energy due to scattering, attenuation, absorption and mode-conversion when the seismic waves encounter a highly heterogeneous and rugose basalt layer. The conventional (short offset) seismic data acquisition, processing and modeling techniques adopted by the oil industry generally fails to image hydrocarbon-bearing sub-trappean Mesozoic sediments hidden below the basalt and is considered as a serious problem for hydrocarbon exploration in the world. To overcome this difficulty of sub-basalt imaging, we have generated dense synthetic seismic data with the help of elastic finite-difference full-wave modeling using staggered-grid scheme for the model derived from ray-trace inversion using sparse wide-angle seismic data acquired along Sinor–Valod profile in the Deccan Volcanic Province of India. The full-wave synthetic seismic data generated have been processed and imaged using conventional seismic data processing technique with Kirchhoff pre-stack time and depth migrations. The seismic image obtained correlates with all the structural features of the model obtained through ray-trace inversion of wide-angle seismic data, validating the effectiveness of robust elastic finite-difference full-wave modeling approach for imaging below thick basalts. Using the full-wave modeling also allows us to decipher small-scale heterogeneities imposed in the model as a measure of the rugose basalt interfaces, which could not be dealt with ray-trace inversion. Furthermore, we were able to accurately image thin low-velocity hydrocarbon-bearing Mesozoic sediments sandwiched between and hidden below two thick sequences of high-velocity basalt layers lying above the basement.

Application of laser-ultrasonics to texture measurements in metal processing

The paper describes in principle how information about textures can be obtained through the application of laser-ultrasonics (LUS) which can be carried out at elevated temperatures, for example in connection with hot rolling. The benefits from getting a measure of texture in this way are explained together with the proposed methodology which is based on the elastic anisotropic properties of the textured material. Measurements are made using only a single laser pulse and in real-time.Two approaches are presented to modelling the propagation of elastic waves, ray tracing and finite difference modelling. These give consistent results but the latter provides a more complete prediction of the ultrasonic spectrum that can be quantitatively related to measured signals through a cross-correlation procedure.Some experimental results are presented for room temperature measurements on a sheet of interstitial-free steel. Agreement between experimental data and modelling results is good and allows estimation of the 4th order coefficients of the orientation distribution function.

Multi-hole seismic modeling in 3-D space and cross-hole seismic tomography analysis for boulder detection

A boulder stone, a common geological feature in south China, is referred to the remnant of a granite body which has been unevenly weathered. Undetected boulders could adversely impact the schedule and safety of subway construction when using tunnel boring machine (TBM) method. Therefore, boulder detection has always been a key issue demanded to be solved before the construction. Nowadays, cross-hole seismic tomography is a high resolution technique capable of boulder detection, however, the method can only solve for velocity in a 2-D slice between two wells, and the size and central position of the boulder are generally difficult to be accurately obtained. In this paper, the authors conduct a multi-hole wave field simulation and characteristic analysis of a boulder model based on the 3-D elastic wave staggered-grid finite difference theory, and also a 2-D imaging analysis based on first arrival travel time. The results indicate that (1) full wave field records could be obtained from multi-hole seismic wave simulations. Simulation results describe that the seismic wave propagation pattern in cross-hole high-velocity spherical geological bodies is more detailed and can serve as a basis for the wave field analysis. (2) When a cross-hole seismic section cuts through the boulder, the proposed method provides satisfactory cross-hole tomography results; however, when the section is closely positioned to the boulder, such high-velocity object in the 3-D space would impact on the surrounding wave field. The received diffracted wave interferes with the primary wave and in consequence the picked first arrival travel time is not derived from the profile, which results in a false appearance of high-velocity geology features. Finally, the results of 2-D analysis in 3-D modeling space are comparatively analyzed with the physical model test vis-a-vis the effect of high velocity body on the seismic tomographic measurements.

Physically based probabilistic seismic hazard analysis using broadband ground motion simulation: a case study for the Prince Islands Fault, Marmara Sea

The main motivation for this study was the impending occurrence of a catastrophic earthquake along the Prince Island Fault (PIF) in the Marmara Sea and the disaster risk around the Marmara region, especially in Istanbul. This study provides the results of a physically based probabilistic seismic hazard analysis (PSHA) methodology, using broadband strong ground motion simulations, for sites within the Marmara region, Turkey, that may be vulnerable to possible large earthquakes throughout the PIF segments in the Marmara Sea. The methodology is called physically based because it depends on the physical processes of earthquake rupture and wave propagation to simulate earthquake ground motion time histories. We included the effects of all considerable-magnitude earthquakes. To generate the high-frequency (0.5–20 Hz) part of the broadband earthquake simulation, real, small-magnitude earthquakes recorded by a local seismic array were used as empirical Green’s functions. For the frequencies below 0.5 Hz, the simulations were obtained by using synthetic Green’s functions, which are synthetic seismograms calculated by an explicit 2D/3D elastic finite difference wave propagation routine. By using a range of rupture scenarios for all considerable-magnitude earthquakes throughout the PIF segments, we produced a hazard calculation for frequencies of 0.1–20 Hz. The physically based PSHA used here followed the same procedure as conventional PSHA, except that conventional PSHA utilizes point sources or a series of point sources to represent earthquakes, and this approach utilizes the full rupture of earthquakes along faults. Furthermore, conventional PSHA predicts ground motion parameters by using empirical attenuation relationships, whereas this approach calculates synthetic seismograms for all magnitudes of earthquakes to obtain ground motion parameters. PSHA results were produced for 2, 10, and 50 % hazards for all sites studied in the Marmara region.

On the consistency between nearest-neighbor peridynamic discretizations and discretized classical elasticity models

The peridynamic theory of solid mechanics is a nonlocal reformulation of the classical continuum mechanics theory. At the continuum level, it has been demonstrated that classical (local) elasticity is a special case of peridynamics. Such a connection between these theories has not been extensively explored at the discrete level. This paper investigates the consistency between nearest-neighbor discretizations of linear elastic peridynamic models and finite difference discretizations of the Navier–Cauchy equation of classical elasticity. Although nearest-neighbor discretizations in peridynamics have been numerically observed to present grid-dependent crack paths or spurious microcracks, this paper focuses on a different, analytical aspect of such discretizations. We demonstrate that, even in the absence of cracks, such discretizations may be problematic unless a proper selection of weights is used. Specifically, we demonstrate that using the standard meshfree approach in peridynamics, nearest-neighbor discretizations do not reduce, in general, to discretizations of corresponding classical models. We study nodal-based quadratures for the discretization of peridynamic models, and we derive quadrature weights that result in consistency between nearest-neighbor discretizations of peridynamic models and discretized classical models. The quadrature weights that lead to such consistency are, however, model-/discretization-dependent. We motivate the choice of those quadrature weights through a quadratic approximation of displacement fields. The stability of nearest-neighbor peridynamic schemes is demonstrated through a Fourier mode analysis. Finally, an approach based on a normalization of peridynamic constitutive constants at the discrete level is explored. This approach results in the desired consistency for one-dimensional models, but does not work in higher dimensions. The results of the work presented in this paper suggest that even though nearest-neighbor discretizations should be avoided in peridynamic simulations involving cracks, such discretizations are viable, for example for verification or validation purposes, in problems characterized by smooth deformations. Moreover, we demonstrate that better quadrature rules in peridynamics can be obtained based on the functional form of solutions.