Comparison of expansion-based explicit time-integration schemes for acoustic wave propagation

We have developed a von Neumann stability and dispersion analysis of two time-integration techniques in the framework of Fourier pseudospectral (PS) discretizations of the second-order wave equation. The first technique is a rapid expansion method (REM) that uses Chebyshev matrix polynomials to approximate the continuous solution operator of the discrete wave equation. The second technique is a Lax-Wendroff method (LWM) that replaces time derivatives in the Taylor expansion of the solution wavefield with their equivalent spatial PS differentiations. In both time-integration schemes, each expansion term J results in an extra application of the spatial differentiation operator; thus, both methods are similar in terms of their implementation and the freedom to arbitrarily increase accuracy by using more expansion terms. Nevertheless, their limiting Courant-Friedrichs-Lewy stability number S and dispersion inaccuracies behave differently as J varies. We establish the S bounds for both methods in cases of practical use, J≤10, and we confirm the results by numerical simulations. For both schemes, we explore the dispersion dependence on modeling parameters J and S on the wavenumber domain, through a new error metric. This norm weights errors by the source spectrum to adequately measure the accuracy differences. Then, we compare the theoretical computational costs of LWM and REM simulations to attain the same accuracy target by using the efficiency metric J/S. In particular, we find optimal (J,S) pairs that ensure a certain accuracy at a minimal computational cost. We also extend our dispersion analysis to heterogeneous media and find the LWM accuracy to be significantly better for representative J values. Moreover, we perform 2D wave simulations on the SEG/EAGE Salt Model, in which larger REM inaccuracies are clearly observed on waveform comparisons in the range J≤3.C. Spa has received funding from the Chilean Agency CONICYT under the project FONDECYT 11140212, whereas O. Rojas and J. de la Puente have received funding fromthe European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no.777778 MATHROCKS. The research leading to these results hasreceived funding from the European Union’s Horizon 2020 research and innovation programme under the ChEESE project, grant agreement No. 823844. We also acknowledge funding from the Spanish Ministry Project Geofísica de Altas Prestaciones TIN2016-80957-P.Peer ReviewedPostprint (author's final draft

High order methods for acoustic scattering: Coupling Farfield Expansions ABC with Deferred-Correction methods

Arbitrary high order numerical methods for time-harmonic acoustic scattering problems originally defined on unbounded domains are constructed. This is done by coupling recently developed high order local absorbing boundary conditions (ABCs) with finite difference methods for the Helmholtz equation. These ABCs are based on exact representations of the outgoing waves by means of farfield expansions. The finite difference methods, which are constructed from a deferred-correction (DC) technique, approximate the Helmholtz equation and the ABCs, with the appropriate number of terms, to any desired order. As a result, high order numerical methods with an overall order of convergence equal to the order of the DC schemes are obtained. A detailed construction of these DC finite difference schemes is presented. Additionally, a rigorous proof of the consistency of the DC schemes with the Helmholtz equation and the ABCs in polar coordinates is also given. The results of several numerical experiments corroborate the high order convergence of the novel method.Comment: 36 pages, 20 figure

Toward an automatic full-wave inversion: Synthetic study cases

Full-waveform inversion (FWI) in seismic scenarios continues to be a complex procedure for subsurface imaging that might require extensive human interaction in terms of model setup, constraints, and data preconditioning. The underlying reason is the strong nonlinearity of the problem that forces the addition of a priori knowledge (or bias) in order to obtain geologically sound results. In particular, when the use of a long-offset receiver is not possible or may not favor the reconstruction of the fine structure of the model, one needs to rely on reflection data. As a consequence, the inversion process is more prone to becoming stuck in local minima. Nevertheless, misfit functionals can be devised that can either cope with missing long-wavenumber features of initial models (e.g., cross-correlation-based misfit) or invert reflection-dominated data whenever the models are sufficiently good (e.g., normalized offset-limited least-squares misfit). By combining both, high-frequency data content with poor initial models can be successfully inverted. If one can figure out simple parameterizations for such functionals, the amount of uncertainty and manual work related to tuning FWI would be substantially reduced. Thus, FWI might become a semiautomatized imaging tool.We want to thank Repsol for funding this research by means of the Aurora project. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 644202. Additionally, the research leading to these results has received funding from the European Union’s Horizon 2020 Programme (2014-2020) and from Brazilian Ministry of Science, Technology and Innovation through Rede Nacional de Pesquisa (RNP) under the HPC4E Project (www.hpc4e.eu), grant agreement No 689772. We acknowledge Chevron for the dataset that was used in our second example.Peer ReviewedPostprint (author's final draft

Artificial neural networks as emerging tools for earthquake detection

As seismic networks continue to spread and monitoring sensors become more ef¿cient, the abundance of data highly surpasses the processing capabilities of earthquake interpretation analysts. Earthquake catalogs are fundamental for fault system studies, event modellings, seismic hazard assessment, forecasting, and ultimately, for mitigating the seismic risk. These have fueled the research for the automation of interpretation tasks such as event detection, event identi¿cation, hypocenter location, and source mechanism analysis. Over the last forty years, traditional algorithms based on quantitative analyses of seismic traces in the time or frequency domain, have been developed to assist interpretation. Alternatively, recentadvancesarerelatedtotheapplicationofArti¿cial Neural Networks (ANNs), a subset of machine learning techniques that is pushing the state-of-the-art forward in many areas. Appropriated trained ANN can mimic the interpretation abilities of best human analysts, avoiding the individual weaknesses of most traditional algorithms, and spending modest computational resources at the operational stage. In this paper, we will survey the latest ANN applications to the automatic interpretation of seismic data, with a special focus on earthquake detection, and the estimation of onset times. For a comparative framework, we give an insight into the labor of human interpreters, who may face uncertainties in the case of small magnitude earthquakes.Peer ReviewedPostprint (published version

Finite difference modelling of rupture propagation with strong velocity-weakening friction

We incorporate rate- and state-dependent friction in explicit finite difference (FD) simulations of mode II dynamic ruptures in elastic media, using the Mimetic Operators Split-Node (MOSN) method, with adjustable order of spatial accuracy (second-, fourth- or mixed-order accurate), including an option that is fourth-order accurate at the fault discontinuity as well as in the elastic volume. At fault points, the rate and state equations combined with the spatially discretized momentum conservation equations form a coupled system of ordinary differential equations (ODEs) for slip velocity and state variable. As a consequence of the rapid damping of velocity perturbations due to the direct effect, this system exhibits numerical stiffness that is inversely proportional to velocity squared. Approximate solutions to this velocity-state system are achieved by two different implicit schemes: (i) a fourth-order Rosenbrock integration of the full system using multiple substeps and (ii) low order integrations (backward Euler and trapezoidal) of the velocity equation, time-staggered with analytic integration of the state equation under the approximation of constant slip velocity over the time step. In assessing the numerical schemes, we use three test problems: ruptures with frictional resistance controlled by (i) a slip evolution law with strong velocity-weakening behaviour at high slip rates, representing thermal weakening due to flash heating of microscopic asperity contacts, (ii) the classic (low-velocity) slip evolution law and (iii) the classic aging evolution law. A convergence analysis is carried out using reference solutions from a spectral boundary integral equation method (BIEM) (a method restricted to homogeneous media, with nominal spectral accuracy in space and second-order accuracy in time for smooth solutions). Errors are measured by root-mean-square differences of fault-plane time histories (slip, slip rate, traction and state). MOSN shows essentially the same convergence rates as BIEM: second-order convergence for slip and state-variable misfits, with slower (but at least first-order) convergence for slip rates and tractions. For a given grid spacing, fourth-order MOSN is as accurate as BIEM for all variables except slip-rate. MOSN-Rosenbrock nominally has fourth-order temporal accuracy for the fault-plane velocity-state ODE integration (compared to lower-order accuracy for the other two MOSN schemes) and therefore provides an important theoretical benchmark. However, it is sensitive to details of the elastic calculation scheme and occasionally its adaptive substepping performs poorly, leading to large excursions from the reference solution. In contrast, MOSN-trapezoidal is robust and reliable, much easier to implement than MOSN-Rosenbrock, and in all cases achieves precision as good as the latter without recourse to substepping. MOSN-Euler has the same advantages as MOSN-trapezoidal, except that its nominal first-order temporal accuracy ultimately leads to larger errors in slip and state variable compared with the higher-order MOSN schemes at sufficiently small grid spacings and time step

A performance analysis of a mimetic finite difference scheme for acoustic wave propagation on GPU platforms

Realistic applications of numerical modeling of acoustic wave dynamics usually demand high-performance computing because of the large size of study domains and demanding accuracy requirements on simulation results. Forward modeling of seismic motion on a given subsurface geological structure is by itself a good example of such applications, and when used as a component of seismic inversion tools or as a guide for the design of seismic surveys, its computational cost increases enormously. In the case of finite difference methods (or any other volumen-discretization scheme), memory and computing demands rise with grid refinement, which may be necessary to reduce errors on numerical wave patterns and better capture target physical devices. In this work, we present several implementations of a mimetic finite difference method for the simulation of acoustic wave propagation on highly dense staggered grids. These implementations evolve as different optimization strategies are employed starting from appropriate setting of compilation flags, code vectorization by using streaming SIMD extensions Advanced Vector Extensions (AVX), CPU parallelization by exploiting the Open Multi-Processing framework to the final code parallelization on graphics processing unit platforms. We present and discuss the increasing processing speed up of this mimetic scheme achieved by the gradual implementation and testing of all these performance optimizations. In terms of simulation times, the performance of our graphics processing unit parallel implementations is consistently better than the best CPU version.Authors from Universidad Central de Venezuela (UCV) were partially supported by: Consejo de Desarrollo Científico y Humanístico de la UCV, Vice-rectorado Académico de la UCV, Coordinación de Investigación de la Facultad de Ciencias UCV, Banco Central de Venezuela (BCV) and Generalitat Valenciana under project PROMETEOII/2015/015

Compact finite difference modeling of 2-D acoustic wave propagation

We present two fourth-order compact finite difference (CFD) discretizations of the velocity–pressure formulation of the acoustic wave equation in 2-D rectangular grids. The first method uses standard implicit CFD on nodal meshes and requires solving tridiagonal linear systems along each grid line, while the second scheme employs a novel set of mimetic CFD operators for explicit differentiation on staggered grids. Both schemes share a Crank–Nicolson time integration decoupled by the Peaceman–Rachford splitting technique to update discrete fields by alternating the coordinate direction of CFD differentiation (ADI-like iterations). For comparison purposes, we also implement a spatially fourth-order FD scheme using non compact staggered mimetic operators in combination to second-order leap-frog time discretization. We apply these three schemes to model acoustic motion under homogeneous boundary conditions and compare their experimental convergence and execution times, as grid is successively refined. Both CFD schemes show four-order convergence, with a slight superiority of the mimetic version, that leads to more accurate results on fine grids. Conversely, the mimetic leap-frog method only achieves quadratic convergence and shows similar accuracy to CFD results exclusively on coarse grids. We finally observe that computation times of nodal CFD simulations are between four and five times higher than those spent by the mimetic CFD scheme with similar grid size. This significant performance difference is attributed to solving those embedded linear systems inherent to implicit CFD.Peer ReviewedPreprin

Long short-term memory networks for earthquake detection in Venezuelan regions

Reliable earthquake detection and location algorithms are necessary to properly catalog and analyze the continuously growing seismic records. This paper reports the results of applying Long Short-Term Memory (LSTM) networks to single-station three-channel waveforms for P-wave earthquake detection in western and north central regions of Venezuela. Precisely, we apply our technique to study the seismicity along the dextral strike-slip Boconó and La Victoria - San Sebastián faults, with complex tectonics driven by the interactions between the South American and Caribbean plates.Peer ReviewedPostprint (author's final draft

A cost-efficient QoS-aware analytical model of future software content delivery networks

Freelance, part-time, work-at-home, and other flexible jobs are changing the concept of workplace, and bringing information and content exchange problems to companies. Geographically spread corporations may use remote distribution of software and data to attend employees' demands, by exploiting emerging delivery technologies. In this context, cost-efficient software distribution is crucial to allow business evolution and make IT infrastructures more agile. On the other hand, container based virtualization technology is shaping the new trends of software deployment and infrastructure design. We envision current and future enterprise IT management trends evolving towards container based software delivery over Hybrid CDNs. This paper presents a novel cost-efficient QoS aware analytical model and a Hybrid CDN-P2P architecture for enterprise software distribution. The model would allow delivery cost minimization for a wide range of companies, from big multinationals to SMEs, using CDN-P2P distribution under various industrial hypothetical scenarios. Model constraints guarantee acceptable deployment times and keep interchanged content amounts below the bandwidth and storage network limits in our scenarios. Indeed, key model parameters account for network bandwidth, storage limits and rental prices, which are empirically determined from their offered values by the commercial delivery networks KeyCDN, MaxCDN, CDN77 and BunnyCDN. This preliminary study indicates that MaxCDN offers the best cost-QoS trade-off. The model is implemented in the network simulation tool PeerSim, and then applied to diverse testing scenarios by varying company types, number and profile (either, technical or administrative) of employees and the number and size of content requests. Hybrid simulation results show overall economic savings between 5\% and 20\%, compared to just hiring resources from a commercial CDN, while guaranteeing satisfactory QoS levels in terms of deployment times and number of served requests.This work was partially supported by Generalitat de Catalunya under the SGR Program (2017-SGR-962) and the RIS3CAT DRAC Project (001-P-001723). We have also received funding from Ministry of Science and Innovation (Spain) under the project EQC2019-005653-P.Peer ReviewedPostprint (author's final draft