There is a growing interest in tidal effects on the global wind-driven oceanic circulation. Tidal models used in such investigations have been verified by comparison with satellite and tide gauge data, but synthetic tests have not been published. In this paper we present three numerical tests in spherical geometry, which are suitable for testing the tidal component of global ocean models. The first test is a tsunami-like propagation of an initial Gaussian depression with no external forcing. The other two tests examine the tidal response of an ocean with an undulating bottom with four Gaussian ridges and an ocean with a flat bottom with a realistic land mask. We provide the results from six model configurations, which differ in the time-stepping scheme and computational grid used. Most of them are implemented in present-day global ocean models. Although the proposed numerical tests are simple compared to realistic simulations, their analytic solutions are not available. We thus check the conservation of time invariants to ensure that the solutions are physically meaningful. We also compare the time evolution of certain physical quantities and the differences in sea surface heights at particular time instants with respect to a reference solution. All tested time stepping schemes are suitable for tidal studies except for the Euler implicit time stepping scheme. Model configurations based on the Arakawa grids B/E use smoothing to suppress the grid-scale noise which results in an energy leakage of around 5%. The B/E-grid energy leakage is probably acceptable if we consider that tuned diffusive terms are used in real-world configurations. The C-grid and B/E-grid solutions differ in the vicinity of solid boundaries as a consequence of different boundary conditions. The B-grid and E-grid solutions are similar, unless the shape of the solid boundaries is complex due to the different shapes of the respective grid cells.

A method for performing a spherical harmonic analysis, using observed horizontal components of a tangent vector on a sphere, is presented. The vector data samples are assumed to be provided in an equiangular grid, which essentially simplifies the least-squares analysis by making use of (1) the block diagonal structure of the normal equations of least squares, (2) the even-odd symmetry of the associated Legendre functions, and (3) the fast Fourier transform of mix-radix. The correct function of the program and its numerical precision is verified by applying it to a data set, derived by evaluating a given set of vector spherical harmonic coefficients. That the program works correctly is demonstrated by the excellent agreement between the input and output spherical harmonic coefficients. Program summary Program Title: SHAVEL Program Files doi : http://dx.doi.org/10.17632/nppz4y7wg7.1 Licensing provisions: GPLv3 Programming language: Fortran 2003, Linux External routines: FFTPACK5.1, CPC program library SPHAN Classification: 4.9, 4.10, 4.11 Nature of problem: The least-squares analysis of horizontal vector field sampled in an equiangular grid on a sphere in terms of horizontal vector spherical harmonics. Solution method: The vector spherical harmonic coefficients of a horizontal vector field are estimated by the method of least-squares adjustment of data samples distributed in an equiangular grid on a sphere. For such a regular grid the normal matrix is sparse and allows the system of the normal equations to be decomposed into a series of subsystems according to azimuthal order m. The solution of each subsystem is sought by the Gauss elimination. The fast Fourier transform of mix-radix is implemented in (i) setting up the right-hand sides of the normal equations, and (ii) performing the spherical harmonic synthesis where the series of spherical harmonics are summed. (C) 2018 Elsevier B.V. All rights reserved.

Diurnal S[Formula: see text] tidal oscillations in the coupled atmosphere-ocean system induce small perturbations of Earth's prograde annual nutation, but matching geophysical model estimates of this Sun-synchronous rotation signal with the observed effect in geodetic Very Long Baseline Interferometry (VLBI) data has thus far been elusive. The present study assesses the problem from a geophysical model perspective, using four modern-day atmospheric assimilation systems and a consistently forced barotropic ocean model that dissipates its energy excess in the global abyssal ocean through a parameterized tidal conversion scheme. The use of contemporary meteorological data does, however, not guarantee accurate nutation estimates per se; two of the probed datasets produce atmosphere-ocean-driven S[Formula: see text] terms that deviate by more than 30 [Formula: see text]as (microarcseconds) from the VLBI-observed harmonic of [Formula: see text] [Formula: see text]as. Partial deficiencies of these models in the diurnal band are also borne out by a validation of the air pressure tide against barometric in situ estimates as well as comparisons of simulated sea surface elevations with a global network of S[Formula: see text] tide gauge determinations. Credence is lent to the global S[Formula: see text] tide derived from the Modern-Era Retrospective Analysis for Research and Applications (MERRA) and the operational model of the European Centre for Medium-Range Weather Forecasts (ECMWF). When averaged over a temporal range of 2004 to 2013, their nutation contributions are estimated to be [Formula: see text] [Formula: see text]as (MERRA) and [Formula: see text] [Formula: see text]as (ECMWF operational), thus being virtually equivalent with the VLBI estimate. This remarkably close agreement will likely aid forthcoming nutation theories in their unambiguous a priori account of Earth's prograde annual celestial motion.

Diurnal S\(_1\) tidal oscillations in the coupled atmosphere–ocean system induce small perturbations of Earth’s prograde annual nutation, but matching geophysical model estimates of this Sun-synchronous rotation signal with the observed effect in geodetic Very Long Baseline Interferometry (VLBI) data has thus far been elusive. The present study assesses the problem from a geophysical model perspective, using four modern-day atmospheric assimilation systems and a consistently forced barotropic ocean model that dissipates its energy excess in the global abyssal ocean through a parameterized tidal conversion scheme. The use of contemporary meteorological data does, however, not guarantee accurate nutation estimates per se; two of the probed datasets produce atmosphere–ocean-driven S\(_1\) terms that deviate by more than 30 \(\upmu \)as (microarcseconds) from the VLBI-observed harmonic of \(-16.2+i113.4\) \(\upmu \)as. Partial deficiencies of these models in the diurnal band are also borne out by a validation of the air pressure tide against barometric in situ estimates as well as comparisons of simulated sea surface elevations with a global network of S\(_1\) tide gauge determinations. Credence is lent to the global S\(_1\) tide derived from the Modern-Era Retrospective Analysis for Research and Applications (MERRA) and the operational model of the European Centre for Medium-Range Weather Forecasts (ECMWF). When averaged over a temporal range of 2004 to 2013, their nutation contributions are estimated to be \(-8.0+i106.0\) \(\upmu \)as (MERRA) and \(-9.4+i121.8\) \(\upmu \)as (ECMWF operational), thus being virtually equivalent with the VLBI estimate. This remarkably close agreement will likely aid forthcoming nutation theories in their unambiguous a priori account of Earth’s prograde annual celestial motion.

We present the results of computations of the secondary magnetic field induced by ocean motions. Ocean velocities are computed using the baroclinic ocean model LSOMG. The velocities are then used to determine the Lorentz force which is plugged into the magnetic induction code TLAM as a principal forcing. The TLAM is a 2D magnetic induction code based on the thin-shell approximation (Vivier et al., 2004; Tyler et al., 1997). In this approximation, the equation of magnetic induction simplifies significantly, time derivatives of main and induced magnetic fields are neglected as well as the self-induction term. The price for simplification of governing equations is the limited applicability of the resulting system. It is only suitable for slowly evolving processes. In order to meet the condition, we restrict ourselves to the wind (buoyancy) driven ocean circulation, although the LSOMG model is able to model both tidallyand wind-driven circulations. We assess the accuracy of thin-shell approximation in our setup by comparing the results with the Swarm satellite magnetic data.

Traditionally, ocean tides have been modeled in frequency domain with a forcing from selected tidal constituents. It is a natural approach; however, it implicitly neglects non-linearities of ocean dynamics. An alternative approach is time-domain modeling with a forcing given by the full lunisolar potential, i.e., all tidal waves are a priori included. This approach has been applied in several ocean tide models; however, some challenging tasks still remain, for example, assimilation of satellite altimetry data. In this paper, we introduce the assimilative scheme applicable in a time-domain model, which is an alternative to existing techniques used in assimilative ocean tide models. We present results from DEBOT, a global barotropic ocean tide model, which has two modes: DEBOT-h, a purely hydrodynamical mode, and DEBOT-a, an assimilative mode. The accuracy of DEBOT in both modes is assessed through a series of tests against tide gauge data which demonstrate that DEBOT is comparable to state-of-the-art global ocean tide models for major tidal constituents. Furthermore, as signals of all tidal frequencies are included in DEBOT, we also discuss modeling of minor tidal constituents and non-linear compound tides. Our modeling approach can be useful for those applications where the frequency domain approach is not suitable.

The purpose of this paper is to present a new global barotropic ocean model-the DEBOT model. The model is based on the shallow water equations which we newly express in geographical coordinates. The derivation includes the boundary conditions and the Reynolds tensor in a form used commonly in oceanography. The numerical model employs finite differences on an Arakawa-C grid in space and a generalized forward-backward scheme in time with a combined third-order Adams-Bashforth and fourth-order Adams-Moulton step. The validity of the model is demonstrated by the tests based on conservation integral invariants. As a practical application, we present ocean circulation simulations generated by the lunisolar tidal force. (C) 2015 Elsevier Ltd. All rights reserved.

Detection of the seismic signal from perforations or string shots is crucial for calibration of velocity model for surface or downhole monitoring.While in the borehole recordings perforation shots have higher signal to noise ratio of the P-waves than microseismic events, in the surface monitoring recordings it is often opposite.We investigated amplitude spectra of microseismic events and perforation shots in the downhole data and found that amplitude ratios in the band of 20-30 Hz relative to band 100-200 Hz are stronger for the microseismic events.Thus we suggest that detectability of the perforations in surface recorded data is limited by attenuation of the higher frequency signal which increases exponentially with frequency.This suggests that longer duration of calibration shots can improve detectability of string shots at the surface.

We present the results of a benchmark study of two numerical codes, LSGbt and DEBOT, that are designed to model tidally induced barotropic ocean circulation. Both modelling codes are formulated in spherical geometry, but they are based on different numerical techniques and approximations. The test examples involve (i) a tsunamilike propagation of an initial Gaussian depression with no external forcing and (ii) a tidally-induced circulation in a flat-bottom ocean that is initially at rest. The performance of these ocean models is evaluated by several criteria, such as the evolution of time-invariant quantities, e.g., global mass and total energy, or a comparison of surface-elevation spatial patterns. This results in an objective assessment of the two numerical codes and provides various insights into code functionality. We describe the experimental setup of test examples, provide the outputs of the LSGbt and DEBOT codes, and discuss the differences in the results. We also demonstrate how the presented numerical examples have helped to improve the performance of the original versions of the LSGbt and DEBOT models. Despite the significant differences in the numerical methods employed, the test computations show a satisfactory agreement between the results provided by the LSGbt and DEBOT models.

PreviousNext No AccessSEG Technical Program Expanded Abstracts 2012Detection of perforation shots in surface monitoring: the attenuation effectAuthors: David EinšpigelLeo EisnerDavid EinšpigelInstitute of Rock Structure and Mechanics, Czech Academy of ScienceSearch for more papers by this author and Leo EisnerInstitute of Rock Structure and Mechanics, Czech Academy of ScienceSearch for more papers by this authorhttps://doi.org/10.1190/segam2012-0425.1 SectionsSupplemental MaterialAboutPDF/ePub ToolsAdd to favoritesDownload CitationsTrack CitationsPermissions ShareFacebookTwitterLinked InRedditEmail Abstract Detection of the seismic signal from perforation or string shots is crucial for calibration of velocity model for surface or down-hole monitoring. While in borehole monitoring perforations have higher signal to noise ratio of the P-waves than micro-seismic events, in surface monitoring it is often opposite. We investigated amplitude spectra of microseismic events and perforations in downhole monitoring and found that amplitude ratio in the band of 20-30 Hz relative to band 100-200 Hz is stronger for the microseismic events. Thus we suggest that detectability of the perforations in surface monitoring is limited by attenuation of the higher frequency signal which increases exponentially with frequency. This suggests that longer duration of calibration shots can be improve detectability of string shots at surface monitoring. Permalink: https://doi.org/10.1190/segam2012-0425.1FiguresReferencesRelatedDetails SEG Technical Program Expanded Abstracts 2012ISSN (print):1052-3812 ISSN (online):1949-4645Copyright: 2012 Pages: 4609 Publisher:Society of Exploration Geophysicists HistoryPublished: 25 Oct 2012 CITATION INFORMATION David Einšpigel and Leo Eisner, (2012), "Detection of perforation shots in surface monitoring: the attenuation effect," SEG Technical Program Expanded Abstracts : 1-5. https://doi.org/10.1190/segam2012-0425.1 Plain-Language Summary PDF DownloadLoading ...