FRINK Linked Data Fragments server

Matches in SemOpenAlex for { <https://semopenalex.org/work/W4315433650> ?p ?o ?g. }

• W4315433650 endingPage "1545" @default.
• W4315433650 startingPage "1531" @default.
• W4315433650 abstract "SUMMARY In viscoacoustically stratified media where the density is constant, 3-D wave propagation in the frequency–radial wavenumber domain is governed by the Helmholtz equation. In the case that the model is a velocity gradient interface where the squared velocity in depth is represented by a smooth Heaviside function of the Fermi–Dirac distribution type, the Helmholtz equation for a point source at arbitrary location is shown to have analytical solution for the Green's function. The velocity depth profile, which is a modification of the Epstein profile which has been thoroughly studied in different branches of physics, is described by four parameters: the velocities at minus and plus infinity, the reference depth of the gradient interface, and its smoothness. The Helmholtz equation is first solved in a model where the point source is absent. The solution to the source-free equation has four unknown constants that must be determined. The radiation conditions at minus and plus infinity and two conditions on the Green's function at the source depth allow the constants to be found. The Green's function solution can be represented in two mathematically equivalent algebraic forms involving ordinary hypergeometric functions. The first form allows a numerically stable implementation over all wavenumber components. The second form allows a physical, intuitive interpretation and is expressed mathematically as the sum of two terms. Each of the terms contains the product of constant-velocity reference phase shift functions and hypergeometric functions which take the role to adjust the amplitude and phase shift calculated by the reference phase shift functions to account for the depth varying velocity profile. Inverse Fourier transforms take the Green's function from the frequency–wavenumber domain to the frequency–space domain or time–space domain. The Green's function solution is valid for any sharpness of the interface. Selected numerical results are presented for the 1-D and 2-D Helmholtz equation to demonstrate the influence of the velocity gradient zone on the wavefield. The 1-D solution in an acoustic model is compared in time domain to the classical finite-difference wave propagation solution. For the purpose of interpretation of seismograms, we model for comparison the wavefield response in a model of two half-spaces in welded contact. For brevity, the latter model is referenced as the HS model." @default.
• W4315433650 created "2023-01-11" @default.
• W4315433650 creator A5048543997 @default.
• W4315433650 creator A5088271748 @default.
• W4315433650 date "2023-01-10" @default.
• W4315433650 modified "2023-10-15" @default.
• W4315433650 title "The viscoacoustic Green's function for the Helmholtz equation in a velocity gradient interface model" @default.
• W4315433650 cites W148904264 @default.
• W4315433650 cites W1968151081 @default.
• W4315433650 cites W1975068428 @default.
• W4315433650 cites W1979714610 @default.
• W4315433650 cites W1990971432 @default.
• W4315433650 cites W2034471740 @default.
• W4315433650 cites W2035196826 @default.
• W4315433650 cites W2036003435 @default.
• W4315433650 cites W2036196220 @default.
• W4315433650 cites W2038534907 @default.
• W4315433650 cites W2055254450 @default.
• W4315433650 cites W2069612851 @default.
• W4315433650 cites W2077917003 @default.
• W4315433650 cites W2117270764 @default.
• W4315433650 cites W2119915381 @default.
• W4315433650 cites W2128516823 @default.
• W4315433650 cites W2135616504 @default.
• W4315433650 cites W2166240476 @default.
• W4315433650 cites W2168724044 @default.
• W4315433650 cites W2170638581 @default.
• W4315433650 cites W2171066597 @default.
• W4315433650 cites W2493666530 @default.
• W4315433650 cites W2793928804 @default.
• W4315433650 cites W2938906899 @default.
• W4315433650 cites W2963172715 @default.
• W4315433650 cites W3099253917 @default.
• W4315433650 cites W3099433731 @default.
• W4315433650 cites W3210262604 @default.
• W4315433650 cites W4235974016 @default.
• W4315433650 cites W4283828235 @default.
• W4315433650 cites W4288056263 @default.
• W4315433650 cites W4300286811 @default.
• W4315433650 cites W993391707 @default.
• W4315433650 doi "https://doi.org/10.1093/gji/ggad007" @default.
• W4315433650 hasPublicationYear "2023" @default.
• W4315433650 type Work @default.
• W4315433650 citedByCount "0" @default.
• W4315433650 crossrefType "journal-article" @default.
• W4315433650 hasAuthorship W4315433650A5048543997 @default.
• W4315433650 hasAuthorship W4315433650A5088271748 @default.
• W4315433650 hasConcept C121130766 @default.
• W4315433650 hasConcept C121332964 @default.
• W4315433650 hasConcept C134306372 @default.
• W4315433650 hasConcept C14036430 @default.
• W4315433650 hasConcept C182310444 @default.
• W4315433650 hasConcept C18591234 @default.
• W4315433650 hasConcept C197320386 @default.
• W4315433650 hasConcept C199360897 @default.
• W4315433650 hasConcept C2011187 @default.
• W4315433650 hasConcept C27592594 @default.
• W4315433650 hasConcept C2777027219 @default.
• W4315433650 hasConcept C33923547 @default.
• W4315433650 hasConcept C41008148 @default.
• W4315433650 hasConcept C62520636 @default.
• W4315433650 hasConcept C78458016 @default.
• W4315433650 hasConcept C86803240 @default.
• W4315433650 hasConceptScore W4315433650C121130766 @default.
• W4315433650 hasConceptScore W4315433650C121332964 @default.
• W4315433650 hasConceptScore W4315433650C134306372 @default.
• W4315433650 hasConceptScore W4315433650C14036430 @default.
• W4315433650 hasConceptScore W4315433650C182310444 @default.
• W4315433650 hasConceptScore W4315433650C18591234 @default.
• W4315433650 hasConceptScore W4315433650C197320386 @default.
• W4315433650 hasConceptScore W4315433650C199360897 @default.
• W4315433650 hasConceptScore W4315433650C2011187 @default.
• W4315433650 hasConceptScore W4315433650C27592594 @default.
• W4315433650 hasConceptScore W4315433650C2777027219 @default.
• W4315433650 hasConceptScore W4315433650C33923547 @default.
• W4315433650 hasConceptScore W4315433650C41008148 @default.
• W4315433650 hasConceptScore W4315433650C62520636 @default.
• W4315433650 hasConceptScore W4315433650C78458016 @default.
• W4315433650 hasConceptScore W4315433650C86803240 @default.
• W4315433650 hasFunder F4320323299 @default.
• W4315433650 hasIssue "3" @default.
• W4315433650 hasLocation W43154336501 @default.
• W4315433650 hasOpenAccess W4315433650 @default.
• W4315433650 hasPrimaryLocation W43154336501 @default.
• W4315433650 hasRelatedWork W1143945821 @default.
• W4315433650 hasRelatedWork W2057172816 @default.
• W4315433650 hasRelatedWork W2068285538 @default.
• W4315433650 hasRelatedWork W2075760745 @default.
• W4315433650 hasRelatedWork W2082424429 @default.
• W4315433650 hasRelatedWork W2385931563 @default.
• W4315433650 hasRelatedWork W2394117945 @default.
• W4315433650 hasRelatedWork W2808085846 @default.
• W4315433650 hasRelatedWork W4247626186 @default.
• W4315433650 hasRelatedWork W4315433650 @default.
• W4315433650 hasVolume "233" @default.
• W4315433650 isParatext "false" @default.
• W4315433650 isRetracted "false" @default.
• W4315433650 workType "article" @default.