3−D Surface Topography Boundary Conditions in Seismic Wave Modelling
New alternative formulations of exact boundary conditions for arbitrary three{dimensional (3−D) free surface topographies on seismic media have been derived. They are shown to be equivalent with previously published formulations, thereby serving as a verification of the validity of each set of formu...
| मुख्य लेखकों: | , |
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| अन्य लेखक: | |
| स्वरूप: | Technical Report |
| प्रकाशित: |
Massachusetts Institute of Technology. Earth Resources Laboratory
2012
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| ऑनलाइन पहुंच: | http://hdl.handle.net/1721.1/68608 |
| _version_ | 1826191412593426432 |
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| author | Hestholm, Stig Ruud, Bent |
| author2 | Massachusetts Institute of Technology. Earth Resources Laboratory |
| author_facet | Massachusetts Institute of Technology. Earth Resources Laboratory Hestholm, Stig Ruud, Bent |
| author_sort | Hestholm, Stig |
| collection | MIT |
| description | New alternative formulations of exact boundary conditions for arbitrary three{dimensional (3−D) free surface topographies on seismic media have been derived. They are shown to be equivalent with previously published formulations, thereby serving as a verification of the validity of each set of formulations. The top of a curved grid represents the free surface topography while the grid's interior represents the physical medium. We assume the velocity{stress version of the viscoelastic wave equations to be valid in this grid before transforming the equations to a rectangular grid. In order to do the numerical discretization we apply the latter version of equations for seismic wave propagation simulation in the interior of the medium. The numerical discretization of the free surface topography boundary conditions by second−order finite−differences (F−Ds) is shown in detail, as well as spatially unconditional stability of the resulting system of equations. The F−D order is increased by two for each point away from the free surface up to eight, which is the order used in the interior. We use staggered grids both in space and time and the second-order leap-frog and Crank-Nicholson methods for wave field time propagation.
We simulate point sources at the surface of a homogeneous medium, with a plane surface containing a hill and a trench, respectively. The main features of these general cases are outlined. Then, we present results using parameters typical of teleseismic earthquakes and explosions with a 200 × 100 km[superscript 2] area of real topography from southwestern Norway over a homogeneous medium. A dipping plane wave simulates a teleseismic P−wave incident on the surface topography. Results show clear conversion from P− to Rg− (short period fundamental mode Rayleigh) waves in the steepest and/or roughest topography, as well as attenuated waves in valleys and fjords. The codes are parallellized for simulation on fast supercomputers to model higher frequencies and/or larger areas than before. |
| first_indexed | 2024-09-23T08:55:47Z |
| format | Technical Report |
| id | mit-1721.1/68608 |
| institution | Massachusetts Institute of Technology |
| last_indexed | 2024-09-23T08:55:47Z |
| publishDate | 2012 |
| publisher | Massachusetts Institute of Technology. Earth Resources Laboratory |
| record_format | dspace |
| spelling | mit-1721.1/686082019-04-10T19:47:51Z 3−D Surface Topography Boundary Conditions in Seismic Wave Modelling Hestholm, Stig Ruud, Bent Massachusetts Institute of Technology. Earth Resources Laboratory Hestholm, Stig New alternative formulations of exact boundary conditions for arbitrary three{dimensional (3−D) free surface topographies on seismic media have been derived. They are shown to be equivalent with previously published formulations, thereby serving as a verification of the validity of each set of formulations. The top of a curved grid represents the free surface topography while the grid's interior represents the physical medium. We assume the velocity{stress version of the viscoelastic wave equations to be valid in this grid before transforming the equations to a rectangular grid. In order to do the numerical discretization we apply the latter version of equations for seismic wave propagation simulation in the interior of the medium. The numerical discretization of the free surface topography boundary conditions by second−order finite−differences (F−Ds) is shown in detail, as well as spatially unconditional stability of the resulting system of equations. The F−D order is increased by two for each point away from the free surface up to eight, which is the order used in the interior. We use staggered grids both in space and time and the second-order leap-frog and Crank-Nicholson methods for wave field time propagation. We simulate point sources at the surface of a homogeneous medium, with a plane surface containing a hill and a trench, respectively. The main features of these general cases are outlined. Then, we present results using parameters typical of teleseismic earthquakes and explosions with a 200 × 100 km[superscript 2] area of real topography from southwestern Norway over a homogeneous medium. A dipping plane wave simulates a teleseismic P−wave incident on the surface topography. Results show clear conversion from P− to Rg− (short period fundamental mode Rayleigh) waves in the steepest and/or roughest topography, as well as attenuated waves in valleys and fjords. The codes are parallellized for simulation on fast supercomputers to model higher frequencies and/or larger areas than before. Research Council of Norway Massachusetts Institute of Technology. Earth Resources Laboratory United States. Army. Corps of Engineers (contract DACA89-99-C-0002) Cold Regions Research and Engineering Laboratory (U.S.) 2012-01-17T18:59:21Z 2012-01-17T18:59:21Z 2001 Technical Report http://hdl.handle.net/1721.1/68608 Earth Resources Laboratory Industry Consortia Annual Report;2001-13 application/pdf Massachusetts Institute of Technology. Earth Resources Laboratory |
| spellingShingle | Hestholm, Stig Ruud, Bent 3−D Surface Topography Boundary Conditions in Seismic Wave Modelling |
| title | 3−D Surface Topography Boundary Conditions in Seismic Wave Modelling |
| title_full | 3−D Surface Topography Boundary Conditions in Seismic Wave Modelling |
| title_fullStr | 3−D Surface Topography Boundary Conditions in Seismic Wave Modelling |
| title_full_unstemmed | 3−D Surface Topography Boundary Conditions in Seismic Wave Modelling |
| title_short | 3−D Surface Topography Boundary Conditions in Seismic Wave Modelling |
| title_sort | 3 d surface topography boundary conditions in seismic wave modelling |
| url | http://hdl.handle.net/1721.1/68608 |
| work_keys_str_mv | AT hestholmstig 3dsurfacetopographyboundaryconditionsinseismicwavemodelling AT ruudbent 3dsurfacetopographyboundaryconditionsinseismicwavemodelling |