{"title":"高性能三维电磁建模使用改进的诺伊曼系列。宽带数值解和实例","authors":"D. Avdeev, A. Kuvshinov, O. Pankratov, G. Newman","doi":"10.5636/JGG.49.1519","DOIUrl":null,"url":null,"abstract":"We present a new, accurate, high-performance, wide-band three-dimensional (3-D) solver for the electromagnetic (EM) field scattering problem in an isotropic earth. The solver relates to those based on the volume integral equation (IE) approach and exploits a modified Neumann series (MNS) technique to solve Maxwell's equations. The solver allows for the conduction, polarization and displacement currents to be taken into account and admits for 3-D earth excitation by arbitrary electric or/and magnetic sources. We estimate the solver efficiency for scatterers discretized into Nx × Ny × Nz prisms, where it requires only about 6NxNyNz (log2(2Nx) log2(2Ny) + 6Nz) multiplications to get one term of the MNS expansion and about 200 NxNyNz2 bytes of memory. Our experience show that the number of terms N which are to be summed up to get the solution to 1% accuracy doesn't exceed fifty for the models with the conductivity contrast of up to 100. We demonstrate the solver versatility for magnetotellurics (MT) and controlled-source simulations. EM fields arising from a 3-D model with two high-contrast thin layers residing in layered earth were simulated due to a 10 Hz electric dipole located at the surface. When the layers were discretized into 16, 384 prisms our code on a Pentium-100 MHz took T ∼ 58 minutes, M ∼ 7 Mbytes and N ∼ 280. We also modeled the 0.1 Hz and 0.01 Hz MT responses within 3-D model with 1 Ω·m and 100 Ω·m blocks. When the blocks were discretized into 8, 000 prisms the code took T ∼ 5 minutes, M ∼ 8 Mbytes, and N ∼ 25. Finally fields for a crosswell model including a 3-D conducting target were simulated for 0.1 kHz and 10 kHz electric and magnetic dipoles in the wellbores. While the target was discretized into 6, 250 prisms the code took T ∼ 16 minutes, M ∼ 13 Mbytes, and N ∼ 24. All simulations showed from very good to excellent agreement with those of the other 3-D solvers.","PeriodicalId":156587,"journal":{"name":"Journal of geomagnetism and geoelectricity","volume":"49 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1997-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"94","resultStr":"{\"title\":\"High-Performance Three-Dimensional Electromagnetic Modelling Using Modified Neumann Series. Wide-Band Numerical Solution and Examples\",\"authors\":\"D. Avdeev, A. Kuvshinov, O. Pankratov, G. Newman\",\"doi\":\"10.5636/JGG.49.1519\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present a new, accurate, high-performance, wide-band three-dimensional (3-D) solver for the electromagnetic (EM) field scattering problem in an isotropic earth. The solver relates to those based on the volume integral equation (IE) approach and exploits a modified Neumann series (MNS) technique to solve Maxwell's equations. The solver allows for the conduction, polarization and displacement currents to be taken into account and admits for 3-D earth excitation by arbitrary electric or/and magnetic sources. We estimate the solver efficiency for scatterers discretized into Nx × Ny × Nz prisms, where it requires only about 6NxNyNz (log2(2Nx) log2(2Ny) + 6Nz) multiplications to get one term of the MNS expansion and about 200 NxNyNz2 bytes of memory. Our experience show that the number of terms N which are to be summed up to get the solution to 1% accuracy doesn't exceed fifty for the models with the conductivity contrast of up to 100. We demonstrate the solver versatility for magnetotellurics (MT) and controlled-source simulations. EM fields arising from a 3-D model with two high-contrast thin layers residing in layered earth were simulated due to a 10 Hz electric dipole located at the surface. When the layers were discretized into 16, 384 prisms our code on a Pentium-100 MHz took T ∼ 58 minutes, M ∼ 7 Mbytes and N ∼ 280. We also modeled the 0.1 Hz and 0.01 Hz MT responses within 3-D model with 1 Ω·m and 100 Ω·m blocks. When the blocks were discretized into 8, 000 prisms the code took T ∼ 5 minutes, M ∼ 8 Mbytes, and N ∼ 25. Finally fields for a crosswell model including a 3-D conducting target were simulated for 0.1 kHz and 10 kHz electric and magnetic dipoles in the wellbores. While the target was discretized into 6, 250 prisms the code took T ∼ 16 minutes, M ∼ 13 Mbytes, and N ∼ 24. All simulations showed from very good to excellent agreement with those of the other 3-D solvers.\",\"PeriodicalId\":156587,\"journal\":{\"name\":\"Journal of geomagnetism and geoelectricity\",\"volume\":\"49 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1997-11-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"94\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of geomagnetism and geoelectricity\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.5636/JGG.49.1519\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of geomagnetism and geoelectricity","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.5636/JGG.49.1519","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
High-Performance Three-Dimensional Electromagnetic Modelling Using Modified Neumann Series. Wide-Band Numerical Solution and Examples
We present a new, accurate, high-performance, wide-band three-dimensional (3-D) solver for the electromagnetic (EM) field scattering problem in an isotropic earth. The solver relates to those based on the volume integral equation (IE) approach and exploits a modified Neumann series (MNS) technique to solve Maxwell's equations. The solver allows for the conduction, polarization and displacement currents to be taken into account and admits for 3-D earth excitation by arbitrary electric or/and magnetic sources. We estimate the solver efficiency for scatterers discretized into Nx × Ny × Nz prisms, where it requires only about 6NxNyNz (log2(2Nx) log2(2Ny) + 6Nz) multiplications to get one term of the MNS expansion and about 200 NxNyNz2 bytes of memory. Our experience show that the number of terms N which are to be summed up to get the solution to 1% accuracy doesn't exceed fifty for the models with the conductivity contrast of up to 100. We demonstrate the solver versatility for magnetotellurics (MT) and controlled-source simulations. EM fields arising from a 3-D model with two high-contrast thin layers residing in layered earth were simulated due to a 10 Hz electric dipole located at the surface. When the layers were discretized into 16, 384 prisms our code on a Pentium-100 MHz took T ∼ 58 minutes, M ∼ 7 Mbytes and N ∼ 280. We also modeled the 0.1 Hz and 0.01 Hz MT responses within 3-D model with 1 Ω·m and 100 Ω·m blocks. When the blocks were discretized into 8, 000 prisms the code took T ∼ 5 minutes, M ∼ 8 Mbytes, and N ∼ 25. Finally fields for a crosswell model including a 3-D conducting target were simulated for 0.1 kHz and 10 kHz electric and magnetic dipoles in the wellbores. While the target was discretized into 6, 250 prisms the code took T ∼ 16 minutes, M ∼ 13 Mbytes, and N ∼ 24. All simulations showed from very good to excellent agreement with those of the other 3-D solvers.