地震学报
地震學報
지진학보
ACTA SEISMOLOGICA SINICA
2015年
2期
278-288
,共11页
全局优化%旋转交错网格%紧致有限差分%数值频散%正演模拟
全跼優化%鏇轉交錯網格%緊緻有限差分%數值頻散%正縯模擬
전국우화%선전교착망격%긴치유한차분%수치빈산%정연모의
global optimization%rotated staggered grid%compact finite differ-ence%numerical dispersion%forward modeling
在地震波场数值模拟中,交错网格有限差分技术得到了广泛的应用,但是在弹性模量变化较大时,通常会因插值而导致模拟误差增大。旋转交错网格可以很好地克服这个缺点,因而适合于各向异性介质正演模拟。但是对于同样大小的网格单元,旋转交错网格需要的步长比常规交错网格要大,这会使梯度和散度算子的误差增大因而更易产生空间数值频散。针对这些问题,本文提出了旋转交错网格与紧致有限差分相结合的方法,并基于模拟退火算法进行全局优化,压制数值频散,拓宽波数范围。数值模拟结果表明,此方法可以有效地压制数值频散,且具有较高的模拟精度。
在地震波場數值模擬中,交錯網格有限差分技術得到瞭廣汎的應用,但是在彈性模量變化較大時,通常會因插值而導緻模擬誤差增大。鏇轉交錯網格可以很好地剋服這箇缺點,因而適閤于各嚮異性介質正縯模擬。但是對于同樣大小的網格單元,鏇轉交錯網格需要的步長比常規交錯網格要大,這會使梯度和散度算子的誤差增大因而更易產生空間數值頻散。針對這些問題,本文提齣瞭鏇轉交錯網格與緊緻有限差分相結閤的方法,併基于模擬退火算法進行全跼優化,壓製數值頻散,拓寬波數範圍。數值模擬結果錶明,此方法可以有效地壓製數值頻散,且具有較高的模擬精度。
재지진파장수치모의중,교착망격유한차분기술득도료엄범적응용,단시재탄성모량변화교대시,통상회인삽치이도치모의오차증대。선전교착망격가이흔호지극복저개결점,인이괄합우각향이성개질정연모의。단시대우동양대소적망격단원,선전교착망격수요적보장비상규교착망격요대,저회사제도화산도산자적오차증대인이경역산생공간수치빈산。침대저사문제,본문제출료선전교착망격여긴치유한차분상결합적방법,병기우모의퇴화산법진행전국우화,압제수치빈산,탁관파수범위。수치모의결과표명,차방법가이유효지압제수치빈산,차구유교고적모의정도。
Staggered grid finite difference techniques have been widely used in numerical simulation of seismic wave field,but the interpolation might enlarge the simulation errors when the elastic moduli change dramatically.Rotated staggered grid can overcome this drawback thus be more applicable for modeling the anisotropic media.However,for the grid cells with the same size,rotated staggered grid needs larger step than conventional staggered grid does,conse-quently,the gradient operator and divergence operator generate larger errors which are more likely to cause spatial numerical dispersion.Aiming at the above problems,a combination of rotated staggered grid and compact finite difference method is proposed,simultaneously,global optimization is preformed based on simulated annealing algorithm to suppress numerical dispersion and to broaden the range of wavenumber.Numerical simulation results show that this method can effectively suppress the numerical dispersion and exhibits high simulation accuracy at the same time.