斯奈爾定律和Zoeppritz方程

1、斯奈爾定律和Zoeppritz方程姓名：學(xué)號(hào)：專業(yè)：地球物理勘察技術(shù)2012級(jí)一、實(shí)驗(yàn)?zāi)康? .利用密度、上下界面的縱橫波速度通過(guò)斯奈爾定律求出該界面的0°90°入射角的反射角度和透射角度。sin:sin*sin1sin：2sin2pVpiVpiVsiVp2Vs22 .利用Zoeppritz方程繪制反射系數(shù)和透射系數(shù)曲線。、實(shí)驗(yàn)步驟1、模型:3Vpi=3300m/sVsi=1585m/spi=2.4g/cm3Vpi=3100m/sVsi=1989m/spi=2.24g/cmvS|=1585m7l口I=2.4f/cm3+a.5a/_1"百）_.，制工囊Sioom/e

2、m辦=1989m由ITT反射系數(shù)和透射系數(shù)曲稅情】地做模型；ib）現(xiàn)波（P）人尉：fcl信施蟲AMN*加.討7WW一薩一而7而7前入射由u）計(jì)算從090度的反射透射系數(shù)曲線如圖1-1-4表1-1-1Zoeppri”方程使用的彈性參做懣rrkM與法我火酊人用縱波VF|入川波rsi的/反射綱波rR%工1_耳射橫枝rS|w四詵射微波3"八選的橫波r$.3胖於比K上巴下面即為平面波人射在平:界血上計(jì)算縱橫波反射桁透射能量的Zoeppricz方程(C.T.Richten1958)/縱波入射(七-Qp/sinM+Q_co§3t-nsina5+“力8$生=0(ap+an)cosa+sin

3、/.acosa,-=02-G/p+)sin2a+."Cos26+“*8年",-sin2atIK、Ki|1rI<VSIVCIrSI(1一1-15)*>lVP1一a<K»vvcos鞏70SI-(，Ppjcos2儲(chǔ)+“：,sin2MPIvv十a(chǎn)*.KJco$2p*Ksin2，=02垂Jl偏振橫波(SV)入射(。$+。皿)sin+drkCOMi-"mCosa?+<is|sin/j：=0伍-aJcos/+f/sini,+1nsina.一八必=0vci/，rv(。、一eos2/-4/-sinlxK-:$ii】2ot,、K-rKatIrimVv

4、n1(>r«一!K產(chǎn),cos2/：-0vsi一(八一?！?sin2/+.dco$2/J+“cos2”、'SISi+act/fS加2戶,=0SIy03rsi3.水平偏振橫波(SH)入射51(I-1-17)三、實(shí)驗(yàn)結(jié)果P波入射的反射透射角度:snellp波入射的反射透射系數(shù)曲線:SV波入射的反射透射角度正弦值:圖3SV波入射的反射透射系數(shù)曲線:SH波入射的反射透射角度正弦值:04網(wǎng)。吊做n=n»目口6SHkT5H圖5SH波入射的反射透射系數(shù)曲線：圖6四、實(shí)驗(yàn)分析因?yàn)楦鞑ǚ瓷浜屯干洳ㄕ穹禂?shù)與其能量成正比，由此可以看出其能量的變化以及入射波能量的分配。當(dāng)上層介質(zhì)為密

5、介質(zhì)，下層介質(zhì)為疏介質(zhì)時(shí)：由圖2知，P波從上層密介質(zhì)入射到界面時(shí)：隨著入射角增大，P波反射系數(shù)、P波透射系數(shù)在減小，即隨著入射角的增大，反射P波、透射P波的能量在減小，而S波反射系數(shù)、S波透射系數(shù)在增大，即隨著入射角的增大，反射S波、透射S波的能量在增大。說(shuō)明當(dāng)入射角發(fā)生變化時(shí)，入射波的能量分配在改變。由圖4可知，SV波從上層密介質(zhì)入射到界面時(shí)：入射角小于29度時(shí)，隨著入射角增大，SV波反射系數(shù)在減小，P波反射系數(shù)、SV波透射系數(shù)、P波透射系數(shù)在增大，SV波透射系數(shù)最大，即反射SV波能量在減小，反射P波、透射SV波、透射P波能量在增大，透射SV波的能量最大；入射角大于等于29度且小于31度時(shí)，

6、SV波反射系數(shù)、SV波透射系數(shù)減小,P波反射系數(shù)、P波透射系數(shù)在增大，SV波透射系數(shù)最大，即隨著入射角的增大，反射SV波、透射SV波能量在減小，反射P波、透射P波能量在增大，透射SV波能量最大；入射角大于等于31度且小于53度時(shí)，SV波透射系數(shù)增大，SV波反射系數(shù)、P波反射系數(shù)、P波透射系數(shù)先減小后增大，SV波透射系數(shù)仍最大，即隨著入射角的增大，透射SV波能量增大，反射SV波、反射P波、透射P波能量先減小后增大，透射SV波能量最大；入射角大于53度時(shí)，SV波反射系數(shù)為1,SV波透射系數(shù)、P波反射系數(shù)、P波透射系數(shù)減小，即隨著入射角的增大，反射SV波能量不變，透射SV波、反射P波、透射P波能量減

7、小。由圖6可知，SH波從上層密介質(zhì)入射到界面時(shí)：不產(chǎn)生轉(zhuǎn)換波，入射角小于臨界角時(shí)，SH波的反射系數(shù)、透射系數(shù)均隨著入射角的增大而增大，即反射、透射SH波能量增大；入射角大于等于臨界角時(shí)，隨著入射角的增大，SH波的反射系數(shù)幾乎不變，透射系數(shù)減小，即反射SH波的能量減小，透射SH波的能量幾乎不變。五、附：源程序代碼P波入射時(shí)，程序：#include<stdio.h>#include<math.h>#include"6GAUS.C"#definePI3.1415926voidmain()FILE*fp1,*fp2;inti,n91;doubleipp,x1

8、,x2,y1,y2,pr,sr,pt,st,a195,a295,b195,b295,vp1=3300,vp2=3100,vs1=1585,vs2=1989,den1=2.4,den2=2.24,k=den2/den1;staticdoublea44=0.0,b4=0.0;fp1=fopen("snell.csv","w");fp2=fopen("P波入射反射透射系數(shù).csv","w");for(i=0;i<=90;i+)ni=i;ipp=i*PI/180;x1=ipp;a1i=x1*180/PI;x2=sin

9、(ipp)*vs1/vp1;a2i=asin(x2)*180/PI;y1=sin(ipp)*vp2/vp1;b1i=asin(y1)*180/PI;y2=sin(ipp)*vs2/vp1;b2i=asin(y2)*180/PI;fprintf(fp1,"%d,%f,%f,%f,%fn",ni,a1i,a2i,b1i,b2i);/*輸出P波入射反射投射角度*/pr=a1i*PI/180;sr=a2i*PI/180;pt=b1i*PI/180;st=b2i*PI/180;a00=sin(pr);a01=cos(sr);a02=-sin(pt);a03=-cos(st);a10=

10、cos(pr);a11=-sin(sr);a12=cos(pt);a13=-sin(st);a20=sin(2*pr);a21=cos(2*sr)*vp1/vs1;a22=sin(2*pt)*k*vp1*pow(vs2/vs1,2)/vp2;a23=cos(2*st)*k*vp1*vs2/pow(vs1,2);a30=cos(2*sr);a31=-sin(2*pr)*vs1/vp1;a32=-cos(2*st)*k*vp2/vp1;a33=sin(2*pt)*k*vs2/vp1;/*輸入系數(shù)矩陣*/b0=-sin(pr);b1=cos(pr);b2=sin(2*pr);b3=-cos(2*sr

11、);if(gaus(a,b,4)!=0)fprintf(fp2,"%d,%f,%f,%f,%fn",ni,b0,b1,b2,b3);)fclose(fp1);fclose(fp2);)SV波入射時(shí)，程序：#include<stdio.h>#include<math.h>#include"4CINV.C"#include"4TCMUL.C"#definePI3.1415926voidmain()FILE*fp1,*fp2;inti,n91;doublein,ipp1,ipp2,ipp3,x1,x2,y1,y2,p

12、r,sr,pt,st,p,rsp,rss,tsp,tss,a191,a291,b191,b291,vp1=3300,vp2=3100,vs1=1585,vs2=1989,den1=2.4,den2=2.24,k=den2/den1;staticdoublear44,ai44,br4,bi4,cr41,ci41;fp1=fopen("snell.csv","w");fp2=fopen("SV波入射反射透射系數(shù).csv","w");ipp1=asin(vs1/vp1);ipp2=asin(vs1/vs2);ipp3=a

13、sin(vs1/vp2);/*臨界角*/for(i=0;i<=90;i+)ni=i;in=i*PI/180;p=sin(in)/vs1;x1=p*vs1;x2=p*vp1;y1=p*vs2;y2=p*vp2;/*snell定律a1i=x1;a2i=x2;b1i=y1;b2i=y2;fprintf(fp1,"%d,%f,%f,%f,%fn",ni,a1i,a2i,b1i,b2i);if(in<ipp1)(sr=asin(x1);pr=asin(x2);st=asin(y1);pt=asin(y2);ar00=-sin(pr);ar01=cos(sr);ar02=s

14、in(pt);ar03=cos(st);ar10=-cos(pr);ar11=-sin(sr);ar12=-cos(pt);ar13=sin(st);ar20=2*cos(pr)*sin(pr)*vs1/vp1;ar21=-(1-2*sin(sr)*sin(sr);ar22=2*cos(pt)*sin(pt)*k*vs2*vs2/(vs1*vp1);ar23=(1-2*sin(st)*sin(st)*k*vs2/vs1;ar30=(1-2*sin(sr)*sin(sr)*vp1/vs1;ar31=2*cos(sr)*sin(sr);ar32=-(1-2*sin(st)*sin(st)*k*vp

15、2/vp1;ar33=2*cos(st)*sin(st)*k*vs2/vp1;br0=cos(sr);br1=sin(sr);br2=1-2*sin(sr)*sin(sr);br3=2*cos(sr)*sin(sr);if(cinv(ar,ai,4)!=0)/*求系數(shù)矩陣的逆矩陣*/(tcmul(ar,ai,br,bi,4,4,1,cr,ci);rsp=sqrt(cr00*cr00+ci00*ci00);rss=sqrt(cr10*cr10+ci10*ci10);tsp=sqrt(cr20*cr20+ci20*ci20);tss=sqrt(cr30*cr30+ci30*ci30);/*求S波入

16、射反射透射系數(shù)*/fprintf(fp2,"%d,%f,%f,%f,%fn",ni,rsp,rss,tsp,tss);*輸出S波入射反射透射系數(shù)*/elseif(in>=ipp1&&in<ipp3)(sr=asin(x1);st=asin(y1);pt=asin(y2);ar00=-p*vp1,ai00=0;ar01=cos(sr),ai01=0;ar02=sin(pt),ai02=0;ar03=cos(st),ai03=0;ar10=0,ai10=-sqrt(p*p*vp1*vp1-1);ar11=-sin(sr),ai11=0;ar12=-c

17、os(pt),ai12=0;ar13=sin(st),ai13=0;ar20=0,ai20=2*p*vp1*sqrt(p*p*vp1*vp1-1)*vs1/vp1;ar21=-(1-2*sin(sr)*sin(sr),ai21=0;ar22=2*cos(pt)*sin(pt)*k*vs2*vs2/(vs1*vp1),ai22=0;ar23=(1-2*sin(st)*sin(st)*k*vs2/vs1,ai23=0;ar30=(1-2*sin(sr)*sin(sr)*vp1/vs1,ai30=0;ar31=2*cos(sr)*sin(sr),ai31=0;ar32=-(1-2*sin(st)*s

18、in(st)*k*vp2/vp1,ai32=0;ar33=2*cos(st)*sin(st)*k*vs2/vp1,ai33=0;/*輸入系數(shù)矩陣br0=cos(sr),bi0=0;br1=sin(sr),bi1=0;br2=1-2*sin(sr)*sin(sr),bi2=0;br3=2*cos(sr)*sin(sr),bi3=0;if(cinv(ar,ai,4)!=0)/*求系數(shù)矩陣的逆矩陣*/(tcmul(ar,ai,br,bi,4,4,1,cr,ci);rsp=sqrt(cr00*cr00+ci00*ci00);rss=sqrt(cr10*cr10+ci10*ci10);tsp=sqrt(

19、cr20*cr20+ci20*ci20);tss=sqrt(cr30*cr30+ci30*ci30);/*求S波入射反射透射系數(shù)*/fprintf(fp2,"%d,%f,%f,%f,%fn",ni,rsp,rss,tsp,tss);*輸出S波入射反射透射系數(shù)*/elseif(in>=ipp3&&in<ipp2)(sr=asin(x1);st=asin(y1);ar00=-p*vp1,ai00=0;ar01=cos(sr),ai01=0;ar02=p*vp2,ai02=0;ar03=cos(st),ai03=0;ar10=0,ai10=-sqrt(

20、p*p*vp1*vp1-1);ar11=-sin(sr),ai11=0;ar12=0,ai12=-sqrt(p*p*vp2*vp2-1);ar13=sin(st),ai13=0;ar20=0,ai20=2*p*vp1*sqrt(p*p*vp1*vp1-1)*vs1/vp1;ar21=-(1-2*sin(sr)*sin(sr),ai21=0;ar22=0,ai22=2*p*vp2*sqrt(p*p*vp2*vp2-1)*k*vs2*vs2/(vs1*vp1);ar23=(1-2*sin(st)*sin(st)*k*vs2/vs1,ai23=0;ar30=(1-2*sin(sr)*sin(sr)*

21、vp1/vs1,ai30=0;ar31=2*cos(sr)*sin(sr),ai31=0;ar32=-(1-2*sin(st)*sin(st)*k*vp2/vp1,ai32=0;ar33=2*cos(st)*sin(st)*k*vs2/vp1,ai33=0;/*輸入系數(shù)矩陣br0=cos(sr),bi0=0;br1=sin(sr),bi1=0;br2=1-2*sin(sr)*sin(sr),bi2=0;br3=2*cos(sr)*sin(sr),bi3=0;/*輸入常數(shù)矩陣if(cinv(ar,ai,4)!=0)/*求系數(shù)矩陣的逆矩陣tcmul(ar,ai,br,bi,4,4,1,cr,ci)

22、;rsp=sqrt(cr00*cr00+ci00*ci00);rss=sqrt(cr10*cr10+ci10*ci10);tsp=sqrt(cr20*cr20+ci20*ci20);tss=sqrt(cr30*cr30+ci30*ci30);/*求S波入射反射透射系數(shù)*/fprintf(fp2,"%d,%f,%f,%f,%fn",ni,rsp,rss,tsp,tss);*輸出S波入射反射透射系數(shù)*/elseif(in>=ipp2)sr=asin(x1);ar00=-p*vp1,ai00=0;ar01=cos(sr),ai01=0;ar02=p*vp2,ai02=0;a

23、r03=0,ai03=sqrt(p*p*vs2*vs2-1);ar10=0,ai10=-sqrt(p*p*vp1*vp1-1);ar11=-sin(sr),ai11=0;ar12=0,ai12=-sqrt(p*p*vp2*vp2-1);ar13=p*vp2,ai13=0;ar20=0,ai20=2*p*vp1*sqrt(p*p*vp1*vp1-1)*vs1/vp1;ar21=-(1-2*sin(sr)*sin(sr),ai21=0;ar22=0,ai22=2*p*vp2*sqrt(p*p*vp2*vp2-1)*k*vs2*vs2/(vs1*vp1);ar23=(1-2*p*p*vs2*vs2)

24、*k*vs2/vs1,ai23=0;ar30=(1-2*sin(sr)*sin(sr)*vp1/vs1,ai30=0;ar31=2*cos(sr)*sin(sr),ai31=0;ar32=-(1-2*p*p*vs2*vs2)*k*vp2/vp1,ai32=0;ar33=0,ai33=2*p*vs2*sqrt(p*p*vs2*vs2-1)*k*vs2/vp1;/*輸入系數(shù)矩陣br0=cos(sr),bi0=0;br1=sin(sr),bi1=0;br2=1-2*sin(sr)*sin(sr),bi2=0;br3=2*cos(sr)*sin(sr),bi3=0;/*輸入常數(shù)矩陣if(cinv(ar

25、,ai,4)!=0)/*求系數(shù)矩陣的逆矩陣tcmul(ar,ai,br,bi,4,4,1,cr,ci);rsp=sqrt(cr00*cr00+ci00*ci00);rss=sqrt(cr10*cr10+ci10*ci10);tsp=sqrt(cr20*cr20+ci20*ci20);tss=sqrt(cr30*cr30+ci30*ci30);/*求S波入射反射透射系數(shù)*/fprintf(fp2,"%d,%f,%f,%f,%fn",ni,rsp,rss,tsp,tss);*輸出S波入射反射透射系數(shù)*/)fclose(fpl);fclose(fp2);)SH波入射時(shí)，程序：#include<stdio.h>#include<math.h>#definePI3.1415926voidmain()FILE*fp1,*fp2;inti,n91