判别分析实际应用

判别分析在地质研究工作中有着广泛的应用，下面列举几个应用算例。例4.3

生油岩热演化阶段的判别为了确定生油岩的热演化阶段，表4.3中列出了我国有关探区的66个生油岩的地层年龄、现今温度以及埋藏深度。这些生油岩处于未成熟、成熟、高成熟和过成熟四个演化阶段。共设计六个变量：、、、、、，取f1=f2=0，引入四个变量，得生油岩演化阶段判别函数式如下：

判别函数中变量的引入顺序及各演化阶段的正判率分别见表4.4和表4.5。

表4.3我国生油岩的演化参数表演化阶段序

号地区

热演化参数未成熟1松辽盆地（青2+3）337125.00510002松辽盆地（青1）32812310003松辽盆地（姚2）33412517504岐口凹陷34733.7516805泌阳凹陷34227.99914606湖北（二叠系）33824232007潜江凹陷34334.3316008高邮凹陷3481519809惠民凹陷3518.04135010沾化凹陷34410.76160011东明凹陷3528.5225012松辽盆地（姚2）228.51271480成

熟13松辽盆地（青2+3）341127155014松辽盆地（青2+1）367127219915松辽盆地（青）362124.2179916松辽盆地（姚2）364120.4185117松辽盆地（姚2）370120.4197018岐口凹陷35935200119泌阳凹陷35331170020泌阳凹陷367312099

21‘辽河凹陷36448.5200122东台凹陷（阜宁组）36434220123湖北（二叠系）348257.6345024高邮凹陷（集宁组）35617.5220025高邮凹陷（集宁组）36018270026沾化凹陷36710.7230027沾化凹陷36412.8220028沾化凹陷36813250029东明凹陷36211.63500演化阶段序

号地区热演化参数高成熟30松辽盆地（青2+3）380129310031松辽盆地（青1）377127.88235032松辽盆地（青1）402127.88249933松辽盆地（姚2）383124.64229934松辽盆地（姚2）377121.80215035松辽盆地（姚2）389125.008240136岐口凹陷41936370137湖北（二叠系）392217.25405038泌阳凹陷37634.01230039泌阳凹陷39234.05279940东台凹陷（阜宁组）41054.25320141东台凹陷（阜宁组）39837.005290042东台凹陷（阜宁组）40335.5370143湖北（二叠系）399271.25400144高邮凹陷（集宁组）38023.5300045高邮凹陷（集宁组）38224340046惠民凹陷38313280047惠民凹陷38613.5310048高邮凹陷（集宁组

）39925410049沾化凹陷38116270050沾化凹陷38516.5300051沾化凹陷38716.5310052东明凹陷41015.05355053东明凹陷41218355054松辽盆地（青2+3）4001303400演化阶段序

号地区热演化参数过成熟55松辽盆地（姚2）434123.205355556江汉盆地（潜江组）44037.005430057东台凹陷(阜宁组)44460.0054100

58东台凹陷(阜宁组)43357.005510059湖北（二叠系）469285570160湖北（二叠系）572285.5719961高邮凹陷（集宁组

）40326400162东明凹陷43520370063东明凹陷42218380064泌阳凹陷43336.05414065湖北（二叠系）454271.29520066湖北（二叠系）440271.294900判别函数中变量的引入顺序及各演化阶段的正判率分别见表4.4和表4.5。表4.4变量引入顺序及检验量

引入顺序变量号变

量

检验量190.1078229.072530.433940.2979表4.5生油岩演化阶段正判率

演化阶段正判率%演化阶段正判率%未成熟83高成熟96成

熟94过成熟92各演化阶段的正判率都超过了80%，故可把上述判别函数用于判别生油岩演化阶段。如珠江口盆地第三系生油岩为中新世至晚渐新世，地层绝对年龄约为16~30百万年，埋藏深度为2200米，地层温度104℃。按上述判别函数式计算，绝对年龄以25百万年计，判别函数值为最大值为，判定属于高成熟阶段。用Matlab程序运行结果如下：调用程序zupanbie.m运行结果如下：

解

liti3.m中的数据为：%T+273

t

H

1/H

ln(T+273)

1/(T+273)

337

125.00510001.0000000e–0036.4134590e+0001.6393443e–00332812310001.0000000e–0036.3985949e+0001.6638935e–003334

125

17505.7142857e–0046.4085288e+0001.6474465e–00334733.7516805.9523810e–0046.4297195e+0001.6129032e–003342

27.99914606.8493151e–0046.4216223e+0001.6260163e–00333824232003.1250000e–0046.4150970e+0001.6366612e–003343

34.3316006.2500000e–0046.4232470e+0001.6233766e–0033481519805.0505051e–0046.4313311e+0001.6103060e–003351

8.0413507.4074074e–0046.4361504e+0001.6025641e–00334410.7616006.2500000e–0046.4248690e+0001.6207455e–003352

8.522504.4444444e–0046.4377516e+0001.6000000e–003228.512714806.7567568e–0046.2176036e+0001.9940179e–0033411271550

6.4516129e–0046.4199949e+0001.6286645e–00336712721994.5475216e–0046.4614682e+0001.5625000e–003362124.21799

5.5586437e–0046.4536250e+0001.5748031e–003364120.41851

5.4024851e–0046.4567697e+0001.5698587e–003370120.419705.0761421e–0046.4661447e+0001.5552100e–003359352001

4.9975012e–0046.4488894e+0001.5822785e–0033533117005.8823529e–0046.4393504e+0001.5974441e–003367

3120994.7641734e–0046.4614682e+0001.5625000e–00336448.520014.9975012e–0046.4567697e+0001.5698587e–003

364342201

4.5433894e–0046.4567697e+0001.5698587e–003

348257.634502.8985507e–0046.4313311e+0001.6103060e–00335617.522004.5454545e–0046.4441313e+0001.5898251e–003

360

1827003.7037037e–0046.4504704e+0001.5797788e–00336710.723004.3478261e–0046.4614682e+0001.5625000e–00336412.8

22004.5454545e–0046.4567697e+0001.5698587e–003368

13

25004.0000000e–0046.4630295e+0001.5600624e–003

36211.6

35002.8571429e–0046.4536250e+0001.5748031e–003380

129

31003.2258065e–0046.4815771e+0001.5313936e–003

377127.88

23504.2553191e–0046.4769724e+0001.5384615e–003402

127.88

24994.0016006e–0046.5147127e+0001.4814815e–003

383124.6422994.3497173e–0046.4861608e+0001.5243902e–003

377121.821504.6511628e–0046.4769724e+0001.5384615e–003389125.00824014.1649313e–0046.4952656e+0001.5105740e–0034193637012.7019724e–0046.5395860e+0001.4450867e–003392217.2540502.4691358e–0046.4997870e+0001.5037594e–00337634.0123004.3478261e–0046.4754327e+0001.5408320e–00339234.0527993.5727045e–0046.4997870e+0001.5037594e–00341054.2532013.1240237e–0046.5264949e+0001.4641288e–003398

37.00529003.4482759e–0046.5087691e+0001.4903130e–00340335.537012.7019724e–0046.5161931e+0001.4792899e–003

399271.25

40012.4993752e–0046.5102583e+0001.4880952e–003

380

23.5

30003.3333333e–0046.4815771e+0001.5313936e–003382

24

34002.9411765e–0046.4846352e+0001.5267176e–003

383

13

28003.5714286e–0046.4861608e+0001.5243902e–003386

13.5

31003.2258065e–0046.4907235e+0001.5174507e–003

399

25

41002.4390244e–0046.5102583e+0001.4880952e–003

381

16

27003.7037037e–0046.4831074e+0001.5290520e–003

385

16.5

30003.3333333e–0046.4892049e+0001.5197568e–00338716.531003.2258065e–0046.4922398e+0001.5151515e–00341015.05

3.5502.8169014e–0046.5264949e+0001.4641288e–00341218

35502.8169014e–0046.5294188e+0001.4598540e–00340013034002.9411765e–0046.5117453e+0001.4858841e–003434123.20535552.8129395e–0046.5610307e+0001.4144272e–00344037.00543002.3255814e–0046.5694814e+0001.4025245e–00344460.00541002.4390244e–0046.5750758e+0001.3947001e–003433

57.00551001.9607843e–0046.5596152e+0001.4164306e–00346928557011.7540782e–0046.6093492e+0001.3477089e–003572285.571991.3890818e–0046.7393366e+0001.1834320e–0034032640012.4993752e–0046.5161931e+0001.4792899e–0034352037002.7027027e–0046.5624441e+0001.4124294e–0034221838002.6315789e–0046.5439118e+0001.4388489e–00343336.0541402.4154589e–0046.5596152e+0001.4164306e–003454271.2952001.9230769e–0046.5889265e+0001.3755158e–003440

271.2949002.0408163e–0046.5694814e+0001.4025245e–003

调用程序zupanbie.m运行结果如下：>>****逐步判别分析的程序实现****请输入需判别样品的组数——样品种类：4请输入需判别样品的总数：66请输入判别样品的变量数：6请输入引入变量f的检验临界值：0请输入剔除变量f的检验临界值：0请输入第1组样品数：12请输入第2组样品数：17请输入第3组样品数：15请输入第4组样品数：12每个变量的总均值为：xe(1)=383.4773xe(2)=80.2577xe(3)=2900.2879xe(4)=0.00040557xe(5)=6.4847xe(6)=0.0015301各组内变量的均值为：gxe(1,1)=332.7083gxe(1,2)=73.3653gxe(1,3)=1695.8333gxe(1,4)=0.00064833gxe(1,5)=6.4048gxe(1,6)=0.0016564gxe(2,1)=360.9412gxe(2,2)=67.0412gxe(2,3)=2248.2941gxe(2,4)=0.00046541gxe(2,5)=6.4519gxe(2,6)=0.0015777gxe(3,1)=391.8gxe(3,2)=99.9349gxe(3,3)=2963.4667gxe(3,4)=0.00035231gxe(3,5)=6.4993gxe(3,6)=0.0015048gxe(4,1)=399.9167gxe(4,2)=37.3133gxe(4,3)=3379.5833gxe(4,4)=0.00030128gxe(4,5)=6.5112gxe(4,6)=0.0014873log(q(1))=–1.7047log(q(2))=–1.3564log(q(3))=–1.4816log(q(4))=–1.7047组内离差阵为：2.034049e+004–1.049067e+004 1.886067e+005–2.810571e–0023.402608e+001 –5.751884e–002–1.049067e+0042.302532e+005 4.545354e+005 –2.017451e–002–1.842707e+001 3.237397e–0021.886067e+0054.545354e+005 1.698066e+007 –2.861530e+0002.896009e+002 –4.473231e–001–2.810571e–002–2.017451e–002 –2.861530e+0006.811783e–007–4.411376e–005 6.958914e–0083.402608e+001–1.842707e+001 2.896009e+002 –4.411376e–0055.737843e–002–9.773769e–005–5.751884e–0023.237397e–002–4.473231e–0016.958914e–008–9.773769e–005 1.676814e–007总离差阵为：6.418626e+004–7.243466e+0031.274620e+006 –2.261507e–0011.022861e+002–1.643471e–001–7.243466e+0032.617312e+0054.722953e+005 –1.567303e–002–1.381642e+0012.580041e–0021.274620e+0064.722953e+005 4.443238e+007 –7.683837e+0001.973368e+003 –3.071575e+000–2.261507e–001–1.567303e–002–7.683837e+0001.622316e–006

–3.549426e–0045.599197e–0071.022861e+002–1.381642e+001 1.973368e+003 –3.549426e–0041.637980e–001–2.645193e–004–1.643471e–0012.580041e–002–3.071575e+0005.599197e–007–2.645193e–004 4.294240e–007--------step1----------s=1im=0x1(n.s.)v(1)=0.3169x2(n.s.)v(2)=0.87973x3(n.s.)v(3)=0.38217x4(n.s.)v(4)=0.41988x5(n.s.)v(5)=0.3503x6(n.s.)v(6)=0.39048f3=44.5489u=0.3169ks=71.8235df=3x1(b.s.)im=1(nvsf)组内离差阵为：4.916303e–005

–5.157529e–001 9.272477e+000 –1.381762e–0061.672825e–003–2.827801e–0065.157529e–0012.248426e+005 5.518098e+005 –3.467011e–002–8.780205e–001 2.708457e–003–9.272477e+0005.518098e+005 1.523181e+007 –2.600921e+000–2.590515e+001 8.601900e–0021.381762e–006–3.467011e–002 –2.600921e+0006.423429e–0072.902189e–006 –9.888204e–009–1.672825e–003–8.780205e–001 –2.590515e+0012.902189e–0064.587299e–004 –1.518708e–0062.827801e–0062.708457e–003 8.601900e–002 –9.888204e–009–1.518708e–006 5.029540e–009总离差阵为： 1.557966e–005–1.128507e–0011.985815e+001 –3.523351e–006 1.593583e–003–2.560472e–0061.128507e–0012.609138e+0056.161371e+005 –4.119430e–002–2.273359e+0007.253720e–003–1.985815e+0016.161371e+0051.912079e+007 –3.192903e+000–5.784466e+0011.920534e–0013.523351e–006–4.119430e–002–3.192903e+0008.255082e–0075.447297e–006–1.913278e–008–1.593583e–003–2.273359e+000–5.784466e+0015.447297e–0067.966545e–004–2.618653e–0062.560472e–0067.253720e–0031.920534e–001 –1.913278e–008–2.618653e–0068.617901e–009--------step2----------s=2im=1x1(b.s.)v(1)=0.3169x2(n.s.)v(2)=0.86175x3(n.s.)v(3)=0.79661x4(n.s.)v(4)=0.77812x5(n.s.)v(5)=0.57582f3=14.9786u=0.18248ks=105.4704df=6x5(b.s.)im=2(nvsf)组内离差阵为：6.149365e–0032.686077e+0001.037394e+002 –1.196502e–005–3.646646e+0002.710390e–006–2.686077e+0002.231621e+005 5.022267e+005 –2.911525e–0021.914025e+003 –1.983883e–004–1.037394e+0025.022267e+0051.376891e+007 –2.437030e+0005.647146e+004 2.553224e–0041.196502e–005–2.911525e–002 –2.437030e+0006.239820e–007

–6.326575e–003 –2.799825e–010–3.646646e+000–1.914025e+003 –5.647146e+0046.326575e–0032.179932e+003 –3.310681e–003–2.710390e–006–1.983883e–004 2.553224e–004 –2.799825e–0103.310681e–0031.581493e–012总离差阵为：3.203293e–0034.434649e+000 1.355674e+002 –1.441982e–005–2.000344e+000 2.677734e–006–4.434649e+0002.544265e+005 4.510697e+005 –2.564972e–0022.853632e+003 –2.189520e–004–1.355674e+0024.510697e+005 1.492072e+007 –2.797377e+0007.260947e+004 1.914416e–0031.441982e–005–2.564972e–002 –2.797377e+0007.882612e–007–6.837715e–003 –1.227183e–009–2.000344e+000–2.853632e+003 –7.260947e+0046.837715e–0031.255249e+003 –3.287062e–003–2.677734e–006–2.189520e–004 1.914416e–003 –1.227183e–0093.287062e–0031.022709e–011--------step3----------s=3im=2x1(b.s.)v(1)=0.52091x2(n.s.)v(2)=0.87712x3(n.s.)v(3)=0.9228x4(n.s.)v(4)=0.79159x5(b.s.)v(5)=0.57582f3=5.2655u=0.14445ks=118.9929df=9x4(b.s.)im=3(nvsf)组内离差阵为：6.378797e–003 2.127784e+000 5.700869e+0011.917526e+001 –3.767960e+000 2.705022e–006–2.127784e+000 2.218035e+005 3.885139e+0054.666040e+004 1.618825e+003–2.114524e–004–5.700869e+001 3.885139e+005 4.250820e+0063.905609e+006 3.176233e+004–8.381798e–0041.917526e+001–4.666040e+004–3.905609e+0061.602610e+006–1.013903e+004–4.487028e–004–3.767960e+000–1.618825e+003–3.176233e+004–1.013903e+004 2.244077e+003–3.307842e–003–2.705022e–006 –2.114524e–004–8.381798e–0044.487028e–0043.307842e–0031.455864e–012总离差阵为：3.467077e–0033.965433e+000 8.439438e+0011.829320e+001–2.125427e+000 2.655285e–006–3.965433e+0002.535918e+005 3.600441e+0053.253962e+0042.631136e+003 –2.588841e–004–8.439438e+0013.600441e+005 4.993396e+0063.548795e+0064.834382e+004 –2.440603e–0031.829320e+001–3.253962e+004 –3.548795e+0061.268615e+006–8.674429e+003 –1.556822e–003–2.125427e+000–2.631136e+003 –4.834382e+004 –8.674429e+0031.314563e+003 –3.276417e–003–2.655285e–006–2.588841e–004 –2.440603e–0031.556822e–0033.276417e–003 8.316582e–012--------step4----------s=4im=3x1(b.s.)v(1)=0.54353x2(n.s.)v(2)=0.87465x3(n.s.)v(3)=0.85129x4(b.s.)v(4)=0.79159x5(b.s.)v(5)=0.58579f4=5.2655f3=3.4356u=0.12297ks=127.8467df=12x3(b.s.)im=4(nvsf)组内离差阵为：7.143353e–003–3.082662e+000–1.341122e–005–3.320373e+001 –4.193931e+0002.716263e–0063.082662e+000 1.862944e+005–9.139740e–002–3.103021e+005 –1.284170e+003–1.348450e–004–1.341122e–005 9.139740e–0022.352487e–0079.187896e–0017.472047e–003–1.971807e–010–3.320373e+001 3.103021e+0059.187896e–0015.191044e+006 1.904386e+004–1.218814e–003–4.193931e+000 1.284170e+0037.472047e–0031.904386e+004 2.481407e+003–3.314105e–003–2.716263e–006 –1.348450e–0041.971807e–0101.218814e–0033.314105e–0031.290591e–012总离差阵为：4.893444e–003

–2.119744e+000

–1.690120e–005 –4.168570e+001–2.942496e+0002.696534e–0062.119744e+0002.276312e+005–7.210406e–002 –2.233429e+005–8.546504e+002–8.290663e–005–1.690120e–0057.210406e–0022.002645e–0077.106977e–0019.681552e–003 –4.887663e–010–4.168570e+0012.233429e+005 7.106977e–0013.790736e+0062.568342e+004 –3.291354e–003–2.942496e+0008.546504e+002 9.681552e–0032.568342e+0041.782606e+003 –3.300046e–003–2.696534e–006–8.290663e–0054.887663e–0103.291354e–0033.300046e–003 7.123697e–012-------step5----------s=5im=4x1(b.s.)v(1)=0.68503x2(n.s.)v(2)=0.8184x3(b.s.)v(3)=0.85129x4(b.s.)v(4)=0.73025x5(b.s.)v(5)=0.71839f4=3.4356f3=4.2899u=0.10064ks=138.9229df=15x2(b.s.)im=5(nvsf)组内离差阵为：7.194363e–0031.654726e–005 –1.492360e–005 –3.833838e+001–4.215181e+0002.714031e–0061.654726e–0055.367849e–006 –4.906074e–007 –1.665655e+000–6.893231e–003 –7.238275e–010–1.492360e–005–4.906074e–007 2.800889e–0071.071026e+0008.102071e–003–1.310248e–010–3.833838e+001–1.665655e+000 1.071026e+0005.707900e+0062.118285e+004 –9.942084e–004–4.215181e+000–6.893231e–003 8.102071e–0032.118285e+0042.490259e+003 –3.313175e–003–2.714031e–0067.238275e–0101.310248e–0109.942084e–0043.313175e–003 1.192986e–012

总离差阵为：4.913183e–0039.312188e–006–1.757265e–005 –4.376551e+001–2.950455e+0002.695762e–0069.312188e–006

4.393071e–006 –3.167583e–007 –9.811613e–001–3.754540e–003 –3.642147e–010–1.757265e–005–3.167583e–007 2.231041e–0077.814434e–001

9.952270e–003 –4.625049e–010–4.376551e+001–9.811613e–001 7.814434e–0014.009871e+0062.652197e+004 –3.210009e–003–2.950455e+000–3.754540e–003 9.952270e–0032.652197e+0041.785815e+003 –3.299734e–003–2.695762e–0063.642147e–0104.625049e–0103.210009e–0033.299734e–003 7.093501e–012--------step6----------s=6im=5x1(b.s.)v(1)=0.68292x2(b.s.)v(2)=0.8184x3(b.s.)v(3)=0.79655x4(b.s.)v(4)=0.70251x5(b.s.)v(5)=0.71712f4=4.2899f3=–18.9981****既不需要删除变量，亦不需要添加变量********由所选变量计算的结果如下：****每组离差系数为：-----group1------b1(1)=–2644455.9755b(1,1)=–1528.4765b(1,2)=–2.4901b(1,3)=2.9798b(1,4)=7955330.2457b(1,5)=903602.3678b(1,6)=0-----group2------b1(2)=–2644031.8974b(2,1)=–1528.2636b(2,2)=–2.4812b(2,3)=2.9749b(2,4)=7922624.1831b(2,5)=903529.137b(2,6)=0-----group3------b1(3)=–2640866.4207b(3,1)=–1527.25b(3,2)=–2.469b(3,3)=2.9741b(3,4)=7915617.1801b(3,5)=902982.0094b(3,6)=0-----group4------b1(4)=–2640210.1641b(4,1)=–1527.0689b(4,2)=