规则形体(球体、水平柱体、垂直台阶)重力异常的正演计算

来源：华佗小知识

注释：gVerticalStep=0.0000000667*0.5*(3.1415926327*（dlow-dup）+X* 垂直台阶剩余异常计算cm3gs2d(dup)D(dlow)100200100200100200100200100200100200100200100200100200100200100200100200100200100200100200100200100200100200100200g垂直[台阶G200100100200100200100200100200100200100200100200100200100200100200100200100200100200100200100200100200100200ln(（X2+D2)arctgX/DarctdX/dD-dX/(X2+d2)）ABC100-8000.045120435-1.32582-1.444100-7800.047372293-1.31979-1.44329100-7600.049794554-1.31347-1.43997100-7400.052404585-1.30683-1.437100-7200.055221979-1.29985-1.43279100-7000.0582608-1.2925-1.42100-6800.061570531-1.28474-1.42478100-6600.065155476-1.27656-1.42042100-00.0690522-1.26791-1.4158100-6200.073310784-1.25875-1.41088100-6000.077961541-1.24905-1.40565100-5800.083058231-1.23874-1.40006100-5600.088658146-1.22777-1.39409100-5400.094827787-1.21609-1.38769100-5200.1014633-1.20362-1.38081100-5000.109199292-1.19029-1.3734100-4800.117598142-1.17601-1.3654100-4600.12696657-1.16067-1.356742100-4400.137452966-1.14417-1.34732X2DXXDd100Xln2Darctg2darctg2Dd]-420X2d0.1492335-1.12638-1.33705100-4000.1625129-1.10715-1.32582100-3800.177560674-1.08632-1.31347100-3600.194661533-1.0637-1.29985100-3400.214186358-1.03907-1.28474100-3200.236576062-1.0122-1.26791100-3000.26232-0.98279-1.24905100-2800.292196753-0.95055-1.22777100-2600.326853221-0.9151-1.20362100-2400.36726951-0.87606-1.17601100-2200.41455608-0.83298-1.14417100-2000.470003629-0.7854-1.10715100-1800.535057937-0.73282-1.0637100-1600.611230058-0.67474-1.0122100-1400.699881213-0.61073-0.95055100-1200.801781022-0.54042-0.87606100-1000.916290732-0.46365-0.7854100-801.040018124-0.38051-0.67474100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200300300300100-60100-40100-201000100201004010060100801001001001201001401001601001801002001002201002401002601002801003001003201003401003601003801004001004201004401004601004801005001005201005401005601005801006001006201000100660100680100700100720100740100760100780100800100-800100-780100-7601.19873581.2770950691.3570239791.3862943611.3570239791.2770950691.19873581.0400181240.9162907320.8017810220.6998812130.6112300580.5350579370.4700036290.414556080.367269510.3268532210.2921967530.262320.2365760620.2141863580.1946615330.1775606740.16251290.14923350.1374529660.126966570.1175981420.1091992920.10146330.0948277870.0886581460.0830582310.0779615410.0733107840.06905220.0651554760.0615705310.05826080.0552219790.0524045850.0497945540.0473722930.0451204350.0709517360.0742842150.077848193-0.29146-0.1974-0.0996700.0996690.1973960.2914570.3805060.46380.540420.6107260.6747410.7328150.7853980.8329810.8760580.9151010.9505470.9827941.0121971.0390721.0636981.0863181.1071491.1263771.1441691.1606691.1760051.190291.2036221.2160911.2277721.2387371.2490461.2587541.2679111.2765621.2847451.2924971.2998491.3068331.3134731.3197941.325818-1.21203-1.20362-1.19484-0.54042-0.38051-0.197400.1973960.3805060.540420.6747410.7853980.8760580.9505471.0121971.0636981.1071491.1441691.1760051.2036221.2277721.2490461.2679111.2847451.2998491.3134731.3258181.3370531.347321.3567361.3654011.3734011.3808081.3876861.3940871.4000611.40581.4108831.41581.4204251.4247841.421.432791.43751.4399691.4432871.4441-1.32582-1.31979-1.31347200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200200300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100-740-720-700-680-660-0-620-600-580-560-540-520-500-480-460-440-420-400-380-360-340-320-300-280-260-240-220-200-180-160-140-120-100-80-60-40-200204060801001201401601800.08166830.0857570090.0901510970.0948758060.0999633020.105449480.1113744410.1177830360.1247254650.1322579580.1404435160.1493527370.15906950.1696678710.1812611110.1939545440.2078703920.2231435510.2399217470.25839860.27839220.3009365390.32542240.3522733790.381639530.4136284190.4482760740.4855078160.5250880710.566560260.60918180.6518655220.6931471810.7312067420.7639732330.73311040.8054144820.8109302160.8054144820.73311040.7639732330.7312067420.6931471810.6518655220.60918180.566560260.525088071-1.185-1.17601-1.1659-1.1553-1.14417-1.13246-1.12014-1.10715-1.09345-1.079-1.0637-1.04752-1.03038-1.0122-0.992-0.97238-0.95055-0.9273-0.90251-0.87606-0.84782-0.81765-0.7854-0.75093-0.71409-0.67474-0.63275-0.588-0.54042-0.496-0.43663-0.38051-0.32175-0.2606-0.1974-0.13255-0.0665700.0665680.1325520.1973960.2606020.3217510.3805060.4366270.49570.54042-1.30683-1.29985-1.2925-1.28474-1.27656-1.26791-1.25875-1.24905-1.23874-1.22777-1.21609-1.20362-1.19029-1.17601-1.16067-1.14417-1.12638-1.10715-1.08632-1.0637-1.03907-1.0122-0.98279-0.95055-0.9151-0.87606-0.83298-0.7854-0.73282-0.67474-0.61073-0.54042-0.46365-0.38051-0.29146-0.1974-0.0996700.0996690.1973960.2914570.3805060.46380.540420.6107260.6747410.7328152002002002002002002002002002002002002002002002002002002002002002002002002002002002002002002003003003003003003003003003003003003003003003003003003003003003003003003003003003003003003003003003003003003003003003003003003003003003003003004004004004004004004004004004004004004004004004001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001001002002202402602803003203403603804004204404604805005205405605806006200660680700720740760780800-800-780-760-740-720-700-680-660-0-620-600-580-560-540-520-5000.4855078160.4482760740.4136284190.381639530.3522733790.32542240.3009365390.27839220.25839860.2399217470.2231435510.2078703920.1939545440.1812611110.1696678710.15906950.1493527370.1404435160.1322579580.1247254650.1177830360.1113744410.105449480.0999633020.0948758060.0901510970.0857570090.08166830.0778481930.0742842150.0709517360.0915671940.0955184260.099712480.1041678350.10045240.1139442590.1193105510.1250288340.1311265820.1376334230.1445812290.152004180.1599387950.16842330.1775004830.1872115420.5880030.6327490.6747410.7140910.7509290.7853980.81750.8478170.8760580.9025070.9272950.9505470.9723770.99241.0121971.0303771.0475181.0636981.07871.0934511.1071491.1201351.132461.1441691.1553041.1659051.1760051.1856391.1948351.2036221.212026-1.10715-1.09694-1.08632-1.07524-1.0637-1.05165-1.03907-1.02593-1.0122-0.99783-0.98279-0.96705-0.95055-0.93325-0.9151-0.6060.7853980.8329810.8760580.9151010.9505470.9827941.0121971.0390721.0636981.0863181.1071491.1263771.1441691.1606691.1760051.190291.2036221.2160911.2277721.2387371.2490461.2587541.2679111.2765621.2847451.2924971.2998491.3068331.3134731.3197941.325818-1.21203-1.20362-1.19484-1.185-1.17601-1.1659-1.1553-1.14417-1.13246-1.12014-1.10715-1.09345-1.079-1.0637-1.04752-1.03038300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300300400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400400100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100100-480-460-440-420-400-380-360-340-320-300-280-260-240-220-200-180-160-140-120-100-80-60-40-200204060801001201401601802002202402602803003203403603804004204400.1976016390.2087163710.2206015360.23330190.2468600780.2613135680.2766929510.2930180060.3102935190.3285040670.3476078330.3675295250.3881526030.4093112670.4307829160.4522821680.47345780.49347810.5131218360.5306282510.5458883270.5583940410.5676928740.57342280.57531450.57342280.5676928740.5583940410.5458883270.5306282510.5131218360.49347810.47345780.4522821680.4307829160.4093112670.3881526030.3675295250.3476078330.3285040670.3102935190.2930180060.2766929510.2613135680.2468600780.23330190.220601536-0.87606-0.85505-0.83298-0.80978-0.7854-0.75976-0.73282-0.70449-0.67474-0.35-0.61073-0.57638-0.54042-0.50284-0.46365-0.42285-0.38051-0.33667-0.29146-0.24498-0.1974-0.148-0.09967-0.0499600.0499580.0996690.1480.1973960.2449790.2914570.3366750.3805060.4228540.46380.5028430.540420.5763750.6107260.35010.6747410.7044940.7328150.7597630.7853980.8097840.832981-1.0122-0.992-0.97238-0.95055-0.9273-0.90251-0.87606-0.84782-0.81765-0.7854-0.75093-0.71409-0.67474-0.63275-0.588-0.54042-0.496-0.43663-0.38051-0.32175-0.2606-0.1974-0.13255-0.0665700.0665680.1325520.1973960.2606020.3217510.3805060.4366270.49570.540420.5880030.6327490.6747410.7140910.7509290.7853980.81750.8478170.8760580.9025070.9272950.9505470.97237730030030030030030030030030030030030030030030030030030040040040040040040040040040040040040040040040040040040010010010010010010010010010010010010010010010010010010046048050052054056058060062006606807007207407607808000.2087163710.1976016390.1872115420.1775004830.16842330.1599387950.152004180.1445812290.1376334230.1311265820.1250288340.1193105510.1139442590.10045240.1041678350.099712480.0955184260.0915671940.8550530.8760580.60550.9151010.9332480.9505470.9670470.9827940.997831.0121971.0259321.0390721.051651.0636981.0752451.0863181.0969451.1071490.99241.0121971.0303771.0475181.0636981.07871.0934511.1071491.1201351.132461.1441691.1553041.1659051.1760051.1856391.1948351.2036221.212026）+X*A+2*dlow*B+2*dup*C)*100000算

G = 6.67*10-8cm3gs2R 、h、X、Y单位用m 单位用 g/cm3g单位：1mgal = 10-5 m/s2 arctgXd]g（单位：mgal） #NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?#NAME?

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