On relations of anisotropy and linear inhomogeneity using Backus average

TL;DR

This paper derives an analytical relationship linking anisotropy and linear inhomogeneity in layered media, using Backus average and seismological data to validate the theoretical model.

Contribution

It introduces a new analytical system connecting anisotropy parameters with inhomogeneity, constrained by field data to ensure practical applicability.

Findings

Derived a system of equations relating Thomsen parameters to inhomogeneity.

Validated the analytical relationship using two seismological methods on field data.

Provided insights into the anisotropy-inhomogeneity relationship in sedimentary layers.

Abstract

The anisotropy of an equivalent medium resulting from the Backus (1962) average is induced by the vertical inhomogeneity among its constituent layers. The velocity field of the constituent isotropic layers increases linearly with depth, which is assumed to be a good seismological description of sedimentary layers Slotnick (1959). We derive an analytical relationship between the anisotropy, characterized by the Thomsen (1986) parameters, and the linear inhomogeneity parameters, which forms a system of three equations for nine unknowns. To obtain well-posedness, we constrain the problem by considering two seismological methods applied to field data. We use the results from the two methods, for a particular region of interest, to assess the validity of the analytical relation.

Tables

Table 1. Table 1 : Description of the well for log data

Field	Well	KB ($m$)	TVD ($m$)	Water depth ($m$)	Spud date	Log data
Mizzen	O-16	21.15	3797	1095	2008	$✓$

Table 2. Table 2 : Description of the well for checkshot data

Field	Well	Offset ($m$)	TVD ($m$)	Water depth ($m$)	Spud date	Checkshot
Mizzen	O-16	26.50	3797	1095	2009	$✓$

Table 3. Table 3 : VSP results

Startup values		VSP results			Using $b_{P_{\mathrm{VSP},\mathrm{out}}}$ as input				Using $a_{P_{\mathrm{layer}}}$ as input
$a_{P_{\mathrm{VSP},\mathrm{in}}}$	$b_{P_{\mathrm{VSP},\mathrm{in}}}$	$a_{P_{\mathrm{VSP},\mathrm{out}}}$	$b_{P_{\mathrm{VSP},\mathrm{out}}}$	$a_{P_{\mathrm{layer}}}$	$a_{P_{+}}$	$a_P$	$a_{P_{-}}$	$b_{P_{\mathrm{VSP},\mathrm{out}}}$	$b_{P_{-}}$	$b_P$	$b_{P_{+}}$
1320.0	0.57	1292.3	0.4317	2097.42	2240.18	2289.65	2342.32	0.4317	0.3857	0.3955	0.405
1325.0	0.57	1295.46	0.4286	2094.83	2223.84	2273.3	2325.98	0.4286	0.3853	0.395	0.4045
1330.0	0.57	1298.58	0.4256	2092.27	2207.69	2257.14	2309.83	0.4256	0.3848	0.3945	0.404
1335.0	0.57	1301.65	0.4226	2089.73	2191.74	2241.18	2293.89	0.4226	0.3843	0.394	0.4035
1340.0	0.57	1304.68	0.4196	2087.22	2175.98	2225.41	2278.13	0.4196	0.3838	0.3935	0.4031
1345.0	0.57	1307.68	0.4167	2084.74	2160.42	2209.84	2262.57	0.4167	0.3834	0.3931	0.4026
1350.0	0.57	1310.63	0.4138	2082.28	2145.04	2194.45	2247.19	0.4138	0.3829	0.3926	0.4021
1355.0	0.57	1313.54	0.4109	2079.84	2129.85	2179.25	2232.0	0.4109	0.3824	0.3921	0.4017
1360.0	0.57	1316.41	0.4081	2077.43	2114.83	2164.22	2216.99	0.4081	0.382	0.3917	0.4012
1365.0	0.57	1319.24	0.4053	2075.04	2100.0	2149.37	2202.16	0.4053	0.3815	0.3912	0.4008
1370.0	0.57	1322.04	0.4025	2072.68	2085.33	2134.7	2187.49	0.4025	0.3811	0.3908	0.4003
1375.0	0.57	1324.8	0.3998	2070.34	2070.85	2120.2	2173.01	0.3998	0.3806	0.3904	0.3999
1380.0	0.57	1327.52	0.3971	2068.02	2056.53	2105.87	2158.69	0.3971	0.3802	0.3899	0.3994
1385.0	0.57	1330.21	0.3944	2065.73	2042.37	2091.7	2144.54	0.3944	0.3798	0.3895	0.399
1390.0	0.57	1332.86	0.3917	2063.45	2028.38	2077.7	2130.55	0.3917	0.3793	0.3891	0.3986
1395.0	0.57	1335.48	0.3891	2061.2	2014.54	2063.85	2116.71	0.3891	0.3789	0.3886	0.3982
1400.0	0.57	1338.06	0.3866	2058.98	2000.87	2050.17	2103.04	0.3866	0.3785	0.3882	0.3977
1405.0	0.57	1340.61	0.384	2056.77	1987.35	2036.64	2089.53	0.384	0.3781	0.3878	0.3973
1410.0	0.57	1343.13	0.3815	2054.58	1973.98	2023.26	2076.16	0.3815	0.3777	0.3874	0.3969
1415.0	0.57	1345.62	0.379	2052.42	1960.77	2010.04	2062.95	0.379	0.3773	0.387	0.3965
1420.0	0.57	1348.07	0.3765	2050.28	1947.7	1996.96	2049.88	0.3765	0.3769	0.3866	0.3961
1425.0	0.57	1350.5	0.3741	2048.15	1934.77	1984.02	2036.96	0.3741	0.3765	0.3862	0.3957
1430.0	0.57	1352.89	0.3717	2046.05	1921.99	1971.23	2024.18	0.3717	0.3761	0.3858	0.3953
1435.0	0.57	1355.26	0.3693	2043.97	1909.36	1958.58	2011.55	0.3693	0.3757	0.3854	0.3949
1440.0	0.57	1357.59	0.3669	2041.9	1896.85	1946.06	1999.04	0.3669	0.3753	0.385	0.3945
1445.0	0.57	1359.9	0.3646	2039.86	1884.49	1933.69	1986.68	0.3646	0.3749	0.3846	0.3941
1450.0	0.57	1362.18	0.3623	2037.83	1872.26	1921.45	1974.45	0.3623	0.3745	0.3842	0.3937
1325.0	0.58	1295.8	0.4303	2098.24	2232.52	2281.99	2334.67	0.4303	0.3859	0.3956	0.4051
1330.0	0.58	1298.91	0.4272	2095.66	2216.37	2265.82	2318.51	0.4272	0.3854	0.3951	0.4047
1335.0	0.58	1301.97	0.4242	2093.11	2200.41	2249.86	2302.56	0.4242	0.3849	0.3946	0.4042
1340.0	0.58	1304.99	0.4212	2090.58	2184.64	2234.08	2286.79	0.4212	0.3845	0.3942	0.4037
1345.0	0.58	1307.97	0.4183	2088.08	2169.07	2218.5	2271.22	0.4183	0.384	0.3937	0.4032
1350.0	0.58	1310.91	0.4154	2085.6	2153.68	2203.1	2255.83	0.4154	0.3835	0.3932	0.4028
1355.0	0.58	1313.81	0.4125	2083.15	2138.48	2187.88	2240.64	0.4125	0.3831	0.3928	0.4023
1360.0	0.58	1316.67	0.4097	2080.73	2123.46	2172.85	2225.62	0.4097	0.3826	0.3923	0.4018
1365.0	0.58	1319.5	0.4069	2078.33	2108.61	2157.99	2210.77	0.4069	0.3821	0.3919	0.4014
1370.0	0.58	1322.28	0.4041	2075.95	2093.94	2143.31	2196.1	0.4041	0.3817	0.3914	0.4009
1375.0	0.58	1325.03	0.4014	2073.59	2079.44	2128.8	2181.6	0.4014	0.3812	0.391	0.4005
1380.0	0.58	1327.74	0.3987	2071.27	2065.11	2114.46	2167.27	0.3987	0.3808	0.3905	0.4001
1385.0	0.58	1330.42	0.396	2068.96	2050.94	2100.28	2153.1	0.396	0.3804	0.3901	0.3996
1390.0	0.58	1333.06	0.3934	2066.67	2036.94	2086.27	2139.11	0.3934	0.3799	0.3897	0.3992
1395.0	0.58	1335.67	0.3907	2064.41	2023.1	2072.41	2125.27	0.3907	0.3795	0.3892	0.3988
1400.0	0.58	1338.25	0.3882	2062.16	2009.41	2058.71	2111.58	0.3882	0.3791	0.3888	0.3983
1405.0	0.58	1340.79	0.3856	2059.95	1995.88	2045.17	2098.05	0.3856	0.3787	0.3884	0.3979
1410.0	0.58	1343.3	0.3831	2057.75	1982.5	2031.79	2084.68	0.3831	0.3783	0.388	0.3975
1415.0	0.58	1345.78	0.3806	2055.57	1969.27	2018.54	2071.45	0.3806	0.3778	0.3876	0.3971
1420.0	0.58	1348.22	0.3781	2053.41	1956.19	2005.45	2058.37	0.3781	0.3774	0.3872	0.3967
1425.0	0.58	1350.64	0.3757	2051.28	1943.25	1992.51	2045.44	0.3757	0.377	0.3868	0.3963
1430.0	0.58	1353.02	0.3733	2049.16	1930.46	1979.7	2032.64	0.3733	0.3766	0.3864	0.3959
1435.0	0.58	1355.38	0.3709	2047.06	1917.8	1967.04	2019.99	0.3709	0.3762	0.386	0.3955
1440.0	0.58	1357.71	0.3685	2044.99	1905.29	1954.51	2007.48	0.3685	0.3759	0.3856	0.3951
1445.0	0.58	1360.01	0.3662	2042.93	1892.91	1942.12	1995.1	0.3662	0.3755	0.3852	0.3947
1450.0	0.58	1362.28	0.3639	2040.89	1880.66	1929.86	1982.86	0.3639	0.3751	0.3848	0.3943
1455.0	0.58	1364.53	0.3616	2038.87	1868.55	1917.74	1970.75	0.3616	0.3747	0.3844	0.3939
1330.0	0.59	1299.36	0.4287	2098.97	2224.48	2273.94	2326.63	0.4287	0.386	0.3958	0.4053
1335.0	0.59	1302.41	0.4257	2096.4	2208.52	2257.97	2310.66	0.4257	0.3856	0.3953	0.4048
1340.0	0.59	1305.42	0.4228	2093.86	2192.75	2242.19	2294.9	0.4228	0.3851	0.3948	0.4043
1345.0	0.59	1308.39	0.4198	2091.35	2177.17	2226.6	2279.32	0.4198	0.3846	0.3943	0.4038
1350.0	0.59	1311.32	0.4169	2088.86	2161.78	2211.2	2263.93	0.4169	0.3841	0.3938	0.4034
1355.0	0.59	1314.21	0.414	2086.39	2146.57	2195.98	2248.72	0.414	0.3837	0.3934	0.4029
1360.0	0.59	1317.06	0.4112	2083.96	2131.54	2180.94	2233.7	0.4112	0.3832	0.3929	0.4024
1365.0	0.59	1319.87	0.4084	2081.54	2116.69	2166.07	2218.84	0.4084	0.3827	0.3925	0.402
1370.0	0.59	1322.64	0.4056	2079.15	2102.01	2151.39	2204.17	0.4056	0.3823	0.392	0.4015
1375.0	0.59	1325.38	0.4029	2076.78	2087.51	2136.87	2189.67	0.4029	0.3819	0.3916	0.4011
1380.0	0.59	1328.08	0.4002	2074.44	2073.16	2122.52	2175.33	0.4002	0.3814	0.3911	0.4007
1385.0	0.59	1330.75	0.3975	2072.12	2058.99	2108.34	2161.16	0.3975	0.381	0.3907	0.4002
1390.0	0.59	1333.38	0.3949	2069.82	2044.98	2094.31	2147.15	0.3949	0.3805	0.3903	0.3998
1395.0	0.59	1335.98	0.3923	2067.54	2031.13	2080.45	2133.3	0.3923	0.3801	0.3898	0.3994
1400.0	0.59	1338.54	0.3897	2065.29	2017.44	2066.75	2119.61	0.3897	0.3797	0.3894	0.3989
1405.0	0.59	1341.07	0.3871	2063.05	2003.9	2053.2	2106.07	0.3871	0.3793	0.389	0.3985
1410.0	0.59	1343.57	0.3846	2060.84	1990.51	2039.8	2092.69	0.3846	0.3788	0.3886	0.3981
1415.0	0.59	1346.04	0.3821	2058.65	1977.28	2026.56	2079.45	0.3821	0.3784	0.3881	0.3977
1420.0	0.59	1348.48	0.3796	2056.48	1964.18	2013.45	2066.36	0.3796	0.378	0.3877	0.3973
1425.0	0.59	1350.88	0.3772	2054.33	1951.24	2000.5	2053.42	0.3772	0.3776	0.3873	0.3969
1430.0	0.59	1353.26	0.3748	2052.21	1938.44	1987.69	2040.62	0.3748	0.3772	0.3869	0.3965
1435.0	0.59	1355.61	0.3724	2050.09	1925.77	1975.01	2027.96	0.3724	0.3768	0.3865	0.3961
1440.0	0.59	1357.93	0.37	2048.01	1913.25	1962.47	2015.44	0.37	0.3764	0.3861	0.3957
1445.0	0.59	1360.22	0.3677	2045.94	1900.86	1950.08	2003.05	0.3677	0.376	0.3858	0.3953
1450.0	0.59	1362.48	0.3654	2043.89	1888.61	1937.81	1990.8	0.3654	0.3756	0.3854	0.3949
1455.0	0.59	1364.72	0.3631	2041.86	1876.48	1925.67	1978.67	0.3631	0.3753	0.385	0.3945
1460.0	0.59	1366.93	0.3608	2039.84	1864.49	1913.67	1966.68	0.3608	0.3749	0.3846	0.3941
1335.0	0.6	1302.97	0.4272	2099.62	2216.08	2265.53	2318.22	0.4272	0.3862	0.3959	0.4054
1340.0	0.6	1305.97	0.4242	2097.07	2200.31	2249.76	2302.46	0.4242	0.3857	0.3954	0.4049
1345.0	0.6	1308.92	0.4212	2094.54	2184.73	2234.17	2286.88	0.4212	0.3852	0.3949	0.4044
1350.0	0.6	1311.84	0.4183	2092.04	2169.34	2218.77	2271.49	0.4183	0.3847	0.3944	0.404
1355.0	0.6	1314.71	0.4155	2089.56	2154.13	2203.55	2256.29	0.4155	0.3843	0.394	0.4035
1360.0	0.6	1317.55	0.4126	2087.11	2139.1	2188.5	2241.25	0.4126	0.3838	0.3935	0.403
1365.0	0.6	1320.35	0.4098	2084.68	2124.25	2173.64	2226.41	0.4098	0.3833	0.3931	0.4026
1370.0	0.6	1323.11	0.4071	2082.27	2109.57	2158.95	2211.72	0.4071	0.3829	0.3926	0.4021
1375.0	0.6	1325.83	0.4043	2079.9	2095.06	2144.43	2197.22	0.4043	0.3824	0.3922	0.4017
1380.0	0.6	1328.52	0.4016	2077.54	2080.72	2130.08	2182.88	0.4016	0.382	0.3917	0.4012
1385.0	0.6	1331.18	0.3989	2075.2	2066.54	2115.89	2168.7	0.3989	0.3816	0.3913	0.4008
1390.0	0.6	1333.8	0.3963	2072.89	2052.53	2101.87	2154.69	0.3963	0.3811	0.3908	0.4004
1395.0	0.6	1336.38	0.3937	2070.6	2038.67	2088.0	2140.84	0.3937	0.3807	0.3904	0.3999
1400.0	0.6	1338.94	0.3911	2068.34	2024.97	2074.29	2127.14	0.3911	0.3803	0.39	0.3995
1405.0	0.6	1341.46	0.3885	2066.09	2011.43	2060.74	2113.6	0.3885	0.3798	0.3896	0.3991
1410.0	0.6	1343.95	0.386	2063.87	1998.04	2047.33	2100.21	0.386	0.3794	0.3891	0.3987
1415.0	0.6	1346.41	0.3835	2061.66	1984.8	2034.08	2086.97	0.3835	0.379	0.3887	0.3982
1420.0	0.6	1348.83	0.381	2059.48	1971.7	2020.98	2073.88	0.381	0.3786	0.3883	0.3978
1425.0	0.6	1351.23	0.3786	2057.32	1958.75	2008.02	2060.94	0.3786	0.3782	0.3879	0.3974
1430.0	0.6	1353.6	0.3762	2055.18	1945.94	1995.2	2048.12	0.3762	0.3778	0.3875	0.397
1435.0	0.6	1355.93	0.3738	2053.06	1933.28	1982.52	2035.46	0.3738	0.3774	0.3871	0.3966
1440.0	0.6	1358.24	0.3714	2050.96	1920.75	1969.98	2022.93	0.3714	0.377	0.3867	0.3962
1445.0	0.6	1360.52	0.3691	2048.88	1908.35	1957.57	2010.54	0.3691	0.3766	0.3863	0.3958
1450.0	0.6	1362.78	0.3668	2046.82	1896.09	1945.3	1998.28	0.3668	0.3762	0.3859	0.3954
1455.0	0.6	1365.0	0.3645	2044.78	1883.96	1933.16	1986.15	0.3645	0.3758	0.3855	0.3951
1460.0	0.6	1367.2	0.3622	2042.75	1871.95	1921.14	1974.15	0.3622	0.3754	0.3852	0.3947
1465.0	0.6	1369.38	0.36	2040.74	1860.08	1909.26	1962.28	0.36	0.3751	0.3848	0.3943
1340.0	0.61	1306.62	0.4255	2100.2	2207.35	2256.8	2309.5	0.4255	0.3863	0.396	0.4055
1345.0	0.61	1309.56	0.4226	2097.66	2191.78	2241.22	2293.93	0.4226	0.3858	0.3955	0.405
1350.0	0.61	1312.46	0.4197	2095.14	2176.39	2225.81	2278.53	0.4197	0.3853	0.395	0.4046
1355.0	0.61	1315.33	0.4168	2092.65	2161.18	2210.6	2263.33	0.4168	0.3848	0.3946	0.4041
1360.0	0.61	1318.15	0.414	2090.19	2146.15	2195.56	2248.3	0.414	0.3844	0.3941	0.4036
1365.0	0.61	1320.93	0.4112	2087.75	2131.3	2180.7	2233.46	0.4112	0.3839	0.3936	0.4032
1370.0	0.61	1323.68	0.4084	2085.33	2116.63	2166.01	2218.78	0.4084	0.3835	0.3932	0.4027
1375.0	0.61	1326.39	0.4057	2082.94	2102.11	2151.49	2204.27	0.4057	0.383	0.3927	0.4023
1380.0	0.61	1329.07	0.4029	2080.57	2087.78	2137.14	2189.94	0.4029	0.3826	0.3923	0.4018
1385.0	0.61	1331.71	0.4003	2078.22	2073.6	2122.96	2175.77	0.4003	0.3821	0.3918	0.4014
1390.0	0.61	1334.32	0.3976	2075.9	2059.58	2108.93	2161.75	0.3976	0.3817	0.3914	0.4009
1395.0	0.61	1336.9	0.395	2073.6	2045.73	2095.07	2147.9	0.395	0.3813	0.391	0.4005
1400.0	0.61	1339.44	0.3924	2071.32	2032.04	2081.36	2134.21	0.3924	0.3808	0.3905	0.4001
1405.0	0.61	1341.95	0.3899	2069.06	2018.49	2067.8	2120.66	0.3899	0.3804	0.3901	0.3996
1410.0	0.61	1344.42	0.3873	2066.83	2005.1	2054.4	2107.27	0.3873	0.38	0.3897	0.3992
1415.0	0.61	1346.87	0.3848	2064.61	1991.86	2041.15	2094.03	0.3848	0.3796	0.3893	0.3988
1420.0	0.61	1349.29	0.3824	2062.42	1978.75	2028.04	2080.93	0.3824	0.3791	0.3889	0.3984
1425.0	0.61	1351.67	0.3799	2060.25	1965.8	2015.08	2067.98	0.3799	0.3787	0.3884	0.398
1430.0	0.61	1354.03	0.3775	2058.1	1953.0	2002.26	2055.18	0.3775	0.3783	0.388	0.3976
1435.0	0.61	1356.35	0.3751	2055.96	1940.32	1989.57	2042.5	0.3751	0.3779	0.3876	0.3972
1440.0	0.61	1358.65	0.3728	2053.85	1927.79	1977.03	2029.97	0.3728	0.3775	0.3872	0.3968
1445.0	0.61	1360.92	0.3704	2051.76	1915.39	1964.62	2017.58	0.3704	0.3771	0.3868	0.3964
1450.0	0.61	1363.17	0.3681	2049.69	1903.13	1952.35	2005.32	0.3681	0.3767	0.3865	0.396
1455.0	0.61	1365.38	0.3658	2047.63	1890.99	1940.2	1993.18	0.3658	0.3764	0.3861	0.3956
1460.0	0.61	1367.57	0.3636	2045.6	1878.99	1928.19	1981.18	0.3636	0.376	0.3857	0.3952
1465.0	0.61	1369.74	0.3613	2043.58	1867.11	1916.3	1969.31	0.3613	0.3756	0.3853	0.3948
1470.0	0.61	1371.88	0.3591	2041.58	1855.36	1904.54	1957.56	0.3591	0.3752	0.3849	0.3945
1345.0	0.62	1310.31	0.4238	2100.71	2198.32	2247.76	2300.46	0.4238	0.3864	0.3961	0.4056
1350.0	0.62	1313.2	0.4209	2098.18	2182.94	2232.37	2285.09	0.4209	0.3859	0.3956	0.4051
1355.0	0.62	1316.04	0.418	2095.68	2167.73	2217.16	2269.88	0.418	0.3854	0.3951	0.4047
1360.0	0.62	1318.85	0.4152	2093.2	2152.71	2202.13	2254.87	0.4152	0.3849	0.3947	0.4042
1365.0	0.62	1321.62	0.4124	2090.75	2137.86	2187.27	2240.02	0.4124	0.3845	0.3942	0.4037
1370.0	0.62	1324.36	0.4096	2088.32	2123.19	2172.59	2225.35	0.4096	0.384	0.3937	0.4033
1375.0	0.62	1327.06	0.4069	2085.92	2108.7	2158.08	2210.85	0.4069	0.3836	0.3933	0.4028
1380.0	0.62	1329.72	0.4042	2083.53	2094.35	2143.73	2196.52	0.4042	0.3831	0.3928	0.4024
1385.0	0.62	1332.35	0.4015	2081.17	2080.19	2129.55	2182.35	0.4015	0.3827	0.3924	0.4019
1390.0	0.62	1334.94	0.3989	2078.84	2066.18	2115.53	2168.34	0.3989	0.3822	0.392	0.4015
1395.0	0.62	1337.5	0.3963	2076.53	2052.32	2101.66	2154.49	0.3963	0.3818	0.3915	0.401
1400.0	0.62	1340.03	0.3937	2074.24	2038.63	2087.96	2140.8	0.3937	0.3814	0.3911	0.4006
1405.0	0.62	1342.53	0.3911	2071.97	2025.09	2074.41	2127.26	0.3911	0.3809	0.3907	0.4002
1410.0	0.62	1344.99	0.3886	2069.72	2011.7	2061.0	2113.87	0.3886	0.3805	0.3902	0.3998
1415.0	0.62	1347.43	0.3861	2067.5	1998.46	2047.75	2100.63	0.3861	0.3801	0.3898	0.3993
1420.0	0.62	1349.83	0.3836	2065.29	1985.36	2034.65	2087.54	0.3836	0.3797	0.3894	0.3989
1425.0	0.62	1352.21	0.3812	2063.11	1972.41	2021.69	2074.59	0.3812	0.3793	0.389	0.3985
1430.0	0.62	1354.55	0.3788	2060.94	1959.6	2008.87	2061.78	0.3788	0.3789	0.3886	0.3981
1435.0	0.62	1356.87	0.3764	2058.8	1946.93	1996.19	2049.11	0.3764	0.3785	0.3882	0.3977
1440.0	0.62	1359.16	0.374	2056.68	1934.4	1983.65	2036.59	0.374	0.3781	0.3878	0.3973
1445.0	0.62	1361.41	0.3717	2054.57	1922.0	1971.23	2024.18	0.3717	0.3777	0.3874	0.3969
1450.0	0.62	1363.65	0.3694	2052.49	1909.73	1958.96	2011.92	0.3694	0.3773	0.387	0.3965
1455.0	0.62	1365.85	0.3671	2050.43	1897.6	1946.82	1999.79	0.3671	0.3769	0.3866	0.3961
1460.0	0.62	1368.03	0.3648	2048.38	1885.6	1934.8	1987.79	0.3648	0.3765	0.3862	0.3957
1465.0	0.62	1370.19	0.3626	2046.35	1873.72	1922.91	1975.91	0.3626	0.3761	0.3858	0.3954
1470.0	0.62	1372.31	0.3603	2044.34	1861.96	1911.15	1964.16	0.3603	0.3757	0.3855	0.395
1475.0	0.62	1374.42	0.3581	2042.35	1850.34	1899.51	1952.53	0.3581	0.3754	0.3851	0.3946
1350.0	0.63	1314.03	0.422	2101.14	2189.0	2238.43	2291.15	0.422	0.3864	0.3962	0.4057
1355.0	0.63	1316.86	0.4192	2098.63	2173.81	2223.24	2275.96	0.4192	0.386	0.3957	0.4052
1360.0	0.63	1319.65	0.4163	2096.14	2158.8	2208.21	2260.95	0.4163	0.3855	0.3952	0.4047
1365.0	0.63	1322.41	0.4135	2093.68	2143.96	2193.37	2246.12	0.4135	0.385	0.3948	0.4043
1370.0	0.63	1325.13	0.4108	2091.24	2129.29	2178.69	2231.45	0.4108	0.3846	0.3943	0.4038
1375.0	0.63	1327.81	0.408	2088.82	2114.8	2164.19	2216.96	0.408	0.3841	0.3938	0.4034
1380.0	0.63	1330.46	0.4053	2086.43	2100.48	2149.85	2202.64	0.4053	0.3837	0.3934	0.4029
1385.0	0.63	1333.08	0.4027	2084.06	2086.31	2135.68	2188.47	0.4027	0.3832	0.3929	0.4025
1390.0	0.63	1335.66	0.4	2081.71	2072.31	2121.66	2174.47	0.4	0.3828	0.3925	0.402
1395.0	0.63	1338.21	0.3974	2079.39	2058.47	2107.81	2160.63	0.3974	0.3823	0.3921	0.4016
1400.0	0.63	1340.72	0.3948	2077.09	2044.77	2094.11	2146.94	0.3948	0.3819	0.3916	0.4012
1405.0	0.63	1343.21	0.3923	2074.81	2031.24	2080.57	2133.41	0.3923	0.3815	0.3912	0.4007
1410.0	0.63	1345.66	0.3898	2072.55	2017.86	2067.17	2120.03	0.3898	0.3811	0.3908	0.4003
1415.0	0.63	1348.08	0.3873	2070.32	2004.62	2053.93	2106.8	0.3873	0.3806	0.3903	0.3999
1420.0	0.63	1350.47	0.3848	2068.1	1991.53	2040.82	2093.71	0.3848	0.3802	0.3899	0.3995
1425.0	0.63	1352.83	0.3823	2065.91	1978.59	2027.87	2080.76	0.3823	0.3798	0.3895	0.399
1430.0	0.63	1355.17	0.3799	2063.73	1965.78	2015.05	2067.96	0.3799	0.3794	0.3891	0.3986
1435.0	0.63	1357.47	0.3775	2061.58	1953.11	2002.37	2055.29	0.3775	0.379	0.3887	0.3982
1440.0	0.63	1359.74	0.3752	2059.44	1940.58	1989.83	2042.77	0.3752	0.3786	0.3883	0.3978
1445.0	0.63	1361.99	0.3728	2057.33	1928.19	1977.43	2030.38	0.3728	0.3782	0.3879	0.3974
1450.0	0.63	1364.21	0.3705	2055.24	1915.93	1965.16	2018.12	0.3705	0.3778	0.3875	0.397
1455.0	0.63	1366.41	0.3682	2053.16	1903.79	1953.01	2005.98	0.3682	0.3774	0.3871	0.3966
1460.0	0.63	1368.58	0.366	2051.1	1891.79	1941.0	1993.98	0.366	0.377	0.3867	0.3963
1465.0	0.63	1370.72	0.3637	2049.07	1879.92	1929.11	1982.11	0.3637	0.3766	0.3863	0.3959
1470.0	0.63	1372.84	0.3615	2047.05	1868.17	1917.35	1970.36	0.3615	0.3762	0.386	0.3955
1475.0	0.63	1374.93	0.3593	2045.05	1856.53	1905.71	1958.73	0.3593	0.3759	0.3856	0.3951
1480.0	0.63	1377.0	0.3571	2043.06	1845.03	1894.19	1947.23	0.3571	0.3755	0.3852	0.3947
1355.0	0.64	1317.77	0.4202	2101.52	2179.42	2228.85	2281.57	0.4202	0.3865	0.3962	0.4058
1360.0	0.64	1320.55	0.4174	2099.02	2164.42	2213.84	2266.57	0.4174	0.386	0.3958	0.4053
1365.0	0.64	1323.29	0.4146	2096.54	2149.59	2199.01	2251.75	0.4146	0.3856	0.3953	0.4048
1370.0	0.64	1325.99	0.4118	2094.09	2134.95	2184.35	2237.1	0.4118	0.3851	0.3948	0.4044
1375.0	0.64	1328.66	0.4091	2091.67	2120.47	2169.86	2222.62	0.4091	0.3847	0.3944	0.4039
1380.0	0.64	1331.3	0.4064	2089.26	2106.15	2155.53	2208.31	0.4064	0.3842	0.3939	0.4034
1385.0	0.64	1333.9	0.4037	2086.88	2092.0	2141.37	2194.16	0.4037	0.3838	0.3935	0.403
1390.0	0.64	1336.46	0.4011	2084.53	2078.01	2127.37	2180.17	0.4011	0.3833	0.393	0.4026
1395.0	0.64	1339.0	0.3985	2082.19	2064.17	2113.52	2166.33	0.3985	0.3829	0.3926	0.4021
1400.0	0.64	1341.5	0.3959	2079.88	2050.49	2099.83	2152.66	0.3959	0.3824	0.3922	0.4017
1405.0	0.64	1343.97	0.3934	2077.59	2036.97	2086.3	2139.14	0.3934	0.382	0.3917	0.4012
1410.0	0.64	1346.41	0.3908	2075.32	2023.59	2072.91	2125.76	0.3908	0.3816	0.3913	0.4008
1415.0	0.64	1348.82	0.3883	2073.07	2010.36	2059.67	2112.53	0.3883	0.3812	0.3909	0.4004
1420.0	0.64	1351.19	0.3859	2070.85	1997.28	2046.58	2099.46	0.3859	0.3807	0.3904	0.4
1425.0	0.64	1353.54	0.3834	2068.64	1984.34	2033.63	2086.52	0.3834	0.3803	0.39	0.3996
1430.0	0.64	1355.86	0.381	2066.46	1971.54	2020.82	2073.72	0.381	0.3799	0.3896	0.3991
1435.0	0.64	1358.15	0.3786	2064.29	1958.88	2008.15	2061.06	0.3786	0.3795	0.3892	0.3987
1440.0	0.64	1360.42	0.3763	2062.15	1946.36	1995.62	2048.54	0.3763	0.3791	0.3888	0.3983
1445.0	0.64	1362.65	0.3739	2060.03	1933.97	1983.22	2036.16	0.3739	0.3787	0.3884	0.3979
1450.0	0.64	1364.86	0.3716	2057.92	1921.71	1970.95	2023.9	0.3716	0.3783	0.388	0.3975
1455.0	0.64	1367.05	0.3693	2055.84	1909.59	1958.81	2011.78	0.3693	0.3779	0.3876	0.3971
1460.0	0.64	1369.2	0.3671	2053.77	1897.59	1946.8	1999.78	0.3671	0.3775	0.3872	0.3968
1465.0	0.64	1371.33	0.3648	2051.72	1885.72	1934.92	1987.91	0.3648	0.3771	0.3868	0.3964
1470.0	0.64	1373.44	0.3626	2049.69	1873.97	1923.16	1976.16	0.3626	0.3767	0.3865	0.396
1475.0	0.64	1375.52	0.3604	2047.68	1862.34	1911.53	1964.54	0.3604	0.3764	0.3861	0.3956
1480.0	0.64	1377.58	0.3582	2045.69	1850.84	1900.01	1953.04	0.3582	0.376	0.3857	0.3952
1485.0	0.64	1379.61	0.3561	2043.72	1839.46	1888.62	1941.66	0.3561	0.3756	0.3853	0.3949
1360.0	0.65	1321.54	0.4184	2101.83	2169.59	2219.02	2271.75	0.4184	0.3866	0.3963	0.4058
1365.0	0.65	1324.26	0.4156	2099.34	2154.79	2204.21	2256.94	0.4156	0.3861	0.3958	0.4053
1370.0	0.65	1326.95	0.4128	2096.88	2140.15	2189.56	2242.31	0.4128	0.3856	0.3954	0.4049
1375.0	0.65	1329.6	0.4101	2094.44	2125.69	2175.08	2227.84	0.4101	0.3852	0.3949	0.4044
1380.0	0.65	1332.22	0.4074	2092.03	2111.39	2160.77	2213.55	0.4074	0.3847	0.3944	0.404
1385.0	0.65	1334.81	0.4047	2089.64	2097.25	2146.62	2199.41	0.4047	0.3843	0.394	0.4035
1390.0	0.65	1337.36	0.4021	2087.27	2083.27	2132.63	2185.43	0.4021	0.3838	0.3935	0.4031
1395.0	0.65	1339.88	0.3995	2084.93	2069.45	2118.8	2171.62	0.3995	0.3834	0.3931	0.4026
1400.0	0.65	1342.36	0.3969	2082.61	2055.79	2105.13	2157.95	0.3969	0.3829	0.3927	0.4022
1405.0	0.65	1344.82	0.3944	2080.3	2042.27	2091.6	2144.44	0.3944	0.3825	0.3922	0.4018
1410.0	0.65	1347.24	0.3918	2078.03	2028.91	2078.23	2131.08	0.3918	0.3821	0.3918	0.4013
1415.0	0.65	1349.64	0.3893	2075.77	2015.69	2065.0	2117.86	0.3893	0.3817	0.3914	0.4009
1420.0	0.65	1352.0	0.3869	2073.53	2002.62	2051.92	2104.79	0.3869	0.3812	0.391	0.4005
1425.0	0.65	1354.34	0.3844	2071.32	1989.69	2038.98	2091.86	0.3844	0.3808	0.3905	0.4001
1430.0	0.65	1356.64	0.382	2069.13	1976.9	2026.18	2079.08	0.382	0.3804	0.3901	0.3996
1435.0	0.65	1358.92	0.3796	2066.95	1964.25	2013.52	2066.43	0.3796	0.38	0.3897	0.3992
1440.0	0.65	1361.17	0.3773	2064.8	1951.73	2000.99	2053.92	0.3773	0.3796	0.3893	0.3988
1445.0	0.65	1363.4	0.3749	2062.66	1939.36	1988.61	2041.54	0.3749	0.3792	0.3889	0.3984
1450.0	0.65	1365.59	0.3726	2060.55	1927.11	1976.35	2029.3	0.3726	0.3788	0.3885	0.398
1455.0	0.65	1367.76	0.3703	2058.46	1914.99	1964.22	2017.18	0.3703	0.3784	0.3881	0.3976
1460.0	0.65	1369.91	0.3681	2056.38	1903.0	1952.22	2005.19	0.3681	0.378	0.3877	0.3972
1465.0	0.65	1372.03	0.3658	2054.32	1891.13	1940.34	1993.33	0.3658	0.3776	0.3873	0.3969
1470.0	0.65	1374.12	0.3636	2052.28	1879.4	1928.59	1981.59	0.3636	0.3772	0.3869	0.3965
1475.0	0.65	1376.19	0.3614	2050.27	1867.78	1916.96	1969.97	0.3614	0.3768	0.3866	0.3961
1480.0	0.65	1378.23	0.3593	2048.26	1856.27	1905.45	1958.47	0.3593	0.3765	0.3862	0.3957
1485.0	0.65	1380.26	0.3571	2046.28	1844.9	1894.06	1947.1	0.3571	0.3761	0.3858	0.3953
1490.0	0.65	1382.25	0.355	2044.31	1833.63	1882.79	1935.84	0.355	0.3757	0.3854	0.395
1365.0	0.66	1325.32	0.4165	2102.08	2159.55	2208.97	2261.7	0.4165	0.3866	0.3963	0.4059
1370.0	0.66	1327.99	0.4137	2099.61	2144.94	2194.35	2247.09	0.4137	0.3862	0.3959	0.4054
1375.0	0.66	1330.63	0.411	2097.16	2130.49	2179.89	2232.65	0.411	0.3857	0.3954	0.4049
1380.0	0.66	1333.23	0.4083	2094.73	2116.2	2165.59	2218.36	0.4083	0.3852	0.395	0.4045
1385.0	0.66	1335.8	0.4056	2092.33	2102.09	2151.46	2204.24	0.4056	0.3848	0.3945	0.404
1390.0	0.66	1338.34	0.403	2089.96	2088.13	2137.49	2190.29	0.403	0.3843	0.3941	0.4036
1395.0	0.66	1340.84	0.4004	2087.6	2074.32	2123.67	2176.48	0.4004	0.3839	0.3936	0.4031
1400.0	0.66	1343.31	0.3978	2085.27	2060.67	2110.01	2162.83	0.3978	0.3835	0.3932	0.4027
1405.0	0.66	1345.75	0.3953	2082.96	2047.17	2096.51	2149.34	0.3953	0.383	0.3927	0.4023
1410.0	0.66	1348.16	0.3928	2080.67	2033.82	2083.14	2135.99	0.3928	0.3826	0.3923	0.4018
1415.0	0.66	1350.54	0.3903	2078.41	2020.62	2069.93	2122.79	0.3903	0.3822	0.3919	0.4014
1420.0	0.66	1352.89	0.3878	2076.16	2007.56	2056.87	2109.73	0.3878	0.3817	0.3915	0.401
1425.0	0.66	1355.21	0.3854	2073.94	1994.65	2043.94	2096.82	0.3854	0.3813	0.391	0.4006
1430.0	0.66	1357.5	0.383	2071.73	1981.87	2031.15	2084.04	0.383	0.3809	0.3906	0.4001
1435.0	0.66	1359.77	0.3806	2069.55	1969.23	2018.5	2071.41	0.3806	0.3805	0.3902	0.3997
1440.0	0.66	1362.01	0.3782	2067.39	1956.73	2005.99	2058.91	0.3782	0.3801	0.3898	0.3993
1445.0	0.66	1364.22	0.3759	2065.24	1944.36	1993.62	2046.55	0.3759	0.3797	0.3894	0.3989
1450.0	0.66	1366.4	0.3736	2063.12	1932.12	1981.36	2034.3	0.3736	0.3793	0.389	0.3985
1455.0	0.66	1368.56	0.3713	2061.02	1920.01	1969.25	2022.2	0.3713	0.3789	0.3886	0.3981
1460.0	0.66	1370.69	0.369	2058.93	1908.03	1957.26	2010.22	0.369	0.3785	0.3882	0.3977
1465.0	0.66	1372.79	0.3668	2056.87	1896.18	1945.39	1998.37	0.3668	0.3781	0.3878	0.3973
1470.0	0.66	1374.88	0.3646	2054.82	1884.45	1933.65	1986.64	0.3646	0.3777	0.3874	0.397
1475.0	0.66	1376.93	0.3624	2052.79	1872.84	1922.03	1975.03	0.3624	0.3773	0.387	0.3966
1480.0	0.66	1378.97	0.3602	2050.78	1861.35	1910.53	1963.55	0.3602	0.3769	0.3867	0.3962
1485.0	0.66	1380.98	0.3581	2048.79	1849.98	1899.15	1952.18	0.3581	0.3766	0.3863	0.3958
1490.0	0.66	1382.96	0.356	2046.81	1838.72	1887.88	1940.93	0.356	0.3762	0.3859	0.3954
1495.0	0.66	1384.93	0.3538	2044.85	1827.58	1876.73	1929.78	0.3538	0.3758	0.3855	0.3951
1370.0	0.67	1329.12	0.4146	2102.27	2149.3	2198.71	2251.46	0.4146	0.3867	0.3964	0.4059
1375.0	0.67	1331.74	0.4118	2099.81	2134.88	2184.28	2237.03	0.4118	0.3862	0.3959	0.4054
1380.0	0.67	1334.32	0.4091	2097.38	2120.62	2170.01	2222.78	0.4091	0.3857	0.3955	0.405
1385.0	0.67	1336.87	0.4065	2094.97	2106.51	2155.89	2208.67	0.4065	0.3853	0.395	0.4045
1390.0	0.67	1339.39	0.4039	2092.58	2092.57	2141.94	2194.73	0.4039	0.3848	0.3945	0.4041
1395.0	0.67	1341.88	0.4013	2090.22	2078.79	2128.15	2180.95	0.4013	0.3844	0.3941	0.4036
1400.0	0.67	1344.34	0.3987	2087.88	2065.16	2114.51	2167.32	0.3987	0.3839	0.3937	0.4032
1405.0	0.67	1346.76	0.3961	2085.56	2051.67	2101.01	2153.84	0.3961	0.3835	0.3932	0.4027
1410.0	0.67	1349.16	0.3936	2083.26	2038.34	2087.67	2140.51	0.3936	0.3831	0.3928	0.4023
1415.0	0.67	1351.52	0.3911	2080.98	2025.16	2074.48	2127.33	0.3911	0.3826	0.3924	0.4019
1420.0	0.67	1353.86	0.3887	2078.73	2012.12	2061.43	2114.29	0.3887	0.3822	0.3919	0.4015
1425.0	0.67	1356.16	0.3862	2076.5	1999.22	2048.51	2101.39	0.3862	0.3818	0.3915	0.401
1430.0	0.67	1358.44	0.3838	2074.28	1986.46	2035.75	2088.63	0.3838	0.3814	0.3911	0.4006
1435.0	0.67	1360.69	0.3814	2072.09	1973.84	2023.11	2076.01	0.3814	0.381	0.3907	0.4002
1440.0	0.67	1362.91	0.3791	2069.92	1961.35	2010.62	2063.53	0.3791	0.3806	0.3903	0.3998
1445.0	0.67	1365.11	0.3768	2067.77	1948.99	1998.25	2051.17	0.3768	0.3802	0.3899	0.3994
1450.0	0.67	1367.28	0.3745	2065.64	1936.77	1986.01	2038.95	0.3745	0.3797	0.3895	0.399
1455.0	0.67	1369.42	0.3722	2063.52	1924.67	1973.91	2026.86	0.3722	0.3793	0.3891	0.3986
1460.0	0.67	1371.54	0.3699	2061.43	1912.71	1961.93	2014.9	0.3699	0.379	0.3887	0.3982
1465.0	0.67	1373.63	0.3677	2059.35	1900.86	1950.08	2003.05	0.3677	0.3786	0.3883	0.3978
1470.0	0.67	1375.7	0.3655	2057.3	1889.14	1938.35	1991.33	0.3655	0.3782	0.3879	0.3974
1475.0	0.67	1377.75	0.3633	2055.26	1877.55	1926.74	1979.74	0.3633	0.3778	0.3875	0.397
1480.0	0.67	1379.77	0.3611	2053.24	1866.07	1915.25	1968.26	0.3611	0.3774	0.3871	0.3967
1485.0	0.67	1381.77	0.359	2051.24	1854.71	1903.88	1956.91	0.359	0.377	0.3868	0.3963
1490.0	0.67	1383.74	0.3568	2049.26	1843.46	1892.62	1945.66	0.3568	0.3767	0.3864	0.3959
1495.0	0.67	1385.69	0.3547	2047.29	1832.33	1881.48	1934.53	0.3547	0.3763	0.386	0.3955
1500.0	0.67	1387.62	0.3527	2045.34	1821.31	1870.45	1923.52	0.3527	0.3759	0.3856	0.3952
1375.0	0.68	1332.92	0.4126	2102.4	2138.88	2188.28	2241.03	0.4126	0.3867	0.3964	0.4059
1380.0	0.68	1335.49	0.4099	2099.96	2124.63	2174.03	2226.79	0.4099	0.3862	0.3959	0.4055
1385.0	0.68	1338.03	0.4072	2097.54	2110.56	2159.94	2212.72	0.4072	0.3858	0.3955	0.405
1390.0	0.68	1340.53	0.4046	2095.15	2096.64	2146.01	2198.8	0.4046	0.3853	0.395	0.4046
1395.0	0.68	1343.0	0.402	2092.77	2082.87	2132.23	2185.03	0.402	0.3849	0.3946	0.4041
1400.0	0.68	1345.44	0.3995	2090.42	2069.26	2118.62	2171.43	0.3995	0.3844	0.3941	0.4037
1405.0	0.68	1347.85	0.3969	2088.1	2055.8	2105.15	2157.97	0.3969	0.384	0.3937	0.4032
1410.0	0.68	1350.23	0.3944	2085.79	2042.49	2091.83	2144.66	0.3944	0.3835	0.3933	0.4028
1415.0	0.68	1352.57	0.3919	2083.5	2029.32	2078.65	2131.49	0.3919	0.3831	0.3928	0.4024
1420.0	0.68	1354.89	0.3895	2081.24	2016.3	2065.61	2118.47	0.3895	0.3827	0.3924	0.4019
1425.0	0.68	1357.19	0.387	2079.0	2003.42	2052.72	2105.6	0.387	0.3823	0.392	0.4015
1430.0	0.68	1359.45	0.3846	2076.78	1990.68	2039.97	2092.86	0.3846	0.3818	0.3916	0.4011
1435.0	0.68	1361.68	0.3822	2074.58	1978.07	2027.35	2080.25	0.3822	0.3814	0.3912	0.4007
1440.0	0.68	1363.89	0.3799	2072.4	1965.6	2014.87	2067.78	0.3799	0.381	0.3907	0.4003
1445.0	0.68	1366.07	0.3776	2070.24	1953.26	2002.53	2055.45	0.3776	0.3806	0.3903	0.3999
1450.0	0.68	1368.23	0.3753	2068.1	1941.06	1990.31	2043.24	0.3753	0.3802	0.3899	0.3995
1455.0	0.68	1370.36	0.373	2065.97	1928.97	1978.21	2031.16	0.373	0.3798	0.3895	0.3991
1460.0	0.68	1372.46	0.3707	2063.87	1917.02	1966.25	2019.21	0.3707	0.3794	0.3891	0.3987
1465.0	0.68	1374.54	0.3685	2061.79	1905.2	1954.42	2007.38	0.3685	0.379	0.3887	0.3983
1470.0	0.68	1376.6	0.3663	2059.73	1893.49	1942.7	1995.68	0.3663	0.3786	0.3884	0.3979
1475.0	0.68	1378.63	0.3641	2057.68	1881.91	1931.11	1984.1	0.3641	0.3782	0.388	0.3975
1480.0	0.68	1380.64	0.3619	2055.65	1870.44	1919.63	1972.63	0.3619	0.3779	0.3876	0.3971
1485.0	0.68	1382.62	0.3598	2053.64	1859.09	1908.27	1961.29	0.3598	0.3775	0.3872	0.3967
1490.0	0.68	1384.59	0.3577	2051.65	1847.86	1897.03	1950.06	0.3577	0.3771	0.3868	0.3964
1495.0	0.68	1386.52	0.3556	2049.68	1836.74	1885.9	1938.94	0.3556	0.3767	0.3865	0.396
1500.0	0.68	1388.44	0.3535	2047.72	1825.73	1874.88	1927.94	0.3535	0.3764	0.3861	0.3956
1505.0	0.68	1390.34	0.3514	2045.78	1814.83	1863.97	1917.04	0.3514	0.376	0.3857	0.3952
1380.0	0.69	1336.74	0.4106	2102.49	2128.27	2177.67	2230.43	0.4106	0.3867	0.3964	0.4059
1385.0	0.69	1339.25	0.4079	2100.06	2114.22	2163.6	2216.37	0.4079	0.3862	0.396	0.4055
1390.0	0.69	1341.74	0.4053	2097.65	2100.32	2149.7	2202.48	0.4053	0.3858	0.3955	0.405
1395.0	0.69	1344.19	0.4027	2095.27	2086.59	2135.95	2188.75	0.4027	0.3853	0.3951	0.4046
1400.0	0.69	1346.61	0.4002	2092.91	2073.0	2122.36	2175.16	0.4002	0.3849	0.3946	0.4041
1405.0	0.69	1349.01	0.3976	2090.58	2059.56	2108.9	2161.72	0.3976	0.3845	0.3942	0.4037
1410.0	0.69	1351.37	0.3951	2088.26	2046.27	2095.61	2148.44	0.3951	0.384	0.3937	0.4033
1415.0	0.69	1353.7	0.3926	2085.97	2033.13	2082.45	2135.3	0.3926	0.3836	0.3933	0.4028
1420.0	0.69	1356.01	0.3902	2083.7	2020.13	2069.44	2122.3	0.3902	0.3832	0.3929	0.4024
1425.0	0.69	1358.28	0.3878	2081.45	2007.26	2056.57	2109.44	0.3878	0.3827	0.3924	0.402
1430.0	0.69	1360.53	0.3854	2079.22	1994.54	2043.84	2096.72	0.3854	0.3823	0.392	0.4016
1435.0	0.69	1362.75	0.383	2077.01	1981.96	2031.24	2084.14	0.383	0.3819	0.3916	0.4011
1440.0	0.69	1364.94	0.3806	2074.82	1969.51	2018.78	2071.69	0.3806	0.3815	0.3912	0.4007
1445.0	0.69	1367.11	0.3783	2072.65	1957.19	2006.45	2059.37	0.3783	0.3811	0.3908	0.4003
1450.0	0.69	1369.25	0.376	2070.5	1944.99	1994.25	2047.18	0.376	0.3807	0.3904	0.3999
1455.0	0.69	1371.36	0.3737	2068.37	1932.93	1982.18	2035.12	0.3737	0.3803	0.39	0.3995
1460.0	0.69	1373.46	0.3715	2066.26	1921.0	1970.23	2023.19	0.3715	0.3799	0.3896	0.3991
1465.0	0.69	1375.52	0.3692	2064.17	1909.19	1958.41	2011.38	0.3692	0.3795	0.3892	0.3987
1470.0	0.69	1377.56	0.367	2062.1	1897.5	1946.71	1999.69	0.367	0.3791	0.3888	0.3983
1475.0	0.69	1379.58	0.3649	2060.04	1885.93	1935.13	1988.12	0.3649	0.3787	0.3884	0.3979
1480.0	0.69	1381.58	0.3627	2058.01	1874.48	1923.67	1976.67	0.3627	0.3783	0.388	0.3976
1485.0	0.69	1383.55	0.3606	2055.99	1863.15	1912.33	1965.34	0.3606	0.3779	0.3876	0.3972
1490.0	0.69	1385.5	0.3584	2053.99	1851.93	1901.1	1954.13	0.3584	0.3776	0.3873	0.3968
1495.0	0.69	1387.42	0.3563	2052.01	1840.82	1889.98	1943.02	0.3563	0.3772	0.3869	0.3964
1500.0	0.69	1389.33	0.3543	2050.04	1829.83	1878.98	1932.03	0.3543	0.3768	0.3865	0.3961
1505.0	0.69	1391.21	0.3522	2048.1	1818.95	1868.09	1921.15	0.3522	0.3764	0.3862	0.3957
1510.0	0.69	1393.07	0.3502	2046.17	1808.17	1857.3	1910.38	0.3502	0.3761	0.3858	0.3953
1385.0	0.7	1340.55	0.4086	2102.52	2117.52	2166.9	2219.67	0.4086	0.3867	0.3964	0.4059
1390.0	0.7	1343.02	0.4059	2100.1	2103.65	2153.03	2205.81	0.4059	0.3862	0.396	0.4055
1395.0	0.7	1345.45	0.4034	2097.71	2089.94	2139.31	2192.1	0.4034	0.3858	0.3955	0.405
1400.0	0.7	1347.86	0.4008	2095.35	2076.37	2125.73	2178.54	0.4008	0.3854	0.3951	0.4046
1405.0	0.7	1350.23	0.3983	2093.0	2062.96	2112.31	2165.13	0.3983	0.3849	0.3946	0.4042
1410.0	0.7	1352.58	0.3958	2090.68	2049.7	2099.04	2151.87	0.3958	0.3845	0.3942	0.4037
1415.0	0.7	1354.9	0.3933	2088.38	2036.58	2085.91	2138.75	0.3933	0.384	0.3938	0.4033
1420.0	0.7	1357.18	0.3908	2086.1	2023.6	2072.92	2125.77	0.3908	0.3836	0.3933	0.4028
1425.0	0.7	1359.44	0.3884	2083.84	2010.76	2060.07	2112.94	0.3884	0.3832	0.3929	0.4024
1430.0	0.7	1361.67	0.386	2081.6	1998.07	2047.36	2100.24	0.386	0.3828	0.3925	0.402
1435.0	0.7	1363.88	0.3837	2079.39	1985.5	2034.79	2087.68	0.3837	0.3823	0.3921	0.4016
1440.0	0.7	1366.06	0.3813	2077.19	1973.07	2022.35	2075.25	0.3813	0.3819	0.3916	0.4012
1445.0	0.7	1368.21	0.379	2075.01	1960.77	2010.04	2062.95	0.379	0.3815	0.3912	0.4008
1450.0	0.7	1370.33	0.3767	2072.86	1948.6	1997.86	2050.79	0.3767	0.3811	0.3908	0.4004
1455.0	0.7	1372.44	0.3744	2070.72	1936.56	1985.81	2038.75	0.3744	0.3807	0.3904	0.3999
1460.0	0.7	1374.51	0.3722	2068.6	1924.65	1973.88	2026.83	0.3722	0.3803	0.39	0.3996
1465.0	0.7	1376.56	0.3699	2066.5	1912.85	1962.08	2015.04	0.3699	0.3799	0.3896	0.3992
1470.0	0.7	1378.59	0.3677	2064.42	1901.18	1950.4	2003.37	0.3677	0.3795	0.3892	0.3988
1475.0	0.7	1380.59	0.3656	2062.36	1889.63	1938.84	1991.82	0.3656	0.3791	0.3888	0.3984
1480.0	0.7	1382.57	0.3634	2060.32	1878.2	1927.39	1980.39	0.3634	0.3787	0.3885	0.398
1485.0	0.7	1384.53	0.3613	2058.29	1866.88	1916.07	1969.08	0.3613	0.3784	0.3881	0.3976
1490.0	0.7	1386.47	0.3592	2056.28	1855.68	1904.85	1957.87	0.3592	0.378	0.3877	0.3972
1495.0	0.7	1388.38	0.3571	2054.29	1844.59	1893.75	1946.79	0.3571	0.3776	0.3873	0.3969
1500.0	0.7	1390.27	0.355	2052.32	1833.61	1882.77	1935.82	0.355	0.3772	0.387	0.3965
1505.0	0.7	1392.14	0.3529	2050.37	1822.75	1871.89	1924.95	0.3529	0.3769	0.3866	0.3961
1510.0	0.7	1393.99	0.3509	2048.43	1811.99	1861.12	1914.19	0.3509	0.3765	0.3862	0.3957
1515.0	0.7	1395.82	0.3489	2046.51	1801.33	1850.45	1903.54	0.3489	0.3761	0.3859	0.3954

Table 4. Table 4 : a ​ b 𝑎 𝑏 ab -model results

Startup values			Using $b_{P_{ab,\mathrm{out}}}$ as input				Using $a_{P_{ab,\mathrm{out}}}$ as input
$a_{P_{ab,\mathrm{in}}}$	$b_{P_{ab,\mathrm{in}}}$	$a_{P_{ab,\mathrm{out}}}$	$a_{P_{+}}$	$a_P$	$a_{P_{-}}$	$b_{P_{ab,\mathrm{out}}}$	$b_{P_{-}}$	$b_P$	$b_{P_{+}}$
1005.0	0.25	2078.35	2246.06	2193.31	2143.9	0.4135	0.4014	0.3919	0.3821
1025.0	0.25	2078.35	2246.05	2193.3	2143.89	0.4135	0.4014	0.3919	0.3821
1045.0	0.25	2077.9	2252.09	2199.35	2149.94	0.4147	0.4013	0.3918	0.3821
1065.0	0.25	2078.04	2250.26	2197.51	2148.1	0.4143	0.4013	0.3918	0.3821
1085.0	0.25	2078.14	2248.84	2196.1	2146.69	0.4141	0.4013	0.3918	0.3821
1105.0	0.25	2078.22	2247.79	2195.05	2145.64	0.4139	0.4014	0.3918	0.3821
1125.0	0.25	2078.27	2247.06	2194.31	2144.91	0.4137	0.4014	0.3918	0.3821
1145.0	0.25	2078.31	2246.58	2193.83	2144.43	0.4136	0.4014	0.3919	0.3821
1165.0	0.25	2078.33	2246.29	2193.55	2144.14	0.4136	0.4014	0.3919	0.3821
1185.0	0.25	2078.35	2246.05	2193.3	2143.89	0.4135	0.4014	0.3919	0.3821
1205.0	0.25	2077.89	2252.2	2199.46	2150.04	0.4147	0.4013	0.3918	0.3821
1225.0	0.25	2078.03	2250.34	2197.6	2148.19	0.4143	0.4013	0.3918	0.3821
1245.0	0.25	2078.13	2248.91	2196.17	2146.76	0.4141	0.4013	0.3918	0.3821
1265.0	0.25	2078.21	2247.85	2195.1	2145.69	0.4139	0.4014	0.3918	0.3821
1285.0	0.25	2078.27	2247.1	2194.35	2144.95	0.4137	0.4014	0.3918	0.3821
1305.0	0.25	2078.31	2246.61	2193.86	2144.45	0.4136	0.4014	0.3919	0.3821
1325.0	0.25	2078.33	2246.3	2193.56	2144.15	0.4136	0.4014	0.3919	0.3821
1345.0	0.25	2078.34	2246.14	2193.4	2143.99	0.4136	0.4014	0.3919	0.3821
1365.0	0.25	2077.65	2255.77	2203.03	2153.62	0.4154	0.4013	0.3917	0.382
1385.0	0.25	2077.89	2252.15	2199.41	2150.0	0.4147	0.4013	0.3918	0.3821
1405.0	0.25	2078.18	2248.29	2195.54	2146.14	0.414	0.4014	0.3918	0.3821
1425.0	0.25	2078.34	2246.14	2193.4	2143.99	0.4136	0.4014	0.3919	0.3821
1445.0	0.25	2078.35	2246.07	2193.32	2143.91	0.4135	0.4014	0.3919	0.3821
1465.0	0.25	2077.89	2252.24	2199.5	2150.08	0.4147	0.4013	0.3918	0.3821
1485.0	0.25	2078.18	2248.34	2195.59	2146.18	0.414	0.4014	0.3918	0.3821
1505.0	0.25	2078.31	2246.54	2193.79	2144.39	0.4136	0.4014	0.3919	0.3821
1525.0	0.25	2077.51	2257.31	2204.57	2155.15	0.4157	0.4012	0.3917	0.382
1545.0	0.25	2078.31	2246.55	2193.8	2144.39	0.4136	0.4014	0.3919	0.3821
1565.0	0.25	2077.5	2257.42	2204.68	2155.27	0.4157	0.4012	0.3917	0.382
1585.0	0.25	2078.35	2246.04	2193.3	2143.89	0.4135	0.4014	0.3919	0.3821
1605.0	0.25	2078.26	2247.25	2194.5	2145.09	0.4138	0.4014	0.3918	0.3821
1625.0	0.25	2078.35	2246.03	2193.28	2143.88	0.4135	0.4014	0.3919	0.3821
1645.0	0.25	2078.32	2246.4	2193.66	2144.25	0.4136	0.4014	0.3919	0.3821
1665.0	0.25	2076.38	2272.56	2219.83	2170.41	0.4185	0.401	0.3915	0.3818
1685.0	0.25	2078.02	2250.52	2197.77	2148.36	0.4144	0.4013	0.3918	0.3821
1705.0	0.25	2078.08	2249.6	2196.86	2147.45	0.4142	0.4013	0.3918	0.3821
1725.0	0.25	2088.21	2108.73	2055.86	2006.56	0.3876	0.4032	0.3937	0.384
1745.0	0.25	2112.27	1775.2	1721.95	1672.96	0.3247	0.4078	0.3983	0.3885
1765.0	0.25	2121.21	1651.7	1598.27	1549.43	0.3013	0.4095	0.3999	0.3902
1785.0	0.25	2135.74	1451.23	1397.43	1348.89	0.2635	0.4122	0.4027	0.393
1805.0	0.25	2138.49	1413.53	1359.65	1311.17	0.2564	0.4127	0.4032	0.3935
1005.0	0.3	2078.19	2248.11	2195.36	2145.95	0.4139	0.4014	0.3918	0.3821
1025.0	0.3	2078.26	2247.28	2194.53	2145.12	0.4138	0.4014	0.3918	0.3821
1045.0	0.3	2078.3	2246.72	2193.97	2144.56	0.4137	0.4014	0.3919	0.3821
1065.0	0.3	2078.32	2246.37	2193.62	2144.22	0.4136	0.4014	0.3919	0.3821
1085.0	0.3	2078.34	2246.18	2193.43	2144.02	0.4136	0.4014	0.3919	0.3821
1105.0	0.3	2078.35	2246.04	2193.29	2143.89	0.4135	0.4014	0.3919	0.3821
1125.0	0.3	2077.99	2250.92	2198.18	2148.77	0.4145	0.4013	0.3918	0.3821
1145.0	0.3	2078.1	2249.35	2196.61	2147.2	0.4142	0.4013	0.3918	0.3821
1165.0	0.3	2078.19	2248.17	2195.43	2146.02	0.4139	0.4014	0.3918	0.3821
1185.0	0.3	2078.25	2247.32	2194.57	2145.17	0.4138	0.4014	0.3918	0.3821
1205.0	0.3	2078.29	2246.75	2194.0	2144.59	0.4137	0.4014	0.3919	0.3821
1225.0	0.3	2078.32	2246.39	2193.64	2144.23	0.4136	0.4014	0.3919	0.3821
1245.0	0.3	2078.34	2246.18	2193.44	2144.03	0.4136	0.4014	0.3919	0.3821
1265.0	0.3	2078.34	2246.09	2193.34	2143.93	0.4135	0.4014	0.3919	0.3821
1285.0	0.3	2078.35	2246.04	2193.3	2143.89	0.4135	0.4014	0.3919	0.3821
1305.0	0.3	2078.1	2249.32	2196.58	2147.17	0.4142	0.4013	0.3918	0.3821
1325.0	0.3	2078.28	2246.93	2194.18	2144.78	0.4137	0.4014	0.3919	0.3821
1345.0	0.3	2078.34	2246.09	2193.34	2143.93	0.4135	0.4014	0.3919	0.3821
1365.0	0.3	2078.35	2246.04	2193.3	2143.89	0.4135	0.4014	0.3919	0.3821
1385.0	0.3	2078.1	2249.38	2196.64	2147.23	0.4142	0.4013	0.3918	0.3821
1405.0	0.3	2078.28	2246.96	2194.21	2144.8	0.4137	0.4014	0.3918	0.3821
1425.0	0.3	2078.34	2246.13	2193.39	2143.98	0.4136	0.4014	0.3919	0.3821
1445.0	0.3	2078.28	2246.96	2194.21	2144.81	0.4137	0.4014	0.3918	0.3821
1465.0	0.3	2078.34	2246.13	2193.39	2143.98	0.4136	0.4014	0.3919	0.3821
1485.0	0.3	2078.34	2246.1	2193.36	2143.95	0.4135	0.4014	0.3919	0.3821
1505.0	0.3	2078.35	2246.03	2193.28	2143.88	0.4135	0.4014	0.3919	0.3821
1525.0	0.3	2078.35	2246.03	2193.28	2143.88	0.4135	0.4014	0.3919	0.3821
1545.0	0.3	2077.4	2258.83	2206.09	2156.67	0.4159	0.4012	0.3917	0.382
1565.0	0.3	2078.15	2248.64	2195.9	2146.49	0.414	0.4014	0.3918	0.3821
1585.0	0.3	2078.16	2248.61	2195.87	2146.46	0.414	0.4014	0.3918	0.3821
1605.0	0.3	2078.34	2246.1	2193.36	2143.95	0.4135	0.4014	0.3919	0.3821
1625.0	0.3	2089.82	2086.36	2033.47	1984.18	0.3834	0.4036	0.394	0.3843
1645.0	0.3	2099.58	1950.92	1897.89	1848.72	0.3578	0.4054	0.3959	0.3861
1665.0	0.3	2115.02	1736.95	1683.64	1634.7	0.3174	0.4083	0.3988	0.3891
1685.0	0.3	2118.47	1689.47	1636.1	1587.21	0.3085	0.409	0.3994	0.3897
1705.0	0.3	2120.86	1656.36	1602.94	1554.09	0.3022	0.4094	0.3999	0.3902
1725.0	0.3	2122.67	1631.48	1578.02	1529.21	0.2975	0.4097	0.4002	0.3905
1745.0	0.3	2124.11	1611.66	1558.16	1509.37	0.2938	0.41	0.4005	0.3908
1765.0	0.3	2125.31	1595.07	1541.55	1492.78	0.2907	0.4102	0.4007	0.391
1785.0	0.3	2126.35	1580.7	1527.16	1478.41	0.2879	0.4104	0.4009	0.3912
1805.0	0.3	2127.28	1567.91	1514.34	1465.61	0.2855	0.4106	0.4011	0.3914
1005.0	0.35	2078.35	2246.04	2193.3	2143.89	0.4135	0.4014	0.3919	0.3821
1025.0	0.35	2077.94	2251.55	2198.81	2149.4	0.4146	0.4013	0.3918	0.3821
1045.0	0.35	2078.07	2249.84	2197.09	2147.68	0.4143	0.4013	0.3918	0.3821
1065.0	0.35	2078.16	2248.53	2195.79	2146.38	0.414	0.4014	0.3918	0.3821
1085.0	0.35	2078.23	2247.58	2194.83	2145.42	0.4138	0.4014	0.3918	0.3821
1105.0	0.35	2078.28	2246.91	2194.17	2144.76	0.4137	0.4014	0.3919	0.3821
1125.0	0.35	2078.31	2246.49	2193.74	2144.33	0.4136	0.4014	0.3919	0.3821
1145.0	0.35	2078.33	2246.24	2193.49	2144.09	0.4136	0.4014	0.3919	0.3821
1165.0	0.35	2078.34	2246.11	2193.36	2143.96	0.4135	0.4014	0.3919	0.3821
1185.0	0.35	2078.35	2246.05	2193.31	2143.9	0.4135	0.4014	0.3919	0.3821
1205.0	0.35	2078.01	2250.62	2197.88	2148.47	0.4144	0.4013	0.3918	0.3821
1225.0	0.35	2078.24	2247.52	2194.77	2145.37	0.4138	0.4014	0.3918	0.3821
1245.0	0.35	2078.34	2246.11	2193.37	2143.96	0.4135	0.4014	0.3919	0.3821
1265.0	0.35	2078.35	2246.05	2193.31	2143.9	0.4135	0.4014	0.3919	0.3821
1285.0	0.35	2078.0	2250.7	2197.96	2148.55	0.4144	0.4013	0.3918	0.3821
1305.0	0.35	2078.23	2247.56	2194.81	2145.4	0.4138	0.4014	0.3918	0.3821
1325.0	0.35	2078.33	2246.29	2193.54	2144.13	0.4136	0.4014	0.3919	0.3821
1345.0	0.35	2078.23	2247.56	2194.82	2145.41	0.4138	0.4014	0.3918	0.3821
1365.0	0.35	2078.33	2246.29	2193.54	2144.13	0.4136	0.4014	0.3919	0.3821
1385.0	0.35	2078.01	2250.57	2197.83	2148.42	0.4144	0.4013	0.3918	0.3821
1405.0	0.35	2078.35	2246.03	2193.29	2143.88	0.4135	0.4014	0.3919	0.3821
1425.0	0.35	2078.34	2246.11	2193.37	2143.96	0.4135	0.4014	0.3919	0.3821
1445.0	0.35	2078.05	2250.1	2197.36	2147.95	0.4143	0.4013	0.3918	0.3821
1465.0	0.35	2076.11	2276.3	2223.58	2174.15	0.4192	0.401	0.3914	0.3817
1485.0	0.35	2077.95	2250.65	2197.91	2148.49	0.4144	0.4013	0.3918	0.3821
1505.0	0.35	2086.72	2129.07	2076.22	2026.9	0.3915	0.403	0.3934	0.3837
1525.0	0.35	2093.01	2041.93	1988.99	1939.74	0.375	0.4042	0.3946	0.3849
1545.0	0.35	2097.33	1982.08	1929.08	1879.88	0.3637	0.405	0.3954	0.3857
1565.0	0.35	2100.41	1939.42	1886.37	1837.21	0.3557	0.4055	0.396	0.3863
1585.0	0.35	2102.73	1907.28	1854.2	1805.07	0.3496	0.406	0.3965	0.3867
1605.0	0.35	2104.57	1881.76	1828.65	1779.54	0.3448	0.4063	0.3968	0.3871
1625.0	0.35	2106.1	1860.55	1807.42	1758.34	0.3408	0.4066	0.3971	0.3874
1645.0	0.35	2107.42	1842.29	1789.13	1740.07	0.3373	0.4069	0.3973	0.3876
1665.0	0.35	2108.59	1826.08	1772.9	1723.85	0.3343	0.4071	0.3976	0.3878
1685.0	0.35	2109.65	1811.37	1758.17	1709.14	0.3315	0.4073	0.3978	0.388
1705.0	0.35	2110.63	1797.8	1744.58	1695.56	0.3289	0.4075	0.398	0.3882
1725.0	0.35	2078.29	2246.83	2194.08	2144.68	0.4137	0.4014	0.3919	0.3821
1745.0	0.35	2078.28	2246.93	2194.18	2144.77	0.4137	0.4014	0.3919	0.3821
1765.0	0.35	2078.27	2247.02	2194.28	2144.87	0.4137	0.4014	0.3918	0.3821
1785.0	0.35	2078.27	2247.13	2194.39	2144.98	0.4137	0.4014	0.3918	0.3821
1805.0	0.35	2078.26	2247.24	2194.49	2145.08	0.4138	0.4014	0.3918	0.3821
1005.0	0.4	2078.27	2247.11	2194.36	2144.95	0.4137	0.4014	0.3918	0.3821
1025.0	0.4	2078.3	2246.61	2193.86	2144.46	0.4136	0.4014	0.3919	0.3821
1045.0	0.4	2078.33	2246.31	2193.56	2144.15	0.4136	0.4014	0.3919	0.3821
1065.0	0.4	2078.34	2246.14	2193.4	2143.99	0.4136	0.4014	0.3919	0.3821
1085.0	0.4	2078.35	2246.07	2193.32	2143.91	0.4135	0.4014	0.3919	0.3821
1105.0	0.4	2077.89	2252.22	2199.47	2150.06	0.4147	0.4013	0.3918	0.3821
1125.0	0.4	2078.18	2248.32	2195.58	2146.17	0.414	0.4014	0.3918	0.3821
1145.0	0.4	2078.34	2246.15	2193.4	2143.99	0.4136	0.4014	0.3919	0.3821
1165.0	0.4	2078.34	2246.07	2193.32	2143.92	0.4135	0.4014	0.3919	0.3821
1185.0	0.4	2078.35	2246.04	2193.29	2143.88	0.4135	0.4014	0.3919	0.3821
1205.0	0.4	2078.17	2248.37	2195.62	2146.21	0.414	0.4014	0.3918	0.3821
1225.0	0.4	2078.31	2246.56	2193.81	2144.4	0.4136	0.4014	0.3919	0.3821
1245.0	0.4	2077.49	2257.63	2204.89	2155.48	0.4157	0.4012	0.3917	0.382
1265.0	0.4	2078.31	2246.56	2193.81	2144.4	0.4136	0.4014	0.3919	0.3821
1285.0	0.4	2077.48	2257.75	2205.01	2155.59	0.4157	0.4012	0.3917	0.382
1305.0	0.4	2078.35	2246.06	2193.31	2143.91	0.4135	0.4014	0.3919	0.3821
1325.0	0.4	2078.35	2246.03	2193.28	2143.88	0.4135	0.4014	0.3919	0.3821
1345.0	0.4	2078.25	2247.32	2194.58	2145.17	0.4138	0.4014	0.3918	0.3821
1365.0	0.4	2078.75	2240.39	2187.64	2138.24	0.4125	0.4015	0.3919	0.3822
1385.0	0.4	2080.24	2219.64	2166.87	2117.49	0.4086	0.4017	0.3922	0.3825
1405.0	0.4	2082.02	2194.86	2142.07	2092.7	0.4039	0.4021	0.3926	0.3828
1425.0	0.4	2083.77	2170.53	2117.72	2068.37	0.3993	0.4024	0.3929	0.3832
1445.0	0.4	2085.38	2148.12	2095.29	2045.95	0.3951	0.4027	0.3932	0.3835
1465.0	0.4	2086.85	2127.75	2074.9	2025.58	0.3912	0.403	0.3935	0.3837
1485.0	0.4	2088.19	2109.14	2056.27	2006.96	0.3877	0.4032	0.3937	0.384
1505.0	0.4	2089.42	2091.92	2039.03	1989.74	0.3844	0.4035	0.394	0.3842
1525.0	0.4	2090.58	2075.83	2022.93	1973.65	0.3814	0.4037	0.3942	0.3845
1545.0	0.4	2091.68	2060.63	2007.72	1958.45	0.3785	0.4039	0.3944	0.3847
1565.0	0.4	2092.72	2046.17	1993.24	1943.99	0.3758	0.4041	0.3946	0.3849
1585.0	0.4	2093.71	2032.33	1979.38	1930.14	0.3732	0.4043	0.3948	0.385
1605.0	0.4	2094.67	2018.99	1966.03	1916.8	0.3707	0.4045	0.3949	0.3852
1625.0	0.4	2077.29	2260.39	2207.65	2158.23	0.4162	0.4012	0.3917	0.3819
1645.0	0.4	2077.16	2262.01	2209.28	2159.86	0.4165	0.4012	0.3916	0.3819
1665.0	0.4	2077.04	2263.71	2210.98	2161.56	0.4169	0.4011	0.3916	0.3819
1685.0	0.4	2076.91	2265.42	2212.69	2163.27	0.4172	0.4011	0.3916	0.3819
1705.0	0.4	2076.78	2267.23	2214.5	2165.08	0.4175	0.4011	0.3916	0.3818
1725.0	0.4	2076.64	2269.04	2216.32	2166.89	0.4179	0.4011	0.3915	0.3818
1745.0	0.4	2076.51	2270.92	2218.19	2168.77	0.4182	0.401	0.3915	0.3818
1765.0	0.4	2076.36	2272.86	2220.14	2170.71	0.4186	0.401	0.3915	0.3818
1785.0	0.4	2076.22	2274.8	2222.08	2172.65	0.419	0.401	0.3915	0.3817
1805.0	0.4	2076.07	2276.82	2224.1	2174.67	0.4193	0.401	0.3914	0.3817
1005.0	0.45	2078.35	2246.05	2193.3	2143.89	0.4135	0.4014	0.3919	0.3821
1025.0	0.45	2078.1	2249.36	2196.62	2147.21	0.4142	0.4013	0.3918	0.3821
1045.0	0.45	2078.28	2246.95	2194.2	2144.79	0.4137	0.4014	0.3918	0.3821
1065.0	0.45	2078.34	2246.09	2193.34	2143.93	0.4135	0.4014	0.3919	0.3821
1085.0	0.45	2078.35	2246.05	2193.3	2143.89	0.4135	0.4014	0.3919	0.3821
1105.0	0.45	2078.1	2249.42	2196.68	2147.27	0.4142	0.4013	0.3918	0.3821
1125.0	0.45	2078.28	2246.98	2194.23	2144.82	0.4137	0.4014	0.3918	0.3821
1145.0	0.45	2078.34	2246.14	2193.39	2143.98	0.4136	0.4014	0.3919	0.3821
1165.0	0.45	2078.28	2246.98	2194.24	2144.83	0.4137	0.4014	0.3918	0.3821
1185.0	0.45	2078.34	2246.14	2193.39	2143.98	0.4136	0.4014	0.3919	0.3821
1205.0	0.45	2078.34	2246.13	2193.39	2143.98	0.4136	0.4014	0.3919	0.3821
1225.0	0.45	2074.25	2302.98	2250.28	2200.84	0.4243	0.4006	0.3911	0.3814
1245.0	0.45	2076.4	2272.97	2220.24	2170.82	0.4186	0.401	0.3915	0.3818
1265.0	0.45	2075.48	2285.83	2233.11	2183.68	0.421	0.4008	0.3913	0.3816
1285.0	0.45	2074.51	2299.51	2246.8	2197.36	0.4236	0.4007	0.3911	0.3814
1305.0	0.45	2073.84	2308.8	2256.1	2206.65	0.4254	0.4005	0.391	0.3813
1325.0	0.45	2073.58	2312.46	2259.77	2210.32	0.4261	0.4005	0.391	0.3812
1345.0	0.45	2073.67	2311.21	2258.51	2209.06	0.4258	0.4005	0.391	0.3813
1365.0	0.45	2074.03	2306.24	2253.54	2204.09	0.4249	0.4006	0.391	0.3813
1385.0	0.45	2074.57	2298.66	2245.96	2196.51	0.4235	0.4007	0.3912	0.3814
1405.0	0.45	2075.24	2289.3	2236.58	2187.15	0.4217	0.4008	0.3913	0.3816
1425.0	0.45	2076.0	2278.75	2226.03	2176.6	0.4197	0.4009	0.3914	0.3817
1445.0	0.45	2076.81	2267.42	2214.69	2165.27	0.4176	0.4011	0.3916	0.3819
1465.0	0.45	2077.66	2255.6	2202.86	2153.45	0.4153	0.4013	0.3917	0.382
1485.0	0.45	2078.53	2243.49	2190.74	2141.33	0.4131	0.4014	0.3919	0.3822
1505.0	0.45	2079.41	2231.21	2178.45	2129.05	0.4107	0.4016	0.3921	0.3823
1525.0	0.45	2078.34	2246.19	2193.44	2144.04	0.4136	0.4014	0.3919	0.3821
1545.0	0.45	2078.32	2246.37	2193.63	2144.22	0.4136	0.4014	0.3919	0.3821
1565.0	0.45	2078.3	2246.63	2193.88	2144.48	0.4136	0.4014	0.3919	0.3821
1585.0	0.45	2078.28	2246.96	2194.21	2144.8	0.4137	0.4014	0.3918	0.3821
1605.0	0.45	2078.25	2247.35	2194.6	2145.2	0.4138	0.4014	0.3918	0.3821
1625.0	0.45	2078.22	2247.81	2195.07	2145.66	0.4139	0.4014	0.3918	0.3821
1645.0	0.45	2078.18	2248.34	2195.59	2146.19	0.414	0.4014	0.3918	0.3821
1665.0	0.45	2078.13	2248.93	2196.19	2146.78	0.4141	0.4013	0.3918	0.3821
1685.0	0.45	2078.08	2249.59	2196.84	2147.43	0.4142	0.4013	0.3918	0.3821
1705.0	0.45	2078.03	2250.31	2197.56	2148.15	0.4143	0.4013	0.3918	0.3821
1725.0	0.45	2077.97	2251.07	2198.33	2148.92	0.4145	0.4013	0.3918	0.3821
1745.0	0.45	2077.91	2251.92	2199.17	2149.76	0.4146	0.4013	0.3918	0.3821
1765.0	0.45	2077.85	2252.8	2200.06	2150.65	0.4148	0.4013	0.3918	0.3821
1785.0	0.45	2077.78	2253.75	2201.01	2151.59	0.415	0.4013	0.3918	0.382
1805.0	0.45	2077.7	2254.75	2202.01	2152.6	0.4152	0.4013	0.3917	0.382
1005.0	0.5	2078.0	2250.75	2198.01	2148.6	0.4144	0.4013	0.3918	0.3821
1025.0	0.5	2078.23	2247.58	2194.84	2145.43	0.4138	0.4014	0.3918	0.3821
1045.0	0.5	2078.33	2246.29	2193.55	2144.14	0.4136	0.4014	0.3919	0.3821
1065.0	0.5	2078.23	2247.59	2194.85	2145.44	0.4138	0.4014	0.3918	0.3821
1085.0	0.5	2078.33	2246.3	2193.55	2144.14	0.4136	0.4014	0.3919	0.3821
1105.0	0.5	2078.0	2250.78	2198.04	2148.63	0.4144	0.4013	0.3918	0.3821
1125.0	0.5	2077.01	2264.06	2211.33	2161.91	0.4169	0.4011	0.3916	0.3819
1145.0	0.5	2078.13	2248.96	2196.21	2146.81	0.4141	0.4013	0.3918	0.3821
1165.0	0.5	2078.03	2250.35	2197.61	2148.2	0.4143	0.4013	0.3918	0.3821
1185.0	0.5	2077.9	2252.13	2199.39	2149.98	0.4147	0.4013	0.3918	0.3821
1205.0	0.5	2074.27	2302.64	2249.94	2200.49	0.4242	0.4006	0.3911	0.3814
1225.0	0.5	2062.99	2460.21	2407.62	2358.08	0.4539	0.3985	0.389	0.3792
1245.0	0.5	2062.17	2471.72	2419.15	2369.59	0.4561	0.3983	0.3888	0.3791
1265.0	0.5	2061.76	2477.48	2424.9	2375.35	0.4572	0.3983	0.3887	0.379
1285.0	0.5	2061.68	2478.6	2426.03	2376.47	0.4574	0.3982	0.3887	0.379
1305.0	0.5	2061.85	2476.13	2423.56	2374.01	0.457	0.3983	0.3888	0.379
1325.0	0.5	2062.23	2470.96	2418.38	2368.83	0.456	0.3983	0.3888	0.3791
1345.0	0.5	2062.74	2463.75	2411.17	2361.62	0.4546	0.3984	0.3889	0.3792
1365.0	0.5	2063.37	2455.03	2402.44	2352.9	0.453	0.3986	0.389	0.3793
1385.0	0.5	2064.07	2445.21	2392.61	2343.08	0.4511	0.3987	0.3892	0.3795
1405.0	0.5	2076.75	2268.1	2215.38	2165.95	0.4177	0.4011	0.3916	0.3818
1425.0	0.5	2076.91	2265.91	2213.18	2163.76	0.4173	0.4011	0.3916	0.3819
1445.0	0.5	2077.07	2263.68	2210.95	2161.53	0.4169	0.4011	0.3916	0.3819
1465.0	0.5	2077.23	2261.48	2208.74	2159.32	0.4164	0.4012	0.3917	0.3819
1485.0	0.5	2077.38	2259.34	2206.61	2157.19	0.416	0.4012	0.3917	0.382
1505.0	0.5	2077.53	2257.31	2204.57	2155.16	0.4157	0.4012	0.3917	0.382
1525.0	0.5	2077.67	2255.41	2202.67	2153.25	0.4153	0.4013	0.3917	0.382
1545.0	0.5	2077.8	2253.65	2200.91	2151.5	0.415	0.4013	0.3918	0.382
1565.0	0.5	2077.91	2252.05	2199.31	2149.9	0.4147	0.4013	0.3918	0.3821
1585.0	0.5	2078.01	2250.63	2197.89	2148.48	0.4144	0.4013	0.3918	0.3821
1605.0	0.5	2078.1	2249.39	2196.64	2147.23	0.4142	0.4013	0.3918	0.3821
1625.0	0.5	2074.36	2301.65	2248.95	2199.51	0.424	0.4006	0.3911	0.3814
1645.0	0.5	2075.22	2289.61	2236.9	2187.47	0.4218	0.4008	0.3913	0.3816
1665.0	0.5	2076.08	2277.68	2224.96	2175.53	0.4195	0.401	0.3914	0.3817
1685.0	0.5	2076.92	2265.86	2213.13	2163.71	0.4173	0.4011	0.3916	0.3819
1705.0	0.5	2077.76	2254.16	2201.42	2152.01	0.4151	0.4013	0.3918	0.382
1725.0	0.5	2078.6	2242.58	2189.83	2140.43	0.4129	0.4014	0.3919	0.3822
1745.0	0.5	2079.42	2231.13	2178.37	2128.98	0.4107	0.4016	0.3921	0.3823
1765.0	0.5	2078.34	2246.18	2193.43	2144.02	0.4136	0.4014	0.3919	0.3821
1785.0	0.5	2094.31	2023.96	1971.01	1921.77	0.3716	0.4044	0.3949	0.3852
1805.0	0.5	2098.54	1965.24	1912.22	1863.04	0.3605	0.4052	0.3957	0.386
1005.0	0.55	2077.2	2261.59	2208.86	2159.44	0.4165	0.4012	0.3916	0.3819
1025.0	0.55	2072.82	2322.87	2270.18	2220.72	0.428	0.4003	0.3908	0.3811
1045.0	0.55	2071.15	2346.18	2293.51	2244.04	0.4324	0.4	0.3905	0.3808
1065.0	0.55	2068.82	2378.74	2326.1	2276.6	0.4386	0.3996	0.3901	0.3803
1085.0	0.55	2066.33	2413.36	2360.75	2311.23	0.4451	0.3991	0.3896	0.3799
1105.0	0.55	2064.08	2444.89	2392.29	2342.76	0.4511	0.3987	0.3892	0.3795
1125.0	0.55	2062.23	2470.71	2418.13	2368.58	0.4559	0.3983	0.3888	0.3791
1145.0	0.55	2060.85	2490.01	2437.44	2387.88	0.4596	0.3981	0.3886	0.3788
1165.0	0.55	2049.91	2643.15	2590.68	2541.04	0.4885	0.396	0.3865	0.3768
1185.0	0.55	2059.35	2510.9	2458.35	2408.78	0.4635	0.3978	0.3883	0.3786
1205.0	0.55	2077.29	2260.29	2207.56	2158.14	0.4162	0.4012	0.3917	0.3819
1225.0	0.55	2077.29	2260.26	2207.53	2158.11	0.4162	0.4012	0.3917	0.3819
1245.0	0.55	2059.37	2510.65	2458.1	2408.52	0.4635	0.3978	0.3883	0.3786
1265.0	0.55	2059.76	2505.18	2452.62	2403.05	0.4624	0.3979	0.3884	0.3786
1285.0	0.55	2060.28	2497.94	2445.38	2395.81	0.4611	0.398	0.3885	0.3787
1305.0	0.55	2060.9	2489.31	2436.74	2387.18	0.4594	0.3981	0.3886	0.3789
1325.0	0.55	2061.59	2479.61	2427.04	2377.48	0.4576	0.3982	0.3887	0.379
1345.0	0.55	2062.34	2469.08	2416.5	2366.95	0.4556	0.3984	0.3888	0.3791
1365.0	0.55	2063.14	2457.91	2405.33	2355.79	0.4535	0.3985	0.389	0.3793
1385.0	0.55	2063.98	2446.27	2393.67	2344.14	0.4513	0.3987	0.3892	0.3794
1405.0	0.55	2064.84	2434.26	2381.65	2332.12	0.449	0.3988	0.3893	0.3796
1425.0	0.55	2065.72	2421.98	2369.37	2319.85	0.4467	0.399	0.3895	0.3798
1445.0	0.55	2066.61	2409.51	2356.89	2307.38	0.4444	0.3992	0.3896	0.3799
1465.0	0.55	2067.51	2396.92	2344.29	2294.79	0.442	0.3993	0.3898	0.3801
1485.0	0.55	2075.12	2290.68	2237.97	2188.53	0.422	0.4008	0.3913	0.3815
1505.0	0.55	2075.37	2287.24	2234.53	2185.09	0.4213	0.4008	0.3913	0.3816
1525.0	0.55	2075.61	2283.89	2231.18	2181.74	0.4207	0.4009	0.3913	0.3816
1545.0	0.55	2075.84	2280.65	2227.93	2178.5	0.4201	0.4009	0.3914	0.3817
1565.0	0.55	2076.07	2277.51	2224.79	2175.36	0.4195	0.401	0.3914	0.3817
1585.0	0.55	2076.29	2274.5	2221.78	2172.35	0.4189	0.401	0.3915	0.3818
1605.0	0.55	2076.5	2271.63	2218.9	2169.48	0.4184	0.401	0.3915	0.3818
1625.0	0.55	2076.69	2268.88	2216.16	2166.73	0.4178	0.4011	0.3916	0.3818
1645.0	0.55	2076.88	2266.29	2213.56	2164.14	0.4174	0.4011	0.3916	0.3819
1665.0	0.55	2083.72	2171.16	2118.35	2068.99	0.3994	0.4024	0.3929	0.3832
1685.0	0.55	2086.98	2125.81	2072.96	2023.64	0.3908	0.403	0.3935	0.3838
1705.0	0.55	2090.47	2077.34	2024.44	1975.16	0.3817	0.4037	0.3941	0.3844
1725.0	0.55	2094.02	2028.12	1975.17	1925.94	0.3724	0.4043	0.3948	0.3851
1745.0	0.55	2097.51	1979.58	1926.58	1877.39	0.3632	0.405	0.3955	0.3858
1765.0	0.55	2100.9	1932.58	1879.53	1830.38	0.3544	0.4056	0.3961	0.3864
1785.0	0.55	2104.15	1887.5	1834.4	1785.29	0.3459	0.4063	0.3967	0.387
1805.0	0.55	2107.26	1844.5	1791.34	1742.28	0.3377	0.4068	0.3973	0.3876
1005.0	0.6	2078.34	2246.15	2193.4	2143.99	0.4136	0.4014	0.3919	0.3821
1025.0	0.6	2078.2	2248.0	2195.26	2145.85	0.4139	0.4014	0.3918	0.3821
1045.0	0.6	2078.12	2249.08	2196.34	2146.93	0.4141	0.4013	0.3918	0.3821
1065.0	0.6	2078.05	2250.05	2197.31	2147.9	0.4143	0.4013	0.3918	0.3821
1085.0	0.6	2078.0	2250.79	2198.05	2148.64	0.4144	0.4013	0.3918	0.3821
1105.0	0.6	2077.96	2251.29	2198.55	2149.14	0.4145	0.4013	0.3918	0.3821
1125.0	0.6	2077.94	2251.53	2198.79	2149.38	0.4146	0.4013	0.3918	0.3821
1145.0	0.6	2077.94	2251.57	2198.83	2149.42	0.4146	0.4013	0.3918	0.3821
1165.0	0.6	2077.95	2251.42	2198.67	2149.26	0.4145	0.4013	0.3918	0.3821
1185.0	0.6	2077.97	2251.12	2198.38	2148.97	0.4145	0.4013	0.3918	0.3821
1205.0	0.6	2078.0	2250.73	2197.99	2148.58	0.4144	0.4013	0.3918	0.3821
1225.0	0.6	2078.04	2250.26	2197.51	2148.1	0.4143	0.4013	0.3918	0.3821
1245.0	0.6	2078.07	2249.75	2197.0	2147.59	0.4142	0.4013	0.3918	0.3821
1265.0	0.6	2078.11	2249.22	2196.48	2147.07	0.4141	0.4013	0.3918	0.3821
1285.0	0.6	2078.15	2248.7	2195.95	2146.55	0.414	0.4014	0.3918	0.3821
1305.0	0.6	2078.19	2248.2	2195.45	2146.04	0.4139	0.4014	0.3918	0.3821
1325.0	0.6	2078.22	2247.72	2194.98	2145.57	0.4139	0.4014	0.3918	0.3821
1345.0	0.6	2078.34	2246.16	2193.42	2144.01	0.4136	0.4014	0.3919	0.3821
1365.0	0.6	2078.34	2246.15	2193.4	2143.99	0.4136	0.4014	0.3919	0.3821
1385.0	0.6	2077.8	2253.48	2200.74	2151.33	0.4149	0.4013	0.3918	0.382
1405.0	0.6	2077.87	2252.53	2199.79	2150.38	0.4148	0.4013	0.3918	0.3821
1425.0	0.6	2077.93	2251.65	2198.91	2149.5	0.4146	0.4013	0.3918	0.3821
1445.0	0.6	2077.99	2250.82	2198.07	2148.66	0.4144	0.4013	0.3918	0.3821
1465.0	0.6	2078.22	2247.74	2195.0	2145.59	0.4139	0.4014	0.3918	0.3821
1485.0	0.6	2078.23	2247.58	2194.83	2145.43	0.4138	0.4014	0.3918	0.3821
1505.0	0.6	2078.24	2247.42	2194.67	2145.27	0.4138	0.4014	0.3918	0.3821
1525.0	0.6	2078.26	2247.28	2194.53	2145.12	0.4138	0.4014	0.3918	0.3821
1545.0	0.6	2078.27	2247.14	2194.4	2144.99	0.4137	0.4014	0.3918	0.3821
1565.0	0.6	2077.57	2256.93	2204.2	2154.78	0.4156	0.4012	0.3917	0.382
1585.0	0.6	2080.04	2222.41	2169.64	2120.25	0.4091	0.4017	0.3922	0.3825
1605.0	0.6	2082.91	2182.5	2129.69	2080.33	0.4015	0.4022	0.3927	0.383
1625.0	0.6	2086.01	2139.39	2086.55	2037.22	0.3934	0.4028	0.3933	0.3836
1645.0	0.6	2089.21	2094.84	2041.96	1992.67	0.385	0.4034	0.3939	0.3842
1665.0	0.6	2092.43	2050.09	1997.16	1947.91	0.3766	0.404	0.3945	0.3848
1685.0	0.6	2095.62	2005.93	1952.96	1903.74	0.3682	0.4046	0.3951	0.3854
1705.0	0.6	2098.72	1962.88	1909.86	1860.68	0.3601	0.4052	0.3957	0.386
1725.0	0.6	2101.72	1921.2	1868.14	1818.99	0.3522	0.4058	0.3963	0.3866
1745.0	0.6	2104.62	1881.06	1827.95	1778.85	0.3447	0.4063	0.3968	0.3871
1765.0	0.6	2107.41	1842.48	1789.33	1740.26	0.3374	0.4069	0.3973	0.3876
1785.0	0.6	2110.08	1805.5	1752.29	1703.27	0.3304	0.4074	0.3978	0.3881
1805.0	0.6	2078.28	2246.95	2194.21	2144.8	0.4137	0.4014	0.3918	0.3821
1005.0	0.65	2078.34	2246.12	2193.38	2143.97	0.4136	0.4014	0.3919	0.3821
1025.0	0.65	2078.34	2246.13	2193.39	2143.98	0.4136	0.4014	0.3919	0.3821
1045.0	0.65	2078.34	2246.14	2193.39	2143.98	0.4136	0.4014	0.3919	0.3821
1065.0	0.65	2078.34	2246.14	2193.39	2143.98	0.4136	0.4014	0.3919	0.3821
1085.0	0.65	2078.34	2246.13	2193.39	2143.98	0.4136	0.4014	0.3919	0.3821
1105.0	0.65	2078.34	2246.13	2193.38	2143.98	0.4136	0.4014	0.3919	0.3821
1125.0	0.65	2078.34	2246.12	2193.38	2143.97	0.4136	0.4014	0.3919	0.3821
1145.0	0.65	2076.92	2265.3	2212.57	2163.15	0.4172	0.4011	0.3916	0.3819
1165.0	0.65	2076.99	2264.31	2211.58	2162.16	0.417	0.4011	0.3916	0.3819
1185.0	0.65	2077.08	2263.22	2210.49	2161.07	0.4168	0.4011	0.3916	0.3819
1205.0	0.65	2077.16	2262.08	2209.35	2159.93	0.4166	0.4012	0.3916	0.3819
1225.0	0.65	2077.25	2260.9	2208.16	2158.75	0.4163	0.4012	0.3917	0.3819
1245.0	0.65	2077.34	2259.7	2206.96	2157.55	0.4161	0.4012	0.3917	0.382
1265.0	0.65	2078.33	2246.22	2193.47	2144.06	0.4136	0.4014	0.3919	0.3821
1285.0	0.65	2078.34	2246.19	2193.45	2144.04	0.4136	0.4014	0.3919	0.3821
1305.0	0.65	2078.34	2246.17	2193.43	2144.02	0.4136	0.4014	0.3919	0.3821
1325.0	0.65	2078.34	2246.16	2193.41	2144.0	0.4136	0.4014	0.3919	0.3821
1345.0	0.65	2078.34	2246.14	2193.39	2143.98	0.4136	0.4014	0.3919	0.3821
1365.0	0.65	2078.34	2246.12	2193.38	2143.97	0.4136	0.4014	0.3919	0.3821
1385.0	0.65	2076.96	2264.81	2212.08	2162.66	0.4171	0.4011	0.3916	0.3819
1405.0	0.65	2077.07	2263.3	2210.57	2161.15	0.4168	0.4011	0.3916	0.3819
1425.0	0.65	2077.18	2261.84	2209.1	2159.69	0.4165	0.4012	0.3916	0.3819
1445.0	0.65	2077.28	2260.44	2207.71	2158.29	0.4163	0.4012	0.3917	0.3819
1465.0	0.65	2071.5	2341.47	2288.79	2239.32	0.4315	0.4001	0.3906	0.3809
1485.0	0.65	2073.41	2314.85	2262.16	2212.7	0.4265	0.4005	0.3909	0.3812
1505.0	0.65	2075.77	2281.91	2229.2	2179.77	0.4203	0.4009	0.3914	0.3817
1525.0	0.65	2078.47	2244.37	2191.62	2142.22	0.4132	0.4014	0.3919	0.3822
1545.0	0.65	2081.38	2203.87	2151.09	2101.71	0.4056	0.402	0.3924	0.3827
1565.0	0.65	2084.4	2161.78	2108.97	2059.62	0.3976	0.4025	0.393	0.3833
1585.0	0.65	2087.47	2119.13	2066.27	2016.95	0.3896	0.4031	0.3936	0.3839
1605.0	0.65	2090.52	2076.63	2023.73	1974.45	0.3816	0.4037	0.3942	0.3844
1625.0	0.65	2093.54	2034.8	1981.86	1932.62	0.3737	0.4043	0.3947	0.385
1645.0	0.65	2096.48	1993.95	1940.97	1891.76	0.366	0.4048	0.3953	0.3856
1665.0	0.65	2099.34	1954.28	1901.25	1852.08	0.3585	0.4053	0.3958	0.3861
1685.0	0.65	2102.11	1915.89	1862.82	1813.68	0.3512	0.4059	0.3963	0.3866
1705.0	0.65	2075.68	2282.14	2229.42	2179.99	0.4203	0.4009	0.3914	0.3816
1725.0	0.65	2078.32	2246.47	2193.72	2144.31	0.4136	0.4014	0.3919	0.3821
1745.0	0.65	2078.3	2246.66	2193.91	2144.51	0.4137	0.4014	0.3919	0.3821
1765.0	0.65	2078.28	2246.9	2194.16	2144.75	0.4137	0.4014	0.3919	0.3821
1785.0	0.65	2078.26	2247.2	2194.45	2145.04	0.4138	0.4014	0.3918	0.3821
1805.0	0.65	2078.23	2247.56	2194.82	2145.41	0.4138	0.4014	0.3918	0.3821

Equations

$$v_P\left(z\right)=a_P+b_{P}z\mathrm{and}{v}_S(z)=a_S+b_{S}z,$$

$$\overline{f}(z)=\underset{-\infty }{\overset{\infty }{\int }}w\left(\zeta -z\right)f\left(\zeta \right)\mathrm{d}\zeta ,$$

$$w\left(z\right)⩾0,w\left(\pm \infty \right)=0,\underset{-\infty }{\overset{\infty }{\int }}w\left(z\right)\mathrm{d}z=1,\underset{-\infty }{\overset{\infty }{\int }}zw\left(z\right)\mathrm{d}z=0,\underset{-\infty }{\overset{\infty }{\int }}{z}^{2}w\left(z\right)\mathrm{d}z={\left({\ell }^{\prime }\right)}^2.$$

$$c_{1111}^{\overline{\mathrm{TI}}}$$

$$c_{1122}^{\overline{\mathrm{TI}}}$$

$$c_{1133}^{\overline{\mathrm{TI}}}$$

$$c_{1212}^{\overline{\mathrm{TI}}}$$

$$c_{2323}^{\overline{\mathrm{TI}}}$$

$$c_{3333}^{\overline{\mathrm{TI}}}$$

$$c_{1212}^{\overline{\mathrm{TI}}}=\overline{c_{2323}}=\frac{1}{h_2-h_1}\underset{h_1}{\overset{h_2}{\int }}{c}_{2323}\mathrm{d}z$$

$$=\frac{1}{3}\left(3a_S^2+3a_S{b}_S\left(h_1+h_2\right)+b_S^2\left(h_1^2+h_1{h}_2+h_2^2\right)\right).$$

$$\overline{\left(\frac{c_{1111}-2c_{2323}}{c_{1111}}\right)}=\frac{1}{h_2-h_1}\underset{h_1}{\overset{h_2}{\int }}\left(1-2\frac{{v_S}^2}{{v_P}^2}\right)\mathrm{d}z=\frac{1}{h_2-h_1}\underset{h_1}{\overset{h_2}{\int }}\left(1-2\frac{{\left(a_S+b_{S}z\right)}^2}{{\left(a_P+b_{P}z\right)}^2}\right)\mathrm{d}z=1-\frac{2I_1}{h_2-h_1}$$

$$I_1=\underset{h_1}{\overset{h_2}{\int }}\frac{{\left(a_S+b_{S}z\right)}^2}{{\left(a_P+b_{P}z\right)}^2}\mathrm{d}z$$

$$+\frac{\ln \left(a_P+h_1{b}_P\right)\left(2a_P{b_S}^2-2a_S{b}_P{b}_S\right)}{{b_P}^3}-\frac{\ln \left(a_P+h_2{b}_P\right)\left(2a_P{b_S}^2-2a_S{b}_P{b}_S\right)}{{b_P}^3}$$

$$+\frac{{a_P}^2{b_S}^2-2a_P{a}_S{b}_P{b}_S+{a_S}^2{b_P}^2}{b_P\left(h_1{b_P}^3+a_p{b_P}^2\right)}-\frac{{a_P}^2{b_S}^2-2a_P{a}_S{b}_P{b}_S+{a_S}^2{b_P}^2}{b_P\left(h_2{b_P}^3+a_P{b_P}^2\right)}.$$

$${\overline{\left(\frac{1}{c_{1111}}\right)}}^{-1}={\overline{\left(\frac{1}{v_P^2}\right)}}^{-1}={\left(\frac{1}{h_2-h_1}\underset{h_1}{\overset{h_2}{\int }}\frac{1}{{\left(a_P+b_{P}z\right)}^2}\mathrm{d}z\right)}^{-1}=\left(h_2-h_1\right){\left(\underset{h_1}{\overset{h_2}{\int }}{\left(a_P+b_{P}z\right)}^{-2}\mathrm{d}z\right)}^{-1}.$$

$${\overline{\left(\frac{1}{c_{1111}}\right)}}^{-1}$$

$$=\left(h_2-h_1\right)\left(-b_P\right){\left({\left(a_P+b_P{h}_2\right)}^{-1}-{\left(a_P+b_P{h}_1\right)}^{-1}\right)}^{-1}$$

$$=\left(a_P+b_P{h}_1\right)\left(a_P+b_P{h}_2\right).$$

$$\overline{\left(\frac{4\left(c_{1111}-c_{2323}\right)c_{2323}}{c_{1111}}\right)}=\frac{4}{h_2-h_1}\left(\underset{h_1}{\overset{h_2}{\int }}{\left(a_S+b_{S}z\right)}^2\mathrm{d}z-\underset{h_1}{\overset{h_2}{\int }}\frac{{\left(a_S+b_{S}z\right)}^4}{{\left(a_P+b_{P}z\right)}^2}\mathrm{d}z\right)=\frac{4}{h_2-h_1}\left(I_2-I_3\right),$$

$$I_2=\underset{h_1}{\overset{h_2}{\int }}{\left(a_S+b_{S}z\right)}^2\mathrm{d}z=\frac{1}{3}\left(h_2-h_1\right)\left(3a_S{}^2+3a_S{b}_S\left(h_1+h_2\right)+b_S{}^2\left(h_1^2+h_1{h}_2+h_2^2\right)\right)$$

$$I_3=\underset{h_1}{\overset{h_2}{\int }}\frac{{\left(a_S+b_{S}z\right)}^4}{{\left(a_P+b_{P}z\right)}^2}\mathrm{d}z$$

$$-h_1\left(\frac{2a_P\left(\frac{2a_P{b_S}^4}{{b_P}^3}-\frac{4a_S{b_S}^3}{{b_P}^2}\right)}{b_P}-\frac{{a_P}^2{b_S}^4}{{b_P}^4}+\frac{6{a_S}^2{b_S}^2}{{b_P}^2}\right)$$

$$+{h_1}^2\left(\frac{a_P{b_S}^4}{{b_P}^3}-\frac{2a_S{b_S}^3}{{b_P}^2}\right)-{h_2}^2\left(\frac{a_P{b_S}^4}{{b_P}^3}-\frac{2a_S{b_S}^3}{{b_P}^2}\right)$$

$$+\frac{\ln \left(a_P+h_1{b}_P\right)\left(4{a_P}^3{b_S}^4-12{a_P}^2{a}_S{b}_P{b_S}^3+12a_P{a_S}^2{b_P}^2{b_S}^2-4{a_S}^3{b_P}^3{b}_S\right)}{{b_P}^5}$$

$$-\frac{\ln \left(a_P+h_2{b}_P\right)\left(4{a_P}^3{b_S}^4-12{a_P}^2{a}_S{b}_P{b_S}^3+12a_P{a_S}^2{b_P}^2{b_S}^2-4{a_S}^3{b_P}^3{b}_S\right)}{{b_P}^5}$$

$$-\frac{{h_1}^3{b_S}^4}{3{b_P}^2}+\frac{{h_2}^3{b_S}^4}{3{b_P}^2}$$

$$+\frac{{a_P}^4{b_S}^4-4{a_P}^3{a}_S{b}_P{b_S}^3+6{a_P}^2{a_S}^2{b_P}^2{b_S}^2-4a_P{a_S}^3{b_P}^3{b}_S+{a_S}^4{b_P}^4}{b_P\left(h_1{b_P}^5+a_P{b_P}^4\right)}$$

$$-\frac{{a_P}^4{b_S}^4-4{a_P}^3{a}_S{b}_P{b_S}^3+6{a_P}^2{a_S}^2{b_P}^2{b_S}^2-4a_P{a_S}^3{b_P}^3{b}_S+{a_S}^4{b_P}^4}{b_P\left(h_2{b_P}^5+a_P{b_P}^4\right)}.$$

$$\overline{\left(\frac{2\left(c_{1111}-2c_{2323}\right)c_{2323}}{c_{1111}}\right)}=\frac{2}{h_2-h_1}\left(\underset{h_1}{\overset{h_2}{\int }}{\left(a_S+b_{S}z\right)}^2\mathrm{d}z-2\underset{h_1}{\overset{h_2}{\int }}\frac{{\left(a_S+b_{S}z\right)}^4}{{\left(a_P+b_{P}z\right)}^2}\mathrm{d}z\right)=\frac{2}{h_2-h_1}\left(I_2-2I_3\right),$$

$${\overline{\left(\frac{1}{c_{2323}}\right)}}^{-1}$$

$$=\left(a_S+b_S{h}_1\right)\left(a_S+b_S{h}_2\right).$$

$$c_{1111}^{\overline{\mathrm{TI}}}\left(h_1,h_2,a_S,b_S,a_P,b_P\right)$$

$$c_{1122}^{\overline{\mathrm{TI}}}\left(h_1,h_2,a_S,b_S,a_P,b_P\right)$$

$$c_{1133}^{\overline{\mathrm{TI}}}\left(h_1,h_2,a_S,b_S,a_P,b_P\right)$$

$$c_{1212}^{\overline{\mathrm{TI}}}\left(h_1,h_2,a_S,b_S\right)$$

$$c_{2323}^{\overline{\mathrm{TI}}}\left(h_1,h_2,a_S,b_S\right)$$

$$c_{3333}^{\overline{\mathrm{TI}}}\left(h_1,h_2,a_P,b_P\right)$$

$$\gamma =\gamma \left(h_1,h_2,a_S,b_S\right)$$

$$\delta =\delta \left(h_1,h_2,a_S,b_S,a_P,b_P\right)$$

$$\epsilon =\epsilon \left(h_1,h_2,a_S,b_S,a_P,b_P\right)$$

$$\gamma =\gamma \left(h_1,h_2,a_S,b_S\right)=\frac{{b_S}^2{\left(h_1-h_2\right)}^2}{6\left(a_S+b_S{h}_1\right)\left(a_S+b_S{h}_2\right)}.$$

$$\delta$$

Full text

1 Introduction

In this article, we parameterize an equivalent medium, resulting from the Backus (1962) average, with respect to linear inhomogeneity parameters of its constituent isotropic layers. Sedimentary basins often show thin layers that induce seismic anisotropy. The parametrization allows us to make a relationship between the anisotropy to layer inhomogeneity, which is, in seismological context, an important relation. We also assume the medium possesses linear inhomogeneity, which was first introduced by Slotnick (1959). The traveltime expression from a source to a receiver in a linearly inhomogeneous media is shown by Slawinski and Slawinski (1999).

To obtain a solution from the analytical relationship between the anisotropy and the linear inhomogeneity parameters, we require to provide one of the inhomogeneity parameter. We use two independent seismological methods, 1-D tomography and $ab$ model, to make the analytical relation to be well posed. The outcomes of the seismological methods are a pair of inhomogeneity parameters, using one of the parameter from each method allows us to obtain the solution of the analytical relation. The resultant solution from the analytical relation then can be examined by comparing with the results of the seismological methods.

2 Equivalent medium parameterization

We parameterize a transversely isotropic equivalent medium resulting from the Backus average of thin, intrinsically homogeneous, isotropic layers, which we refer to as the Backus* medium*. We assume that a stack of such constituent layers is inhomogeneous and possesses a constant-velocity gradient that increases linearly with depth (see e.g., Slawinski and Slawinski, 1999). Specifically, for both $P$ and $S$ waves,

[TABLE]

where $a_{P,S}$ are the wavespeeds at the top of the medium, $b_{P,S}$ are positive velocity-gradient constants, and $z$ is the depth.

2.1 Backus average

Following the definition of Backus (1962, Section 3), the average of a function $f(z)$ of width $\ell^{\prime}$ is the moving average given by

[TABLE]

where the properties of the weighting function are

[TABLE]

The result of performing average (2) on isotropic layers results is a homogeneous TI medium, where the corresponding elasticity parameters, which are referred to as Backus parameters, are

[TABLE]

Since the weighting function, $w$ , in integral (2), is continuous and symmetric, the Backus average may be written as a weighted average (e.g., Slawinski, 2018, Section 4.2.2). Herein, the Backus average is weighted by layer thickness. For density-scaled VSP measurements, $v_{P}=\sqrt{c_{1111}}$ and $v_{S}=\sqrt{c_{2323}}$ ; this allows for a reparameterization of parameters (3a)–(3f) in terms of linear-inhomogeneity parameters (1). For example, Backus parameter (3d) may be rewritten as

[TABLE]

For Backus parameter (3a), we begin with the first term, where

[TABLE]

and

[TABLE]

For the second term in parameter (3a),

[TABLE]

Substituting $u$ for $a_{P}+b_{P}z$ , which gives $\mathrm{d}z=\dfrac{\mathrm{d}u}{b_{P}}$ , and changing the limits, $h_{1}\to a_{P}+b_{P}\,h_{1}$ and $h_{2}\to a_{P}+b_{P}\,h_{2}$ , we obtain

[TABLE]

For the last term in parameter (3a),

[TABLE]

where

[TABLE]

and

[TABLE]

The first two terms in parameter (3b) are given by formulæ (5) and (7), whereas the third term is

[TABLE]

where $I_{2}$ and $I_{3}$ are given by integration constants (9) and (10). Finally, in a manner similar to obtaining the second term in parameter (3a), we use $u$ substitution and change limits of integration to obtain the term in parameter (3e), where

[TABLE]

Thus, using formulæ (4), (5), (7), (8), (11), (12), along with integration constants (6), (9), (10), we may restate Backus parameters (3a)–(3f) as

[TABLE]

2.2 Anisotropy parameters

The anisotropy of any transversely isotropic medium may be described by the Thomsen (1986) parameters. Thus, using Backus parameters (13), we define

[TABLE]

Explicitly, parameter (14a) is

[TABLE]

where

[TABLE]

2.3 Total differentials of anisotropy parameters

To quantify the uncertainty of expressions (15a)–(15c), i.e., the sensitivity to changes in model parameters, we require the total differential. We demonstrate this, we differentiate $\gamma$ with respect to each of its coordinates directions to obtain its linear functional

[TABLE]

We do not list the the resultant expressions since they would require half-a-dozen pages. However, the expressions for the partial derivatives of differentials (16b) and (16c) may be derived using a symbolic software, such as Mathematica.

3 Methods for well-posedness

Expressions (15a)–(15c) form an ill-posed system of three equations with nine unknowns, where

[TABLE]

We use differentials (16a)–(16c) to form a measure of error. To obtain solutions, we require well-posedness, which necessitates information for six of the nine unknown parameters. Using the Backus average on a region of interest of a well log, we reduce the number of unknowns to four. In particular, we specify $h_{1}$ and $h_{2}$ , and calculate values for $\gamma=:\gamma^{\overline{\rm TI}}\,,\delta=:\delta^{\overline{\rm TI}}\,,\,\varepsilon=:\varepsilon^{\overline{\rm TI}}$ , where ${}^{\overline{\rm TI}}$ denotes a quantity obtained using the Backus (1962) average. Information for any of $a_{S}\,,b_{S}\,,a_{P}\,,b_{P}$ must be obtained using additional methods.

To obtain information for the remaining model parameters, we use 1-D tomography and the $ab$ model.

3.1 1-D tomography

To obtain linear inhomogeneity parameters from VSP data, we use a 1-D tomography method. The inversion algorithm, therein, is based on the Levenberg-Marquardt least-square solution. As a result of inversion, we obtain a velocity profile corresponding to discrete depths. The inverted velocity profile represents the velocity of a vertically inhomogeneous medium. To calculate the linear inhomogeneity parameters for a particular region, we apply the linear regression to the resultant velocities for the required depths. The 1-D tomography can provide relatively good results in the case of a better initial model, a sufficient number of data, and that the assumption of linear inhomogeneity holds firmly for the medium.

3.2 $\boldsymbol{ab}$ model

The $ab$ model is a traveltime inversion method. In this method, the velocity model is a linear function of depth. To obtain the traveltime in a depth segment from borehole velocity, we assume the medium is composed of multiple thin isotropic layers. Based on that assumption, we calculate Fermat’s traveltime. In general, the borehole data contains high-frequency contents, which restricts the ray to travel from a source to a receiver with high offset. To synthesize sufficient traveltime data, we need traveltime for both near and high offsets. That is possible only if we remove the higher frequencies from the data. We apply a weighted average in every twelve consecutive data points to filter out those contents. As an outcome, we get a smoother velocity, which allows rays to travel from source to receiver with sufficiently more significant offset. In the inversion, we minimize the difference between the Fermat’s traveltime and the model traveltime (Slawinski and Slawinski, 1999) and obtain linear inhomogeneity parameters.

3.3 Mizzen O-16

The VSP and well log data used, herein, was obtained from the Mizzen O-16 discovery well, which is a site in the Flemish Pass basin and was drilled in 2009 by Statoil (Enachescu, 2011). The well log data used is supplied by IHS energy; the data description is provided in Ikon Science and Nalcor Energy (2016). We use $P$- and $S$-wavespeed measurements for depths of at depth 1865m to 2648.60 m .

The checkshot (VSP) data is provided by the Canada-Newfoundland & Labrador Offshore Petroleum Board (C-NLOPB, ). Therein, the traveltime data corresponds to a single source and multiple receivers. The source is located at a 26.5 m offset and the receivers are placed along vertical axis, starting at depth 1865 m and ending at 2650 m. We consider our last receiver at depth 2650m so that the velocity inversion from traveltime merges with the region where the well log data are recorded. The descriptions of the data are given in Tables 1 and 2, which are collected with the permission of the Petroleum Development Section of Natural Resources, Government of Newfoundland and Labrador.

4 Numerical search

4.1 Restrictions

In our numerical search, we have two restrictions. First, the stability conditions of isotropy restrict the values for $a_{S}$ and $a_{P}$ such that

[TABLE]

Second, to remain consistent with the assumption of constantly increasing velocity gradient with depth of Slawinski and Slawinski (1999), we restrict our solutions to positive values of $b_{P}$ and $b_{S}$ . However, it is worth noting that there do exist solutions for negative values of $b_{P}$ and $b_{S}$ .

We may demonstrate this with a numerical example. For, say, an input of $a_{P}=2040.36\,{\rm ms}^{-1}$ , there exist two solutions, as illustrated by the two instances of triple-point intersection in the left- and right-hand plots of Figure 1. Therein, the left-hand plot corresponds to a solution of positive $b_{P}$ and $b_{S}$ , where

[TABLE]

However, the right-hand plot corresponds to a solution of negative $b_{P}$ and $b_{S}$ , where

[TABLE]

Throughout the entirety of the numerical results, we consider positive solutions only.

4.2 Calculations

Let us obtain a solution to system (17) using the methodology of Section 3.1 with the VSP data of Mizzen O-16. Using results from 1-D tomography on traveltime data, we recover a velocity profile as a function of depth. For a region of interest, whose depth ranges from 1865 m to 2648.60 m , we recover two parameters, namely $a_{P}$ and $b_{P}$ . We may use either parameter as input to system (17) to obtain values for the remaining three unknowns.

For example, we use $a_{P_{\rm VSP,in}}=1415\,{\rm ms}^{-1}$ and $b_{P_{\rm VSP,in}}=0.70\,{\rm s}^{-1}$ as startup values for the tomography. For the region of interest, we recover $a_{P_{\rm VSP,out}}=1354.9\,{\rm ms}^{-1}$ and $b_{P_{\rm VSP,out}}=0.3933\,{\rm s}^{-1}$ , where, at the top of the region, $a_{P_{\rm layer}}=a_{P_{\rm VSP,out}}+b_{P_{\rm VSP,out}}\cdot 1865\,{\rm m}=2088.38\,{\rm ms}^{-1}$ . We input $b_{P}=b_{P_{\rm VSP,out}}$ into system (17), for

[TABLE]

[TABLE]

and obtain

[TABLE]

It is clear that $a_{P_{\rm layer}}\neq a_{P}$ but we may perform an error analysis to assess the “closeness” of our result. To do so, we recall expressions (16a), (16b), (16c), which are total differentials ${\rm d}\gamma\,,{\rm d}\delta\,,{\rm d}\varepsilon$ . Using uncertainty measures for parameters (19), where

[TABLE]

we obtain

[TABLE]

We obtain a new set of solutions for the lower limit of anisotropy by subtracting values (21) from the left-hand sides of system (17), which are

[TABLE]

Similarly, the upper limit of anisotropy is obtained adding values (21), which results in

[TABLE]

Thus, we find that $a_{P_{\rm layer}}$ falls within the range determined by $a_{P_{-}}$ and $a_{P_{+}}$ . In particular, such startup values provide results that are within 0.12% and 0.13% , respectively, of the theoretical predictions. We may repeat this entire process using $a_{P}=a_{P_{\rm VSP,out}}$ as input. In addition, this process may be repeated for a range of VSP startup values, in order to find the combination of startup values that are closest to the predicted model parameters indicated by the analytical relation. We tabulate the results of such a process, for values of $a_{P_{\rm VSP,in}}$ ranging from 1325 ms*-1* to 1515 ms*-1* , with increments of 20 ms*-1* , and $b_{P_{\rm VSP,in}}$ ranging from 0.57 s*-1* to 0.7 s*-1* , with increments of 0.01 s*-1* , in Table LABEL:tab:VSP_results of Appendix A.

To compare the results from VSP with the $ab$ model, we repeat this process for the same range of values of $a_{P_{\rm ab,in}}$ and $b_{P_{\rm ab,in}}$ . The results are tabulated in Table LABEL:tab:ab_results of Appendix A. In comparison, the startup values of  $a_{P_{ab,{\rm in}}}=1625\,{\rm ms}^{-1}$ and $b_{P_{ab,{\rm in}}}=0.6\,{\rm s}^{-1}$, provide results that are within 0.03% and 0.03% , respectively, of the theoretical predictions.

We illustrate the entirety of the results of Tables LABEL:tab:VSP_results and LABEL:tab:ab_results in Figures 2(a) and 2(b). Therein, the solid red line represents the solution to system (17) corresponding to the value on the horizontal axis, and the solid black lines represent solutions for the lower and upper limits of anisotropy, corresponding to uncertainty parameters (20). Orange diamonds represent the solutions from 1-D tomography and blue dots represent solutions from the $ab$ model.

5 Discussion

For each solution method, we obtain some $a_{P_{{\rm VSP},ab}}$ and $b_{P_{{\rm VSP},ab}}$ parameter. Using the outputted $a_{P_{{\rm VSP},ab}}$ as input to system (17), we calculate $b_{P}$ , $b_{P_{-}}$ , $b_{P_{+}}$ , and compare them to the outputted $b_{P_{{\rm VSP},ab}}$ . These results are illustrated in Figure 2(a); the opposite operation is performed and those results are illustrated in Figure 2(b).

In both subplots of Figure 2, we observe that the area of solutions for 1-D tomography overlaps the line of $ab$-model solutions. To discern which startup values lead to common outputs, we turn our attention to Figure 3. Therein, startup values of $a_{P_{{\rm VSP,in}}}=1415$ ms*-1* and $b_{P_{{\rm VSP,in}}}=0.7$ ms*-1* result in$a_{P_{{\rm VSP,out}}}=2088.38$ ms*-1* and $b_{P_{{\rm VSP,out}}}=0.3932$ ms*-1* . These results, as stated in Section 4.2, are within 0.12% and 0.13% , respectively, of the theoretical predictions. Similarly, startup values of $a_{P_{ab,in}}=1625$ ms*-1* and $b_{P_{ab,in}}=0.6$ ms*-1* result in outputs that are within 0.03% of the theoretical predictions.

6 Conclusion and future work

In this article, we show that we can obtain multiple solution from VSP and $ab$-model that do not lie in the theoretical range. However, we also show that there exist some common solution.

Based on the initial model, we find that there are some initial values that lead to that common solution, which may allow us to conclude that, by tuning initial model parameters, we can obtain the common solution set.

The number of traveltime data from the field measurement plays an important role in the VSP method. As a future work, we plan to apply the analytical relation and seismic methods to a site that possesses more data, which may produces a stable solution for different initial models in the VSP method.

By far, we have shown that the relationship between inhomogeneity and anisotropy provides reasonable solution in compare to the seismic methods. In addition to our future project, we wish to examine the limitation of the analytical relationship by calculating Backus average from a sparse well log data.

Appendix A Tables