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mkigrf.py
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mkigrf.py
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import numpy as np
def doigrf(long,lat,date):
"""
Calculates the interpolated (<2015) or extrapolated (>2015) main field and
secular variation coefficients and passes them to the Malin and Barraclough
routine (function pmag.magsyn) to calculate the field from the coefficients.
Parameters:
-----------
lon : east longitude in degrees (0 to 360 or -180 to 180)
lat : latitude in degrees (-90 to 90)
date : Required date in years and decimals of a year (A.D.)
Return
-----------
x : north component of the magnetic field in nT
y : east component of the magnetic field in nT
z : downward component of the magnetic field in nT
f : total magnetic field in nT
By default, igrf12 coefficients are used between 1900 and 2020
from http://www.ngdc.noaa.gov/IAGA/vmod/igrf.html.
To check the results you can run the interactive program at the NGDC
www.ngdc.noaa.gov/geomag-web
"""
models,igrf12coeffs=get_igrf12()
model,alt = date-date%5,0
if date<2015:
gh=igrf12coeffs[models.index(model)]
sv=(igrf12coeffs[models.index(model+5)]-gh)/5.
else:
gh=igrf12coeffs[models.index(2015)]
sv=igrf12coeffs[models.index('2015.20')]
x,y,z,f=magsyn(gh,sv,model,date,1,alt,90.-lat,long%360)
return x,y,z,f
#
def get_igrf12():
"""
returns the available models (dates) and gauss coefficients (coeffs) for the desired field model.
These coefficients are the IGRF12 coefficients from the NOAA website.
"""
models= [1900, 1905, 1910, 1915, 1920, 1925, 1930, 1935, 1940, 1945, 1950, 1955, 1960, 1965, 1970, 1975, 1980, 1985, 1990, 1995, 2000, 2005, 2010, 2015, '2015.20']
coeffs=np.array([[-31543, -2298, 5922, -677, 2905, -1061, 924, 1121, 1022, -1469, -330, 1256, 3, 572, 523, 876, 628, 195, 660, -69, -361, -210, 134, -75, -184, 328, -210, 264, 53, 5, -33, -86, -124, -16, 3, 63, 61, -9, -11, 83, -217, 2, -58, -35, 59, 36, -90, -69, 70, -55, -45, 0, -13, 34, -10, -41, -1, -21, 28, 18, -12, 6, -22, 11, 8, 8, -4, -14, -9, 7, 1, -13, 2, 5, -9, 16, 5, -5, 8, -18, 8, 10, -20, 1, 14, -11, 5, 12, -3, 1, -2, -2, 8, 2, 10, -1, -2, -1, 2, -3, -4, 2, 2, 1, -5, 2, -2, 6, 6, -4, 4, 0, 0, -2, 2, 4, 2, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-31464, -2298, 5909, -728, 2928, -1086, 1041, 1065, 1037, -1494, -357, 1239, 34, 635, 480, 880, 643, 203, 653, -77, -380, -201, 146, -65, -192, 328, -193, 259, 56, -1, -32, -93, -125, -26, 11, 62, 60, -7, -11, 86, -221, 4, -57, -32, 57, 32, -92, -67, 70, -54, -46, 0, -14, 33, -11, -41, 0, -20, 28, 18, -12, 6, -22, 11, 8, 8, -4, -15, -9, 7, 1, -13, 2, 5, -8, 16, 5, -5, 8, -18, 8, 10, -20, 1, 14, -11, 5, 12, -3, 1, -2, -2, 8, 2, 10, 0, -2, -1, 2, -3, -4, 2, 2, 1, -5, 2, -2, 6, 6, -4, 4, 0, 0, -2, 2, 4, 2, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-31354, -2297, 5898, -769, 2948, -1128, 1176, 1000, 1058, -1524, -389, 1223, 62, 705, 425, 884, 660, 211, 644, -90, -400, -189, 160, -55, -201, 327, -172, 253, 57, -9, -33, -102, -126, -38, 21, 62, 58, -5, -11, 89, -224, 5, -54, -29, 54, 28, -95, -65, 71, -54, -47, 1, -14, 32, -12, -40, 1, -19, 28, 18, -13, 6, -22, 11, 8, 8, -4, -15, -9, 6, 1, -13, 2, 5, -8, 16, 5, -5, 8, -18, 8, 10, -20, 1, 14, -11, 5, 12, -3, 1, -2, -2, 8, 2, 10, 0, -2, -1, 2, -3, -4, 2, 2, 1, -5, 2, -2, 6, 6, -4, 4, 0, 0, -2, 2, 4, 2, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-31212, -2306, 5875, -802, 2956, -1191, 1309, 917, 1084, -1559, -421, 1212, 84, 778, 360, 887, 678, 218, 631, -109, -416, -173, 178, -51, -211, 327, -148, 245, 58, -16, -34, -111, -126, -51, 32, 61, 57, -2, -10, 93, -228, 8, -51, -26, 49, 23, -98, -62, 72, -54, -48, 2, -14, 31, -12, -38, 2, -18, 28, 19, -15, 6, -22, 11, 8, 8, -4, -15, -9, 6, 2, -13, 3, 5, -8, 16, 6, -5, 8, -18, 8, 10, -20, 1, 14, -11, 5, 12, -3, 1, -2, -2, 8, 2, 10, 0, -2, -1, 2, -3, -4, 2, 2, 1, -5, 2, -2, 6, 6, -4, 4, 0, 0, -2, 1, 4, 2, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-31060, -2317, 5845, -839, 2959, -1259, 1407, 823, 1111, -1600, -445, 1205, 103, 839, 293, 889, 695, 220, 616, -134, -424, -153, 199, -57, -221, 326, -122, 236, 58, -23, -38, -119, -125, -62, 43, 61, 55, 0, -10, 96, -233, 11, -46, -22, 44, 18, -101, -57, 73, -54, -49, 2, -14, 29, -13, -37, 4, -16, 28, 19, -16, 6, -22, 11, 7, 8, -3, -15, -9, 6, 2, -14, 4, 5, -7, 17, 6, -5, 8, -19, 8, 10, -20, 1, 14, -11, 5, 12, -3, 1, -2, -2, 9, 2, 10, 0, -2, -1, 2, -3, -4, 2, 2, 1, -5, 2, -2, 6, 6, -4, 4, 0, 0, -2, 1, 4, 3, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-30926, -2318, 5817, -893, 2969, -1334, 1471, 728, 1140, -1645, -462, 1202, 119, 881, 229, 891, 711, 216, 601, -163, -426, -130, 217, -70, -230, 326, -96, 226, 58, -28, -44, -125, -122, -69, 51, 61, 54, 3, -9, 99, -238, 14, -40, -18, 39, 13, -103, -52, 73, -54, -50, 3, -14, 27, -14, -35, 5, -14, 29, 19, -17, 6, -21, 11, 7, 8, -3, -15, -9, 6, 2, -14, 4, 5, -7, 17, 7, -5, 8, -19, 8, 10, -20, 1, 14, -11, 5, 12, -3, 1, -2, -2, 9, 2, 10, 0, -2, -1, 2, -3, -4, 2, 2, 1, -5, 2, -2, 6, 6, -4, 4, 0, 0, -2, 1, 4, 3, 0, 0, -6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [-30805, -2316, 5808, -951, 2980, -1424, 1517, 644, 1172, -1692, -480, 1205, 133, 907, 166, 896, 727, 205, 584, -195, -422, -109, 234, -90, -237, 327, -72, 218, 60, -32, -53, -131, -118, -74, 58, 60, 53, 4, -9, 102, -242, 19, -32, -16, 32, 8, -104, -46, 74, -54, -51, 4, -15, 25, -14, -34, 6, -12, 29, 18, -18, 6, -20, 11, 7, 8, -3, -15, -9, 5, 2, -14, 5, 5, -6, 18, 8, -5, 8, -19, 8, 10, -20, 1, 14, -12, 5, 12, -3, 1, -2, -2, 9, 3, 10, 0, -2, -2, 2, -3, -4, 2, 2, 1, -5, 2, -2, 6, 6, -4, 4, 0, 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-54.100000000000001, -6.7999999999999998, -19.5, 51.799999999999997, 5.7000000000000002, 15.0, 24.399999999999999, 9.4000000000000004, 3.3999999999999999, -2.7999999999999998, -27.399999999999999, 6.7999999999999998, -2.2000000000000002, 24.199999999999999, 8.8000000000000007, 10.1, -16.899999999999999, -18.300000000000001, -3.2000000000000002, 13.300000000000001, -20.600000000000001, -14.6, 13.4, 16.199999999999999, 11.699999999999999, 5.7000000000000002, -15.9, -9.0999999999999996, -2.0, 2.1000000000000001, 5.4000000000000004, 8.8000000000000007, -21.600000000000001, 3.1000000000000001, 10.800000000000001, -3.2999999999999998, 11.800000000000001, 0.69999999999999996, -6.7999999999999998, -13.300000000000001, -6.9000000000000004, -0.10000000000000001, 7.7999999999999998, 8.6999999999999993, 1.0, -9.0999999999999996, -4.0, -10.5, 8.4000000000000004, -1.8999999999999999, -6.2999999999999998, 3.2000000000000002, 0.10000000000000001, -0.40000000000000002, 0.5, 4.5999999999999996, -0.5, 4.4000000000000004, 1.8, -7.9000000000000004, -0.69999999999999996, -0.59999999999999998, 2.1000000000000001, -4.2000000000000002, 2.3999999999999999, -2.7999999999999998, -1.8, -1.2, -3.6000000000000001, -8.6999999999999993, 3.1000000000000001, -1.5, -0.10000000000000001, -2.2999999999999998, 2.0, 2.0, -0.69999999999999996, -0.80000000000000004, -1.1000000000000001, 0.59999999999999998, 0.80000000000000004, -0.69999999999999996, -0.20000000000000001, 0.20000000000000001, -2.2000000000000002, 1.7, -1.3999999999999999, -0.20000000000000001, -2.5, 0.40000000000000002, -2.0, 3.5, -2.3999999999999999, -1.8999999999999999, -0.20000000000000001, -1.1000000000000001, 0.40000000000000002, 0.40000000000000002, 1.2, 1.8999999999999999, -0.80000000000000004, -2.2000000000000002, 0.90000000000000002, 0.29999999999999999, 0.10000000000000001, 0.69999999999999996, 0.5, -0.10000000000000001, -0.29999999999999999, 0.29999999999999999, -0.40000000000000002, 0.20000000000000001, 0.20000000000000001, -0.90000000000000002, -0.90000000000000002, -0.10000000000000001, 0.0, 0.69999999999999996, 0.0, -0.90000000000000002, -0.90000000000000002, 0.40000000000000002, 0.40000000000000002, 0.5, 1.6000000000000001, -0.5, -0.5, 1.0, -1.2, -0.20000000000000001, -0.10000000000000001, 0.80000000000000004, 0.40000000000000002, -0.10000000000000001, -0.10000000000000001, 0.29999999999999999, 0.40000000000000002, 0.10000000000000001, 0.5, 0.5, -0.29999999999999999, -0.40000000000000002, -0.40000000000000002, -0.29999999999999999, -0.80000000000000004], [10.300000000000001, 18.100000000000001, -26.600000000000001, -8.6999999999999993, -3.2999999999999998, -27.399999999999999, 2.1000000000000001, -14.1, 3.3999999999999999, -5.5, 8.1999999999999993, -0.69999999999999996, -0.40000000000000002, -10.1, 1.8, -0.69999999999999996, 0.20000000000000001, -1.3, -9.0999999999999996, 5.2999999999999998, 4.0999999999999996, 2.8999999999999999, -4.2999999999999998, -5.2000000000000002, -0.20000000000000001, 0.5, 0.59999999999999998, -1.3, 1.7, -0.10000000000000001, -1.2, 1.3999999999999999, 3.3999999999999999, 3.8999999999999999, 0.0, -0.29999999999999999, -0.10000000000000001, 0.0, -0.69999999999999996, -2.1000000000000001, 2.1000000000000001, -0.69999999999999996, -1.2, 0.20000000000000001, 0.29999999999999999, 0.90000000000000002, 1.6000000000000001, 1.0, 0.29999999999999999, -0.20000000000000001, 0.80000000000000004, -0.5, 0.40000000000000002, 1.3, -0.20000000000000001, 0.10000000000000001, -0.29999999999999999, -0.59999999999999998, -0.59999999999999998, -0.80000000000000004, 0.10000000000000001, 0.20000000000000001, -0.20000000000000001, 0.20000000000000001, 0.0, -0.29999999999999999, -0.59999999999999998, 0.29999999999999999, 0.5, 0.10000000000000001, -0.20000000000000001, 0.5, 0.40000000000000002, -0.20000000000000001, 0.10000000000000001, -0.29999999999999999, -0.40000000000000002, 0.29999999999999999, 0.29999999999999999, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]])
return models,coeffs
def magsyn(gh,sv,b,date,itype,alt,colat,elong):
"""
# Computes x, y, z, and f for a given date and position, from the
# spherical harmonic coefficients of the International Geomagnetic
# Reference Field (IGRF).
# From Malin and Barraclough (1981), Computers and Geosciences, V.7, 401-405.
#
# Input:
# date = Required date in years and decimals of a year (A.D.)
# itype = 1, if geodetic coordinates are used, 2 if geocentric
# alt = height above mean sea level in km (if itype = 1)
# alt = radial distance from the center of the earth (itype = 2)
# colat = colatitude in degrees (0 to 180)
# elong = east longitude in degrees (0 to 360)
# gh = main field values for date (calc. in igrf subroutine)
# sv = secular variation coefficients (calc. in igrf subroutine)
# begin = date of dgrf (or igrf) field prior to required date
#
# Output:
# x - north component of the magnetic force in nT
# y - east component of the magnetic force in nT
# z - downward component of the magnetic force in nT
# f - total magnetic force in nT
#
# NB: the coordinate system for x,y, and z is the same as that specified
# by itype.
#
# Modified 4/9/97 to use DGRFs from 1945 to 1990 IGRF
# Modified 10/13/06 to use 1995 DGRF, 2005 IGRF and sv coefficient
# for extrapolation beyond 2005. Coefficients from Barton et al. PEPI, 97: 23-26
# (1996), via web site for NOAA, World Data Center A. Modified to use
#degree and
# order 10 as per notes in Malin and Barraclough (1981).
# coefficients for DGRF 1995 and IGRF 2005 are from http://nssdcftp.gsfc.nasa.gov/models/geomagnetic/igrf/fortran_code/
# igrf subroutine calculates
# the proper main field and secular variation coefficients (interpolated between
# dgrf values or extrapolated from 1995 sv values as appropriate).
"""
#
# real gh(120),sv(120),p(66),q(66),cl(10),sl(10)
# real begin,dateq
p=np.zeros((66),'f')
q=np.zeros((66),'f')
cl=np.zeros((10),'f')
sl=np.zeros((10),'f')
begin=b
t = date - begin
r = alt
one = colat*0.0174532925
ct = np.cos(one)
st = np.sin(one)
one = elong*0.0174532925
cl[0] = np.cos(one)
sl[0] = np.sin(one)
x,y,z = 0.0,0.0,0.0
cd,sd = 1.0,0.0
l,ll,m,n = 1,0,1,0
if itype!=2:
#
# if required, convert from geodectic to geocentric
a2 = 40680925.0
b2 = 40408585.0
one = a2 * st * st
two = b2 * ct * ct
three = one + two
rho = np.sqrt(three)
r = np.sqrt(alt*(alt+2.0*rho) + (a2*one+b2*two)/three)
cd = (alt + rho) /r
sd = (a2 - b2) /rho * ct * st /r
one = ct
ct = ct*cd - st*sd
st = st*cd + one*sd
ratio = 6371.2 /r
rr = ratio * ratio
#
# compute Schmidt quasi-normal coefficients p and x(=q)
p[0] = 1.0
p[2] = st
q[0] = 0.0
q[2] = ct
for k in range(1,66):
if n < m: # else go to 2
m = 0
n = n + 1
rr = rr * ratio
fn = n
gn = n - 1
# 2
fm = m
if k != 2: # else go to 4
if m == n: # else go to 3
one = np.sqrt(1.0 - 0.5/fm)
j = k - n - 1
p[k] = one * st * p[j]
q[k] = one * (st*q[j] + ct*p[j])
cl[m-1] = cl[m-2]*cl[0] - sl[m-2]*sl[0]
sl[m-1] = sl[m-2]*cl[0] + cl[m-2]*sl[0]
else:
# 3
gm = m * m
one = np.sqrt(fn*fn - gm)
two = np.sqrt(gn*gn - gm) /one
three = (fn + gn) /one
i = k - n
j = i - n + 1
p[k] = three*ct*p[i] - two*p[j]
q[k] = three*(ct*q[i] - st*p[i]) - two*q[j]
#
# synthesize x, y, and z in geocentric coordinates.
# 4
one = (gh[l-1] + sv[ll+l-1]*t)*rr
if m != 0: # else go to 7
two = (gh[l] + sv[ll+l]*t)*rr
three = one*cl[m-1] + two*sl[m-1]
x = x + three*q[k]
z = z - (fn + 1.0)*three*p[k]
if st != 0.0: # else go to 5
y = y + (one*sl[m-1] - two*cl[m-1])*fm*p[k]/st
else:
# 5
y = y + (one*sl[m-1] - two*cl[m-1])*q[k]*ct
l = l + 2
else:
# 7
x = x + one*q[k]
z = z - (fn + 1.0)*one*p[k]
l = l + 1
m = m + 1
#
# convert to coordinate system specified by itype
one = x
x = x*cd + z*sd
z = z*cd - one*sd
f = np.sqrt(x*x + y*y + z*z)
#
return x,y,z,f
#
def cart2dir(x,y,z):
"""
Converts a direction in cartesian coordinates into declination, inclinations
Parameters
----------
cart : input list of [x,y,z] or list of lists [[x1,y1,z1],[x2,y2,z2]...]
Returns
-------
direction_array : returns an array of [declination, inclination, intensity]
Examples
--------
>>> pmag.cart2dir([0,1,0])
array([ 90., 0., 1.])
"""
B=np.sqrt(x**2+y**2+z**2) # calculate resultant vector length
Dec=np.degrees(np.arctan2(y,x))%360. # calculate declination taking care of correct quadrants (arctan2) and making modulo 360.
Inc=np.degrees(np.arcsin(z/B)) # calculate inclination (converting to degrees) #
return Dec,Inc,B
#
def magMap(date,**kwargs):
"""
generates the data for a map of the magnetic field.
Inputs:
required:
date = decimal year for evaluation (between 1900 and 2020)
optional:
lon_0 = desired zero longitude
Returns:
Bdec = declinations
Binc = inclinations
B = field strength (in microtesla)
lons = array of longitudes
lats = array of latitudes
"""
if 'lon_0' in kwargs.keys(): # check if there are keyword arguments
lon_0=kwargs['lon_0'] # if lon_0 is set, use that one
else: # otherwise.....
lon_0=0. # set the default lon_0 to 0.
incr=10 # we can vary to the resolution of the model
lonmax=(lon_0+180.)%360+incr # get some parameters for our arrays of lat/lon
lonmin=(lon_0-180.)
latmax=90+incr
lons=np.arange(lonmin,lonmax,incr) # make a 1D array of longitudes (like elons)
lats=np.arange(-90,latmax,incr)# make a 1D array of longitudes (like elats)
# set up some containers for the field elements
lenLats, lenLons = len(lats), len(lons)
B=np.zeros((lenLats,lenLons))
Binc=np.zeros((lenLats,lenLons))
Bdec=np.zeros((lenLats,lenLons))
Brad=np.zeros((lenLats,lenLons))
for j in range(lenLats): # step through the latitudes
for i in range(lenLons): # and the longitudes
x,y,z,f=doigrf(lons[i],lats[j],date) # get the field elements
Dec,Inc,Int=cart2dir(x,y,z) # turn them into polar coordites
B[j][i]=Int*1e-3 # convert the string to microtesla (from nT)
Binc[j][i]=Inc # store the inclination value
Bdec[j][i]=Dec # store the declination value
return Bdec,Binc,B,lons,lats # return the arrays.