ApparentDip (1).xls

8/10/2019 ApparentDip (1).xls

1/14

Apparent Dip Calculator

current value

A. D. bearing: S 70.0 E

increment: +i

decrement: +d

Angular Precision: 1 Angular Field Width: 4

Projection: Equal Area

Quadrant Quadrant

Data Set App. Dip bearing Strike & Dip App Dip Azimuth App Dip pole plunge Pole azimuth Pole plunge

Data 1 S 70.0 E N 50.0 E 40.0 E 110.000 0.000 320.000 50

App. dip pole Planar pole Theta

Cos(alpha) Cos(beta) Cos(gamma) Cos(alpha) Cos(beta) Cos(gamma) Angle(radian

0.342 0.940 0.000 -0.413 0.492 0.766 1

Lower Hemisphere Cross-product Answer App.Dip

Flag Cos(alpha) Cos(beta) Cos(gamma) Azimuth Angle

0.588 0.760 -0.277 0.588 110.000 36.005

Planar pole

A.D. Az=110.0

True Dip=40.0

A.D.=36.0

Equal Area

N

-4

-3

-2

-1

0

1

2

3

4

-4 -2 0 2 4

Y

X

Stereographic Projection


2/14

Symbolic Block NamesSymbolic block names are used extensively in the "ApparentDip" worksheet to add

clarity to the claculation formulae. The blue names below refer to cells where data is entered.

The various block names with definitions are listed below:

Name Definition or Value

AnswerAz Azimuth of apparent dip answer vector.

AnswerPl Plunge of apparent dip answer vector.

AppDip Apparent dip direction bearing in quadrant format (i.e. N 45.0 E)

AppDipSeed Apparent dip starting bearing for interactive graphical macro

AppDipStep Apparent dip increment/decrement amount for interactive macro

StrikeAndDip Strike & Dip in quadrant format; quadrantd d\specified with "E" or "W"

AppDipAz Apparent dip direction azimuth angle (0-360).

Az_1 Azimuth of pole to apparent dip plane.

Az_2 Azimuth of pole to strike & dip plane.

fl Field size (characters) for reported angular values.

LowerFlag Positive if cross product has a positive plunge angle, negative if not.

Ndec Number of decimal places for reported angular values.

Pl_1 Plunge angle of pole to apparent dip plane.Pl_2 Plunge angle of pole to strike & dip plane

Radius Radius of the stereographic projection.

Theta_S Calculated angle (radians) between the apparent dip vectors.

TrueDipAz Azimuth of true dip vector.

TrueDipPl Plunge of true dip vector.

X_1,Y_1,Z_1 Directional components of pole to apparent dip plane..

X_2,Y_2,Z_2 Directional components of pole to strike and dip plane.

X_3,Y_3,Z_3 Direction components of true dip vector.

X_Ans,Y_Ans,Z_Ans Directional components of the cross product solution (intesection of strike & dip and apparent dip plane

X_S,Y_S,Z_S Directional components of start position for drawing great circle

Xcenter, Ycenter Coordinates of the center of the stereographic projection.

Usage

This spreadsheet can be used to calculate an apparent dip angle given the strike and dip of a plane, and the bearing direction oAll angular values are decimal degrees, with the precision set by the angular precison value. Be sure to match the number of de

angles to this setting. All orientations must be in quadrant format, however, the spreadsheet can be easily modified to accept az

Blue cells contain values that should be inputed by the user, whereas the magenta cells generally contain formulae that should

contains the apparent dip answer (F39). It is recommended that the user turn on sheet protection with "Tools > Protection > Pro

are not over-typed. The azimuth of the apparent dip direction can be incremented/decremented with the +I and +d m

The up/down graphical arrows in the chart graph also increment/decrement the azimuth of the apparent dip direction using the c

Calculation MethodThe calculation method uses the cross-product of two vectors to extract the apparent dip answer. The 1st vector is the pole to th

apparent dip direction. The 2nd vector is the pole to the strike and dip plane. The intersection of the two planes perpindicular to

apparent dip angle as the plunge of the cross-product resultant vector. The cross-product always calulates the vector perpindic

input vectors.


3/14

Xcenter= 0.00 Ycenter= 0.00

Radius= 3.75

Primitive

Angle Magnitude X Y Item

0.000 3.750 0.000 primitive

2.000 3.748 0.131 primitive

4.000 3.741 0.262 primitive

6.000 3.729 0.392 primitive

8.000 3.714 0.522 primitive

10.000 3.693 0.651 primitive

12.000 3.668 0.780 primitive

14.000 3.639 0.907 primitive

16.000 3.605 1.034 primitive

18.000 3.566 1.159 primitive

20.000 3.524 1.283 primitive

22.000 3.477 1.405 primitive

24.000 3.426 1.525 primitive26.000 3.370 1.644 primitive

28.000 3.311 1.761 primitive

30.000 3.248 1.875 primitive

32.000 3.180 1.987 primitive

34.000 3.109 2.097 primitive

36.000 3.034 2.204 primitive

38.000 2.955 2.309 primitive

40.000 2.873 2.410 primitive

42.000 2.787 2.509 primitive

44.000 2.698 2.605 primitive

46.000 2.605 2.698 primitive

48.000 2.509 2.787 primitive50.000 2.410 2.873 primitive

52.000 2.309 2.955 primitive

54.000 2.204 3.034 primitive

56.000 2.097 3.109 primitive

58.000 1.987 3.180 primitive

60.000 1.875 3.248 primitive

62.000 1.761 3.311 primitive

64.000 1.644 3.370 primitive

66.000 1.525 3.426 primitive

68.000 1.405 3.477 primitive

70.000 1.283 3.524 primitive

72.000 1.159 3.566 primitive

74.000 1.034 3.605 primitive

76.000 0.907 3.639 primitive

78.000 0.780 3.668 primitive

80.000 0.651 3.693 primitive

82.000 0.522 3.714 primitive

84.000 0.392 3.729 primitive

86.000 0.262 3.741 primitive


4/14

88.000 0.131 3.748 primitive

90.000 0.000 3.750 primitive

92.000 -0.131 3.748 primitive

94.000 -0.262 3.741 primitive

96.000 -0.392 3.729 primitive

98.000 -0.522 3.714 primitive

100.000 -0.651 3.693 primitive

102.000 -0.780 3.668 primitive

104.000 -0.907 3.639 primitive

106.000 -1.034 3.605 primitive

108.000 -1.159 3.566 primitive

110.000 -1.283 3.524 primitive

112.000 -1.405 3.477 primitive

114.000 -1.525 3.426 primitive

116.000 -1.644 3.370 primitive

118.000 -1.761 3.311 primitive

120.000 -1.875 3.248 primitive

122.000 -1.987 3.180 primitive124.000 -2.097 3.109 primitive

126.000 -2.204 3.034 primitive

128.000 -2.309 2.955 primitive

130.000 -2.410 2.873 primitive

132.000 -2.509 2.787 primitive

134.000 -2.605 2.698 primitive

136.000 -2.698 2.605 primitive

138.000 -2.787 2.509 primitive

140.000 -2.873 2.410 primitive

142.000 -2.955 2.309 primitive

144.000 -3.034 2.204 primitive

146.000 -3.109 2.097 primitive148.000 -3.180 1.987 primitive

150.000 -3.248 1.875 primitive

152.000 -3.311 1.761 primitive

154.000 -3.370 1.644 primitive

156.000 -3.426 1.525 primitive

158.000 -3.477 1.405 primitive

160.000 -3.524 1.283 primitive

162.000 -3.566 1.159 primitive

164.000 -3.605 1.034 primitive

166.000 -3.639 0.907 primitive

168.000 -3.668 0.780 primitive

170.000 -3.693 0.651 primitive

172.000 -3.714 0.522 primitive

174.000 -3.729 0.392 primitive

176.000 -3.741 0.262 primitive

178.000 -3.748 0.131 primitive

180.000 -3.750 0.000 primitive

182.000 -3.748 -0.131 primitive

184.000 -3.741 -0.262 primitive


5/14

186.000 -3.729 -0.392 primitive

188.000 -3.714 -0.522 primitive

190.000 -3.693 -0.651 primitive

192.000 -3.668 -0.780 primitive

194.000 -3.639 -0.907 primitive

196.000 -3.605 -1.034 primitive

198.000 -3.566 -1.159 primitive

200.000 -3.524 -1.283 primitive

202.000 -3.477 -1.405 primitive

204.000 -3.426 -1.525 primitive

206.000 -3.370 -1.644 primitive

208.000 -3.311 -1.761 primitive

210.000 -3.248 -1.875 primitive

212.000 -3.180 -1.987 primitive

214.000 -3.109 -2.097 primitive

216.000 -3.034 -2.204 primitive

218.000 -2.955 -2.309 primitive

220.000 -2.873 -2.410 primitive222.000 -2.787 -2.509 primitive

224.000 -2.698 -2.605 primitive

226.000 -2.605 -2.698 primitive

228.000 -2.509 -2.787 primitive

230.000 -2.410 -2.873 primitive

232.000 -2.309 -2.955 primitive

234.000 -2.204 -3.034 primitive

236.000 -2.097 -3.109 primitive

238.000 -1.987 -3.180 primitive

240.000 -1.875 -3.248 primitive

242.000 -1.761 -3.311 primitive

244.000 -1.644 -3.370 primitive246.000 -1.525 -3.426 primitive

248.000 -1.405 -3.477 primitive

250.000 -1.283 -3.524 primitive

252.000 -1.159 -3.566 primitive

254.000 -1.034 -3.605 primitive

256.000 -0.907 -3.639 primitive

258.000 -0.780 -3.668 primitive

260.000 -0.651 -3.693 primitive

262.000 -0.522 -3.714 primitive

264.000 -0.392 -3.729 primitive

266.000 -0.262 -3.741 primitive

268.000 -0.131 -3.748 primitive

270.000 0.000 -3.750 primitive

272.000 0.131 -3.748 primitive

274.000 0.262 -3.741 primitive

276.000 0.392 -3.729 primitive

278.000 0.522 -3.714 primitive

280.000 0.651 -3.693 primitive

282.000 0.780 -3.668 primitive


6/14

284.000 0.907 -3.639 primitive

286.000 1.034 -3.605 primitive

288.000 1.159 -3.566 primitive

290.000 1.283 -3.524 primitive

292.000 1.405 -3.477 primitive

294.000 1.525 -3.426 primitive

296.000 1.644 -3.370 primitive

298.000 1.761 -3.311 primitive

300.000 1.875 -3.248 primitive

302.000 1.987 -3.180 primitive

304.000 2.097 -3.109 primitive

306.000 2.204 -3.034 primitive

308.000 2.309 -2.955 primitive

310.000 2.410 -2.873 primitive

312.000 2.509 -2.787 primitive

314.000 2.605 -2.698 primitive

316.000 2.698 -2.605 primitive

318.000 2.787 -2.509 primitive320.000 2.873 -2.410 primitive

322.000 2.955 -2.309 primitive

324.000 3.034 -2.204 primitive

326.000 3.109 -2.097 primitive

328.000 3.180 -1.987 primitive

330.000 3.248 -1.875 primitive

332.000 3.311 -1.761 primitive

334.000 3.370 -1.644 primitive

336.000 3.426 -1.525 primitive

338.000 3.477 -1.405 primitive

340.000 3.524 -1.283 primitive

342.000 3.566 -1.159 primitive344.000 3.605 -1.034 primitive

346.000 3.639 -0.907 primitive

348.000 3.668 -0.780 primitive

350.000 3.693 -0.651 primitive

352.000 3.714 -0.522 primitive

354.000 3.729 -0.392 primitive

356.000 3.741 -0.262 primitive

358.000 3.748 -0.131 primitive

360.000 3.750 0.000 primitive

320.000 1.814 -1.166 1.389 Plane Pole

110.000 3.750 3.524 -1.283 A.D. Az=110.0

140.000 2.241 1.441 -1.717 True Dip=40.0

110.000 2.407 2.262 -0.823 A.D.=36.0

-3.188 -3.713 Equal Area

0.000 3.938 N

0.000 0.000 App Dip start

110.000 3.750 3.524 -1.283 App Dip end


7/14

Great Circle

Az Pl Cos(alpha) Cos(beta) Cos(gamma)

230.000 0.000 -0.766 -0.643 0.000

Rotation t_dot flag Cos(alpha) Cos(beta) Cos(gammaazimuth magnitude

0 0.000 1.000 -0.766 -0.643 0.000 230.000 3.750

1 0.000 1.000 -0.757 -0.653 0.011 229.234 3.729

2 0.000 1.000 -0.748 -0.663 0.022 228.468 3.708

3 0.000 1.000 -0.739 -0.673 0.034 227.701 3.686

4 0.000 1.000 -0.730 -0.682 0.045 226.934 3.665

5 0.000 1.000 -0.720 -0.691 0.056 226.166 3.643

6 0.000 1.000 -0.710 -0.701 0.067 225.397 3.622

7 0.000 1.000 -0.700 -0.710 0.078 224.627 3.600

8 0.000 1.000 -0.690 -0.718 0.089 223.855 3.578

9 0.000 1.000 -0.680 -0.727 0.101 223.082 3.556

10 0.000 1.000 -0.669 -0.735 0.112 222.307 3.535

11 0.000 1.000 -0.658 -0.743 0.123 221.531 3.513

12 0.000 1.000 -0.647 -0.751 0.134 220.752 3.49013 0.000 1.000 -0.636 -0.758 0.145 219.971 3.468

14 0.000 1.000 -0.624 -0.766 0.156 219.187 3.446

15 0.000 1.000 -0.612 -0.773 0.166 218.401 3.424

16 0.000 1.000 -0.601 -0.780 0.177 217.611 3.402

17 0.000 1.000 -0.589 -0.786 0.188 216.819 3.379

18 0.000 1.000 -0.576 -0.793 0.199 216.023 3.357

19 0.000 1.000 -0.564 -0.799 0.209 215.224 3.335

20 0.000 1.000 -0.551 -0.805 0.220 214.421 3.312

21 0.000 1.000 -0.539 -0.810 0.230 213.614 3.290

22 0.000 1.000 -0.526 -0.816 0.241 212.803 3.267

23 0.000 1.000 -0.513 -0.821 0.251 211.987 3.245

24 0.000 1.000 -0.500 -0.826 0.261 211.167 3.22325 0.000 1.000 -0.486 -0.831 0.272 210.343 3.200

26 0.000 1.000 -0.473 -0.835 0.282 209.513 3.178

27 0.000 1.000 -0.459 -0.839 0.292 208.678 3.156

28 0.000 1.000 -0.445 -0.843 0.302 207.838 3.134

29 0.000 1.000 -0.431 -0.847 0.312 206.993 3.111

30 0.000 1.000 -0.417 -0.850 0.321 206.141 3.089

31 0.000 1.000 -0.403 -0.853 0.331 205.284 3.067

32 0.000 1.000 -0.389 -0.856 0.341 204.421 3.045

33 0.000 1.000 -0.374 -0.859 0.350 203.551 3.023

34 0.000 1.000 -0.360 -0.861 0.359 202.674 3.001

35 0.000 1.000 -0.345 -0.863 0.369 201.791 2.980

36 0.000 1.000 -0.330 -0.865 0.378 200.901 2.958

37 0.000 1.000 -0.315 -0.867 0.387 200.004 2.936

38 0.000 1.000 -0.300 -0.868 0.396 199.099 2.915

39 0.000 1.000 -0.285 -0.869 0.405 198.187 2.894

40 0.000 1.000 -0.270 -0.870 0.413 197.268 2.873

41 0.000 1.000 -0.255 -0.870 0.422 196.340 2.852

42 0.000 1.000 -0.240 -0.870 0.430 195.404 2.831

43 0.000 1.000 -0.224 -0.870 0.438 194.460 2.810


8/14

44 0.000 1.000 -0.209 -0.870 0.447 193.507 2.790

45 0.000 1.000 -0.193 -0.869 0.455 192.546 2.770

46 0.000 1.000 -0.178 -0.869 0.462 191.576 2.750

47 0.000 1.000 -0.162 -0.868 0.470 190.598 2.730

48 0.000 1.000 -0.147 -0.866 0.478 189.610 2.710

49 0.000 1.000 -0.131 -0.865 0.485 188.612 2.691

50 0.000 1.000 -0.115 -0.863 0.492 187.606 2.672

51 0.000 1.000 -0.099 -0.861 0.500 186.590 2.653

52 0.000 1.000 -0.084 -0.858 0.507 185.564 2.634

53 0.000 1.000 -0.068 -0.855 0.513 184.529 2.616

54 0.000 1.000 -0.052 -0.853 0.520 183.484 2.598

55 0.000 1.000 -0.036 -0.849 0.527 182.429 2.580

56 0.000 1.000 -0.020 -0.846 0.533 181.364 2.563

57 0.000 1.000 -0.004 -0.842 0.539 180.289 2.546

58 0.000 1.000 0.012 -0.838 0.545 179.204 2.529

59 0.000 1.000 0.028 -0.834 0.551 178.109 2.513

60 0.000 1.000 0.043 -0.830 0.557 177.005 2.497

61 0.000 1.000 0.059 -0.825 0.562 175.889 2.48162 0.000 1.000 0.075 -0.820 0.568 174.764 2.466

63 0.000 1.000 0.091 -0.815 0.573 173.629 2.451

64 0.000 1.000 0.107 -0.809 0.578 172.484 2.437

65 0.000 1.000 0.123 -0.803 0.583 171.330 2.423

66 0.000 1.000 0.138 -0.798 0.587 170.165 2.409

67 0.000 1.000 0.154 -0.791 0.592 168.991 2.396

68 0.000 1.000 0.170 -0.785 0.596 167.808 2.384

69 0.000 1.000 0.185 -0.778 0.600 166.615 2.371

70 0.000 1.000 0.201 -0.771 0.604 165.414 2.360

71 0.000 1.000 0.216 -0.764 0.608 164.203 2.349

72 0.000 1.000 0.232 -0.757 0.611 162.984 2.338

73 0.000 1.000 0.247 -0.749 0.615 161.757 2.32874 0.000 1.000 0.262 -0.741 0.618 160.522 2.318

75 0.000 1.000 0.277 -0.733 0.621 159.279 2.309

76 0.000 1.000 0.292 -0.725 0.624 158.029 2.300

77 0.000 1.000 0.307 -0.716 0.626 156.772 2.292

78 0.000 1.000 0.322 -0.708 0.629 155.508 2.285

79 0.000 1.000 0.337 -0.699 0.631 154.238 2.278

80 0.000 1.000 0.352 -0.690 0.633 152.962 2.272

81 0.000 1.000 0.367 -0.680 0.635 151.682 2.266

82 0.000 1.000 0.381 -0.671 0.637 150.396 2.261

83 0.000 1.000 0.395 -0.661 0.638 149.106 2.256

84 0.000 1.000 0.410 -0.651 0.639 147.812 2.252

85 0.000 1.000 0.424 -0.641 0.640 146.515 2.249

86 0.000 1.000 0.438 -0.630 0.641 145.216 2.246

87 0.000 1.000 0.452 -0.620 0.642 143.914 2.244

88 0.000 1.000 0.465 -0.609 0.642 142.610 2.242

89 0.000 1.000 0.479 -0.598 0.643 141.305 2.242

90 0.000 1.000 0.492 -0.587 0.643 140.000 2.241

91 0.000 1.000 0.506 -0.576 0.643 138.695 2.242

92 0.000 1.000 0.519 -0.564 0.642 137.390 2.242


9/14


10/14


11/14


12/14


13/14


14/14

2.878 0.461

2.892 0.510

2.905 0.559

2.917 0.609

2.928 0.659

2.939 0.708

2.949 0.758

2.959 0.808

2.967 0.859

2.975 0.909

2.983 0.960

2.990 1.011

2.996 1.062

3.001 1.113

3.005 1.164

3.009 1.215

3.012 1.266

3.014 1.3183.016 1.369

3.017 1.421

3.017 1.473

3.016 1.525

3.014 1.577

3.012 1.629

3.009 1.681

3.005 1.733

3.000 1.785

2.994 1.837

2.987 1.889

2.980 1.9412.972 1.993

2.962 2.046

2.952 2.098

2.941 2.150

2.930 2.202

2.917 2.254

2.903 2.306

2.888 2.358

2.873 2.410

-2.824 -2.435

Documents

ApparentDip (1).xls