P6 I=J+90 seismic bin grid coordinate operation

Formula

Note: These formulas have been transcribed from EPSG Guidance Note #7-2. Users are encouraged to use that document rather than the text which follows as reference because limitations in the transcription will be avoided.

The P6 (I = J+90) seismic bin grid operation is a special case of the Affine Geometric Transformation (method code 9623). In practice bin grid definitions are based on an identified map grid. As such the example bin grids in the EPSG Dataset are described with the map grid (projected CRS) as source CRS. However to retain consistency with the syntax used in the description of the affine geometric transformation, in the formulas below the bin grid is the affine source CRS and the map grid is the affine target CRS.

Map grid Easting = XT = XT0   +   XS .  k . dSX . cos q   +   YS .  k .  dSY  . sin q

Map grid Northing = YT = YT0   –   XS .  k .  dSX . sin q    +   YS .  k .  dSY  . cos q

Bin grid I = XS = {[( XT  – XTO) * cos q  –  (YT – YTO) * sin q ] * [IncSX  / (k * MX)]} + XSO

Bin grid J = YS = {[(XT   – XTO) * sin q   +  (YT – YTO) * cos q] * [IncSY  / (k * MY)]} + YSO 

where:

XT0 ,YT0  = the map grid coordinates (easting, northing) of the origin point of the bin grid;
dSX , dSY  = the length of one unit of the bin grid, expressed in units of map grid, for the bin grid I and J axes respectively;
k = point scale factor of the map grid at a chosen reference point;
q  = the angle through which the bin grid axes must be rotated to coincide with the map grid axes (counter-clockwise is positive). Alternatively, the bearing (clockwise positive) of the bin grid J-axis measured relative to map grid north.

Example

This example is given in the P6/98 document. The bin grid is based on projected CRS WGS 84 / UTM Zone 31N. The origin of the bin grid is defined to be at map grid easting = 456781.0mE, northing = 5836723.0mN.  The map grid point scale factor at this point is 0.99984.

The bin width on the I-axis (XS axis) is 25 metres, whilst the bin width on the J-axis (YS axis) is 12.5 metres. At its origin the bin grid has bin node values of 1,1.

In the map grid, the bearing of the bin grid I and J axes are 110° and 20° respectively. The latter is one of the transformation parameters.

The transformation parameter values are:

Bin grid origin I:                   1 bin
Bin grid origin J:                   1 bin
Bin grid origin Easting:             456781.00 m
Bin grid origin Northing:            5836723.00 m
Scale factor of bin grid:            0.99984
Bin Width on I-axis:                 25 m
Bin Width on J-axis:                 12.5 m
Map grid bearing of bin grid J-axis: 20°
Bin node increment on I-axis:        1
Bin node increment on J-axis:        1

Calculation of map grid coordinates for bin node with coordinates: I = 300, J = 247:
Easting = XT   = XTO   +   [(XS – XSO) * cos q * k * MX / IncSX]  +  [(YS – YSO) * sin q * k * MY / IncSY]
= 456781.000 + 7023.078 + 1051.544 
= 464855.62 m.

Northing = YT = YTO   –   [(XS – XSO) * sin q * k * MX / IncSX]   +  [(YS – YSO) * cos q * k * MY / IncSY]
= 5836723.000 - 2556.192 + 2889.092
= 5837055.90 m.

Calculation of bin node coordinates for this point, map grid location 464 855.62mE, 5 837 055.90mN:
Bin grid I = XS = {[( XT  – XTO) * cos q  –  (YT – YTO) * sin q ] * [IncSX  / (k * MX)]} + XSO
= 1 + (7473.804 * 0.040006401) 
= 300 bins, 

Bin grid J = YS = {[(XT   – XTO) * sin q   +  (YT – YTO) * cos q] * [IncSY  / (k * MY)]} + YSO 
= 1 + (3074.508 * 0.080012802) 
= 247 bins

EPSG:9666

P6 I=J+90 seismic bin grid coordinate operation

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Formula

Example