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 = XSO - {[( XT  – XTO) * cos q  –  (YT – YTO) * sin q ] * [IncSX  / (k * MX)]}

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

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, expressed in units of the map grid, for the bin grid I and J axes respectively;
k = point scale factor in 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 system J-axis measured relative to map grid north.

Example

This example is given in the IOGP P6/11 user guide. 

The bin grid is based on projected CRS NAD27/ BLM 16N (ftUS) in which the origin of the bin grid is defined at east = 871200.0 ftUS, north = 10280160.0 ftUS. As the survey was acquired on the map grid, the bin grid scale factor at the bin grid origin is defined to be 1.

The bin width on the I-axis (XS axis) is 82.5 US survey feet, whilst the bin width on the J-axis (YS axis) is 41.25 US survey feet. The origin of the bin grid has bin node values of I=5000, J=0.

In the map grid, the bearing of the bin grid I and J axes are 250° and 340° respectively. The latter is one of the transformation parameters.

The transformation parameter values are:

Bin grid origin I:                   5000 bins
Bin grid origin J:                   0 bins
Bin grid origin Easting:             871200 ftUS
Bin grid origin Northing:            10280160 ftUS
Scale factor of bin grid:            1.0
Bin Width on I-axis:                 82.5 ftUS
Bin Width on J-axis:                 41.25 ftUS
Map grid bearing of bin grid J-axis: 340°
Bin node increment on I-axis:        1
Bin node increment on J-axis:        1

Calculation of map grid coordinates of bin node with coordinates: I = 4700, J = 247:
Easting = XT = XTO   -   [(XS – XSO) * cos q * k * MX / IncSX]  +  [(YS – YSO) * sin q * k * MY / IncSY]
= 871200.000 – (–23257.392 –3484.758) 
= 890972.63 ftUS.

Northing = YT = YTO + [(XS – XSO) * sin q * k * MX / IncSX]   +  [(YS – YSO) * cos q * k * MY / IncSY]
= 10280160.000 + (8464.999 + 9574.293) 
= 10298199.29 ftUS.

Calculation of bin node coordinates for the point with map grid location east = 890972.63ftUS, north = 10298199.29ftUS:
Bin node I = XS = XSO - {[( XT  – XTO) * cos q  –  (YT – YTO) * sin q ] * [IncSX  / (k * MX)]}
= 5000 - (24750 * 0.012121212) 
= 4700 bins 

Bin node J = YS = YSO + {[(XT   – XTO) * sin q   +  (YT – YTO) * cos q] * [IncSY  / (k * MY)]}
=  0 + (10188.75 * 0.024242424)  
= 247 bins

EPSG:1049

P6 I=J-90 seismic bin grid coordinate operation

Attributes

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Formula

Example