how to determine the sigma value in the structural uncertainty analysis in Petrel

1. Simple experiment for GRFS error surface
in Make Horizon process

3. Sr = Sbc + U1s * Ugrfs
Assume:
Sbc is set to zero
Stdev is set to 1
Then, Sr = Ugrfs
Make point
1 point input
Make simple model
Basecase surface of Z=0
(10000*10000)

4. Sr = U1s*Ugrfs
As assumption, Sr = Ugrfs

5. Ugrfs statistics Ugrfs histotram

6. 1σ: 7.1+8.4+9.5+10.2+9.6+8.9+8.2+6.3 = 68.2
2σ: 2.0+2.9+3.8+5.3+ 1σ +5.0+3.4+2.7+1.8 = 95.1
Normal (Gaussian) distribution curve
Histogram of modelled Ugrfs surface
Ugrfs surface follow standard normal distribution (μ=0, σ=1)

7. Several realization shows similar result
Try 1 Try 2
Try 3 Try 4

8. Stdev = 50 → max 179.06, min -172.81
Example) stdev to 50

9. Example) stdev to 50 devide by Stdev
/ 50 (U1s)
Stadard normal distribution!!!

10. Conclusion
1. In Make horizon process,
the uncertainty is apply by multiples of 1σ and Ugrfs
2. Ugrfs surface is randomly build by following standard normal distribution
which is mean of 0, stdev 1
3. Normal distribution has probability of 3σ for 99.7%, 2σ for 95.4%, 1σ for 68.2%
4. Hence, when apply 1σ value for the make horizon process, we can expect there is
99.7% of probability for the 3σ (almost min/max), 95.4% of probability for the 2σ, 68.2% of
probability for the 1σ.
5. Be aware for determin 1σ when apply min / max value in structural uncertainty