Hi Vivian,

I have never conducted unconditional simulations by using SGeMS before, but I assume it is possible to conduct such kind of simulations (i.e. with no hard data for conditioning the simulated field). Of course, the variogram is mandatory regardless of the type of simulation to be conducted (i.e. unconditional or conditional). Nevertheless, I have conducted unconditional simulations with GCOSIM3D and also with the classical version of GSLIB libraries. In both Add your answercases the results are perfect.

If you need help to use GCOSIM3D or GSLIB do not hesitate to contact me!

Best regards

Jorge

Hi Vivian,

Typically you need at least an univariate distribution of your variable otherwise it could hardly be considered sequential gaussian simulation.

The problem you've mentioned is probably a bug. Anyway an old trick to achieve this is to manipulate your hard-data to be outside the range of the variogram (by comparison with the grid space, for instance add 10000 to your X coordinate column in hard-data). And with this you do an "apparently" conditioned simulation with no hard-data in the premises (so in fact not spatially conditioned by hard-data, just statistically).

I don't know how GsTL (SGeMS geostatistics library) works but probably it will rely only on the global distribution (mean and variance at least) to generate a stochastic value since all hard-data is outside of variogram (maybe search depending on implementation) range. Obviously this is only useful to jump start the simulation since from the point where enough nodes have been simulated those will start to be used to condition the following ones (otherwise the variogram model would not be honored).

Hope it helps. Best,

Pedro

PS: apart from Jorge sugestion (thanks Jorge, I did not knew GCOMSIM3D, is there an official link by the way?) our own GEOMS2 is able to do this also (by following the trick above) although still in early beta: http://sourceforge.net/projects/geoms2/

Hi Pedro,

you can download the source files from the personal web site of Jaime Gómez Hernández which is a prominent member of  the hydrogeological & geostatistical community:

http://jgomez.webs.upv.es/?p=1002

As you will see the web is written in spanish and it might be a problem. To solve this inconvenient I add a direct download link just bellow:

http://jgomez.webs.upv.es/wordpress/wp-content/uploads/2014/07/gcosim3dv12.zip

If you have any more question related to GCOSIM3D please do not hesitate to contact me.

Best regards

Jorge

Hi,

I believe I've met Mr. Jaime Hernández in a conference in Madrid (I think IAMG). Didn't knew he had released a software. I'll be sure to check it out (I'm Portuguese so I understand Spanish well enough). Thanks for the information.

Best,

Pedro

Thanks everyone for responses. To clarify a little - and add another question or two if you are interested! - perhaps it is the randomness of the output that makes it appear not to be a std normal distribution...sometimes mean is close to 0 and variance close to 1...I am creating 10 realizations - somewhere I read if you don't create enough realizations it is less accurate.  Has anyone run into that issue?  I set the "contribution" of the variogram to 1(sill) and my nugget is 0.  As mentioned I increased the variogram range to create more structure needed for my thesis (topic is callibration).  I feel I am trying to create a shortcut (advisors believe it can work) to using hard data.  So if I assume of SGeMS sim is at least close to std normal - I then back transform lnK using a "made-up" mean and variance of lnK.  I am beginning to wonder is it too much "making things up?"  Though nature varies so much anyway - I am just trying to create a K reality with a certain range of K's - about .03 - 30 m/day. It is so far hard for me to find right combo of numbers to create this. I am beginning to think I would be better off just creating some hard data to create a "real" variogram in SGeMs and then use that for my simulation. Or other option is not to worry about coming up with a larger range Ks. I am somewhat new to geostats so could easily be missing something here. 

Thanks so much for your responses- I am new to research gate - this is so great - talking about our research across the globe!

Vivian

Hi Vivian,

I believe SGeMS does both gaussian transform and back transform (to your original distribution) automatically so your simulations will always be following (approximately) the original distribution. But this is something that should be checked out (try simulating with a log-normal or pareto to see what happens).

Notice that typically sequential simulation in geostatistics (whatever the method: gaussian or direct) should at least:

1) honor the hard-data

2) honor the probability distribution of your variable (let's call it the histogram with due consideration) 

3) honor the imposed variogram

Also stochastic sequential simulation, being a simulation in space (whatever that space may be), relies on some very few essential steps:

a) you generate a random walk (which is basically the order from which each node will be simulated).

b) For each node you'll consider the neighbors (hard-data or already simulated nodes) and perform kriging.

c) The kriging procedure will give you both a mean value (the kriged value) and a kriging variance. With a mean and a variance you can build a local gaussian distribution and randomly generate a value from there (and it is this generated value that will either be the simulated value or a local equivalent that should be transformed to a global value, depending on method and implementation).

Now many different methods for stochastic simulation have been published but most if not all use a local gaussian function to perform simulation. Gaussian function has some nice properties such as symmetry  and the fact that the closer you are to the mean the most probable the value is. In practical terms this means that a single simulated value will not follow the imposed variogram, but in average your simulation will. So in average the variogram value for direction north (for example), distance 3 will have the same behavior you've imposed on your variogram model.

And just another quick conclusion: if the local gaussian functions are built with the mean and variance from kriging that if you calculate the mean from each node on your simulations you'll get something that converges to the kriging image.

So consider the implications: the average image of your simulations is (or has as limit) the kriging image. Every single equiprobable simulation you do is no more or less than exploring (is this the right word?!) the mathematical (statistical) uncertainty that exists with the kriging parametrizations you've imposed (random walk is also important but I believe the local gaussian is the main factor for this).

Now to answer directly to your questions and considering the information above:

1) More simulations means a better characterization of the uncertainty space determined by kriging mean and variance. So typically the more simulations the "safer" your result (and the closer the mean of those simulations will be to kriging). Instead of 10 I would advise do at least 30 (if possible more) simulations.

2) It's perfectly correct to use 2 structures  (or more) when needed just make sure your contribution for each structure will add up to the max (in your case probably 1).

3) Nugget effect is a very rarely occurring phenomena in nature so it seldom should be used, specially if you don't have any real-data to support it.

4) Hypothesis based studies are more and more common this days. If your supervisors believe you can achieve a good result it's probably because they're experience tells them you can. Nevertheless you should consider your case-study as any in any other science. With  unconditional gaussian simulation (SGS) you're just using the variogram as a modeling parameter. The conclusion you have to make is: Is the variogram ellipsoid enough to accurately (enough) describe my case-study? 

If yes than you'll be working in just that parameter, if not you need to find other ways to condition your simulations. Not necessarily hard-data, you can use secondary images and perform collocated co-simulation for instance. There are many other ways but let's keep it simple for brevity sake.

5) You can create hard-data sets but should first design the criteria you'll be using to do that generation. Remember guessing adds uncertainty and you want to try to avoid that.

Sorry for the long answer but better safe than sorry. I hope it will help and if you have any other questions feel free to ask. I'll just leave some keyword suggestions in case you want to explore better other possibilities of conditioning your data (without hard-data).

keywords: Block Sequential Simulation (http://www.sciencedirect.com/science/article/pii/S1877705811021746), Direct Sequential Simulation and CoSimulation (http://link.springer.com/article/10.1023%2FA%3A1012246006212), Block centroid Indicator Simulation (http://link.springer.com/chapter/10.1007/978-3-642-32408-6_158), Characterization optimization using genetic procedures (http://link.springer.com/article/10.1007%2Fs11004-013-9466-1), Distribution modeling and transformation (experimental desktop app: https://github.com/armatita/simdist)

Pedro, Thank you so much for your detailed answer!  This will help me alot! Vivian

The sequential Gaussian simulation algorithm is based on Simple kriging (as opposed to Ordinary kriging or Universal kriging). In turn Simple kriging is based on the assumption that the mean (of the random function) is known and also that the covariance function is known, i..e the covariance function is used in the Simple kriging equations. It is not possible to use a variogram in those equations. However if you are using one of the variogram models that corresponds to a covariance function (e.g., gaussian, exponential, spherical) then you use the corresponding covariance function instead but you still need to know the constant mean. See the GSLIB book for an explanation of sequential gaussian simulation. In general, none of the geostatistical simulation algorithms will reproduce the covariance frunction EXCEPT "on average". If you are computing the sample variogram for the simulated realization, it need not match the variogram model you used. However if you generated a large number of realizations and then averaged the sample variograms it should approximate the model. But note that for a given data set, the sample variogram is not unique, i.e. it depends on your choice of the lag distances, the number of data locations and the geographic extent of the region containing the data locations as well as the geographc pattern of the data locations. In any case you will never be able to generate an entire realization, you will only get a partial realization. Finally the reason that multivariate normality is so important (not just univariate) is that in that case the Simple kriging estimator is the same as the conditional expectation. if the distribution is not multivariate normal or if you use Ordinary krigiing or Univeral kriging then the kriging estimator is only an approximation to the conditional expectation