tutorial/deterministic_inversion_input.md

+# Deterministic Inversion Input
+
+## Methodology
+
+The SHEMAT-Suite provides an approach for deterministic Bayesian inversion. Its specialty is that derivates are calculated by Automatic Differentiation (AD) instead of divided differences. The approach and methodology is explained in [Rath et al. (2006)](https://academic.oup.com/gji/article/167/1/453/2085661).
+
+## Compilation
+
+Deterministic Inversion for parameters is available in SHEMAT-Suite when
+compiling with the `ad`-mode flag instead of `fw` or `sm` (note that you might have to checkout the respective code-branch that contains the AD-code-files).
+
+## Input file adaptions 
+
+**1. Set runmode 2 or 3.**
+```
+# runmode
+2
+```
+
+**2. Give measurement data**
+
+```
+ # data, records=1
+  20.3  0.5  50  1  20  2  1
+ !<value> <error> <i-index> <j-index> <k-index> <variable-flag> <flag>
+```
+The variable-flag defines for which variable the measured value is given: 1=head, 2=temperature. 
+
+**3. Specify inversion options**
+
+**3.1 Options for parameter optimization**
+
+```
+# errors
+0.0 0.0 0.0 6.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
+0.0 0.0 0.0 6.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
+```
+
+`# errors` defines the uncertainty range of the 17 parameters. Each
+entry stands for a property (one of 17) of a unit. Each row represents
+the according unit. In the example above, log(permeability) would range
+over 6 magnitudes.
+
+```
+# enable unit
+0 1
+```
+
+| Property | Meaning |
+| ------ | ------ |
+| 0 | not activated for inversion |
+| 1 | activated for inversion | 
+
+
+Analogue to `# enable unit` there is the command
+
+```
+# enable property
+1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0
+```
+
+| Property | Meaning |
+| ------ | ------ |
+| 0 | not activated for inversion|
+| 1 | activated for inversion, linear | 
+| 2 | activated for inversion, logarithmic | 
+
+
+So in this example, porosity and permeability of unit 2 of 2 are enabled for
+inversion, with porosity varying linearly and permeability logarithmically.
+
+**3.2 Options for boundary condition optimization**
+
+Another option is to invert for boundary conditions. We distinguish between stationary boundary conditions and time-dependent boundary conditions. The following keywords specify the according options:
+
+```
+# bcerrors, records=1
+1 0.005 temp
+!<bc-unit> <error> <pv-type> 
+```
+| Property | Values/Meaning                                                                                                |
+| ------   | ------                                                                                                        |
+| bc-unit  | Specifies the bcindex that is defined at the respective bc-input ([Boundary condition section](./input_file)) |
+| pv-type  | head / temp / conc                                                                                            |
+
+a) for stationary boundary conditions
+
+```
+# optimize bc, records=1
+1 1 temp
+!<bc-unit> <1 (lin)/2 (log)> <pv-type>
+```
+
+b) for time-dependent boundary conditions
+
+```
+# optimize tp, records=1
+!<tp entry index> <bc index number> <alphy-beta keyword>
+```
+Here the bc-index needs to be assoziated with a unit number and defines this the dependency to the tp period table 
+(where to find the tp-entry). 
+
+*Note: Information on "optimize tp" are from the read_inverse.f90 routine. Not sure about the meaning of the input options. An example on how to use this option in the input file is missing...*
+
+4. Specify inversion control:
+
+```
+# inverse
+1                !<1 (on)/0 (off)>
+20 0.0001 1.0    !<max number of iterations> <break-off criterion> <time weighting>
+0 0              !<covariance-matrix output: 0/1> <resolution-matrix output: 0/1>
+1                !<output frequency: every nth iteration> 
+```
+Time weighting can range between 0.0 (fully explicit) and 1.0 (fully implicit).
+
+## Example model
+
+An example model for deterministic inversion with SHEMAT-Suite is provided in SHEMAT-Suite_Models/ad_const_TemperatureInversion.