The management of the logic trees is the most complicated thing in the OpenQuake libraries. The issue is that it is necessary to manage them in an efficient way, by avoiding redundant computation and storage, otherwise the engine will not be able to cope with large computations.

Historically the engine did not fare well in the case of complex logic
trees. In recent years we improved the situation by introducing the
concept of *effective realizations*. After realizing that in many
calculations it is possible to reduce the full logic tree (the tree of
the potential realizations) to a much smaller one
(the tree of the effective realizations), we implemented an engine
optimization to take advantage of such situations. Here I will
explain how the optimization work.

First, it is best to give some terminology.

- for each source model in the source model logic tree there is a different GMPE logic tree
- the total number of realizations is the sum of the number of realizations of each GMPE logic tree
- a GMPE logic tree is
*trivial*if it has no tectonic region types with multiple GMPEs - a GMPE logic tree is
*simple*if it has at most one tectonic region type with multiple GMPEs - a GMPE logic tree is
*complex*if it has more than one tectonic region type with multiple GMPEs.

Here is an example of trivial GMPE logic tree, in its XML input representation:

```
<?xml version="1.0" encoding="UTF-8"?>
<nrml xmlns:gml="http://www.opengis.net/gml"
xmlns="http://openquake.org/xmlns/nrml/0.4">
<logicTree logicTreeID='lt1'>
<logicTreeBranchingLevel branchingLevelID="bl1">
<logicTreeBranchSet uncertaintyType="gmpeModel" branchSetID="bs1"
applyToTectonicRegionType="active shallow crust">
<logicTreeBranch branchID="b1">
<uncertaintyModel>SadighEtAl1997</uncertaintyModel>
<uncertaintyWeight>1.0</uncertaintyWeight>
</logicTreeBranch>
</logicTreeBranchSet>
</logicTreeBranchingLevel>
</logicTree>
</nrml>
```

The logic tree is trivial since there is a single branch (“b1”) and GMPE (“SadighEtAl1997”) for each tectonic region type (“active shallow crust”). A logic tree with multiple branches can be simple, complex, or even trivial if the tectonic region type with multiple branches is not present in the underlying source model. This is the key to the logic tree reduction concept.

The simplest case of logic tree reduction is when the actual sources do not span the full range of tectonic region types in the GMPE logic tree file. This happens very often in SHARE calculations. The GMPE logic tree (actually there are three of them, one for each source model) potentially contains 1280 realizations coming from 7 different tectonic region types:

- Active_Shallow:
- 4 GMPEs (b1, b2, b3, b4)
- Stable_Shallow:
- 5 GMPEs (b21, b22, b23, b24, b25)
- Shield:
- 2 GMPEs (b31, b32)
- Subduction_Interface:
- 4 GMPEs (b41, b42, b43, b44)
- Subduction_InSlab:
- 4 GMPEs (b51, b52, b53, b54)
- Volcanic:
- 1 GMPE (b61)
- Deep:
- 2 GMPEs (b71, b72)

The number of paths in the logic tree is 4 * 5 * 2 * 4 * 4 * 1 * 2 =
1280, pretty large. We say that there are 1280 *potential
realizations* per source model. However, in most computations, the
user will be interested only in a subset of them. For instance, if the
sources contributing to your region of interest are only of kind
**Active_Shallow** and **Stable_Shallow**, you would consider only 4 *
5 = 20 effective realizations instead of 1280. Doing so will improve
the computation time and the needed storage by a factor of 1280 / 20 =
64, which is very significant.

Having motivated the need for the concept of effective realizations, let explain how it works in practice. For sake of simplicity let us consider the simplest possible situation, when there are two tectonic region types in the logic tree file, but the engine contains only sources of one tectonic region type. Let us assume that for the first tectonic region type (T1) the GMPE logic tree file contains 3 GMPEs (A, B, C) and that for the second tectonic region type (T2) the GMPE logic tree file contains 2 GMPEs (D, E). The total number of realizations (assuming full enumeration) is

total_num_rlzs = 3 * 2 = 6

The realizations are identified by an ordered pair of GMPEs, one for each tectonic region type. Let’s number the realizations, starting from zero, and let’s identify the logic tree path with the notation <GMPE of first region type>_<GMPE of second region type>:

# | lt_path |
---|---|

0 | A_D |

1 | B_D |

2 | C_D |

3 | A_E |

4 | B_E |

5 | C_E |

Now assume that the source model does not contain sources of tectonic region type T1, or that such sources are filtered away since they are too distant to have an effect: in such a situation we would expect to have only 2 effective realizations corresponding to the GMPEs in the second tectonic region type. The weight of each effective realizations will be three times the weight of a regular representation, since three different paths in the first tectonic region type will produce exactly the same result. It is not important which GMPE was chosen for the first tectonic region type because there are no sources of kind T1; so let’s denote the path of the effective realizations with the notation @_<GMPE of second region type>:

# | path |
---|---|

0 | @_D |

1 | @_E |

The “@” character should be read as “any”, meaning that for the first tectonic region type any path (i.e. “A”, “B” and “C”) will give the same contribution, i.e. there is independence from the GMPE combinations coming from the first tectonic region type.

In such a situation the engine will perform the computation only for the 2 effective realizations, not for the 6 potential realizations; moreover, it will export only two files with names like:

```
hazard_curve-smltp_sm-gsimltp_@_D-ltr_0.csv
hazard_curve-smltp_sm-gsimltp_@_E-ltr_1.csv
```

oq-lite provide some facilities to explore the logic tree of a
computation without running it. The command you need is the *info* command:

```
$ oq-lite info -h
usage: oq-lite info [-h] [-c] [-g] [-v] [-r] [input_file]
positional arguments:
input_file job.ini file or zip archive [default: '']
optional arguments:
-h, --help show this help message and exit
-c, --calculators list available calculators
-g, --gsims list available GSIMs
-v, --views list available views
-r, --report build a report in rst format
```

Let’s assume that you have a zip archive called SHARE.zip containing the SHARE source model, the SHARE source model logic tree file and the SHARE GMPE logic tree file as provided by the SHARE collaboration, as well as a job.ini file. If you run

oq-lite info SHARE.zip

all the files will be parsed and the full logic tree of the computation will be generated. This is very fast, it runs in exactly 1 minute on my laptop, which is impressive, since the XML of the SHARE source models is larger than 250 MB. Such speed come with a price: all the sources are parsed, but they are not filtered, so you will get the complete logic tree, not the one used by your computation, which will likely be reduced because filtering will likely remove some tectonic region types.

The output of the info command will start with a CompositionInfo object, which contains information about the composition of the source model. You will get something like this:

```
<CompositionInfo
b1, area_source_model.xml, trt=[0, 1, 2, 3, 4, 5, 6], weight=0.500: 1280 realization(s)
b2, faults_backg_source_model.xml, trt=[7, 8, 9, 10, 11, 12, 13], weight=0.200: 1280 realization(s)
b3, seifa_model.xml, trt=[14, 15, 16, 17, 18, 19], weight=0.300: 640 realization(s)>
<RlzsAssoc...>
```

You can read the lines above as follows. The SHARE model is composed by three submodels:

- area_source_model.xml contains 7 Tectonic Region Types numbered from 0 to 7 and produces 1280 potential realizations;
- faults_backg_source_model.xml contains 7 Tectonic Region Types numbered from 7 to 13 and produces 1280 potential realizations;
- seifa_model.xml contains 6 Tectonic Region Types numbered from 14 to 19 and produces 640 potential realizations;

In practice, you want to know if your complete logic tree will be reduced by the filtering, i.e. you want to know the effective realizations, not the potential ones. You can perform that check by using the –report flag. This will generate a report with a name like report_<calc_id>.rst:

```
$ oq-lite info SHARE.zip --report
...
Generated /home/michele/report_5580.rst
```

If you open that file you will find a lot of useful information about the source model, its composition, the number of sources and ruptures and the effective realizations.

Depending on the location of the points and the maximum distance, one or more submodels could be completely filtered out and could produce zero effective realizations, so the reduction effect could be even stronger. Such a situation is covered by our tests and will be discussed later on.

The info commands produces more output, which I have denoted simply as <RlzsAssoc...>. This output is the string representation of a Python object containing the associations between the pairs

(trt_model_id, gsim) -> realizations

In the case of the SHARE model there are simply too many realizations to make it possible to understand what it is in the association object. So, it is better to look at a simpler example. Consider for instance our QA test classical/case_7; you can run the command and get:

```
$ oq-lite info classical/case_7/job.ini
<CompositionInfo
b1, source_model_1.xml, trt=[0], weight=0.70: 1 realization(s)
b2, source_model_2.xml, trt=[1], weight=0.30: 1 realization(s)>
<RlzsAssoc(2)
0,SadighEtAl1997: ['<0,b1,b1,w=0.7>']
1,SadighEtAl1997: ['<1,b2,b1,w=0.3>']>
```

In other words, this is an example containing two submodels, each one with a single tectonic region type and with a single GMPE (SadighEtAl1997). There are only two realizations with weights 0.7 and 0.3 and they are associated to the tectonic region types as shown in the RlzsAssoc object. This is a case when there is a realization for tectonic region type, but more complex cases are possibile. For instance consider our test classical/case_19, which is a reduction of the SHARE model with just a simplified area source model:

```
$ oq-lite info classical/case_19/job.ini -f
<CompositionInfo
b1, simple_area_source_model.xml, trt=[0, 1, 2, 3, 4], weight=1.0:: 4 realization(s)>
<RlzsAssoc(8)
0,AtkinsonBoore2003SInter: ['<0,b1,@_@_@_@_b51_@_@,w=0.2>', '<1,b1,@_@_@_@_b52_@_@,w=0.2>', '<2,b1,@_@_@_@_b53_@_@,w=0.2>', '<3,b1,@_@_@_@_b54_@_@,w=0.4>']
1,FaccioliEtAl2010: ['<0,b1,@_@_@_@_b51_@_@,w=0.2>', '<1,b1,@_@_@_@_b52_@_@,w=0.2>', '<2,b1,@_@_@_@_b53_@_@,w=0.2>', '<3,b1,@_@_@_@_b54_@_@,w=0.4>']
2,ToroEtAl2002SHARE: ['<0,b1,@_@_@_@_b51_@_@,w=0.2>', '<1,b1,@_@_@_@_b52_@_@,w=0.2>', '<2,b1,@_@_@_@_b53_@_@,w=0.2>', '<3,b1,@_@_@_@_b54_@_@,w=0.4>']
3,AkkarBommer2010: ['<0,b1,@_@_@_@_b51_@_@,w=0.2>', '<1,b1,@_@_@_@_b52_@_@,w=0.2>', '<2,b1,@_@_@_@_b53_@_@,w=0.2>', '<3,b1,@_@_@_@_b54_@_@,w=0.4>']
4,AtkinsonBoore2003SSlab: ['<0,b1,@_@_@_@_b51_@_@,w=0.2>']
4,LinLee2008SSlab: ['<1,b1,@_@_@_@_b52_@_@,w=0.2>']
4,YoungsEtAl1997SSlab: ['<2,b1,@_@_@_@_b53_@_@,w=0.2>']
4,ZhaoEtAl2006SSlab: ['<3,b1,@_@_@_@_b54_@_@,w=0.4>']>
```

This is a case where a lot of tectonic region types have been completely filtered out, so the original 160 realizations have been reduced to merely 4 for 5 different tectonic region types:

- the first TRT with GSIM AtkinsonBoore2003SInter contributes to all the realizations;
- the second TRT with GSIM FaccioliEtAl2010 contributes to all the realizations;
- the third TRT with GSIM ToroEtAl2002SHARE contributes to all the realizations;
- the fourth TRT with GSIM AtkinsonBoore2003SInter contributes to all the realizations;
- the fifth TRT contributes to one realization for each of four different GSIMs.