# What are ensembles, multi-ensembles and hyper-ensembles?

Classically, numerical earthquake prediction was supposed to be based on a single, deterministic prediction. However, this approach is not used by Quantectum. Since seismic systems are chaotic, Quantectum uses several models to predict or forecast earthquakes. For each model, numerous forecasts are produced, all activated from the same starting time, but with slightly different starting conditions, and by using slightly different physical parameters. In this way, computers produce ensembles of forecasts for each model. Ensemble forecasting is a type of probability forecasting. It conveys a message, which explicitly reminds the user about the forecast uncertainty that should be considered and taken into account when making any practical use of the forecast. The uncertainty associated with every forecast means that different scenarios are possible, and the forecast should reflect that. Single deterministic forecasts can be misleading as they fail to provide this information.

The structure of the Quantectum Ensemble Earthquake Forecasting System (QEEFS) is the following:

## MULTI-ENSEMBLE

**Ordinary tectonic waves**

**1. Model-Ensemble**; ordinary tectonic waves**2. Model-Ensemble**; ordinary tectonic waves weighted by the Cosserat characteristic lengths**3. Model-Ensemble**; traction field around the ordinary tectonic waves

**Inverse/accelerated tectonic waves**

**4. Model-Ensemble**; inverse/accelerated tectonic waves**5. Model-Ensemble**; inverse/accelerated tectonic waves weighted by the Cosserat characteristic lengths**6. Model-Ensemble**; traction field around inverse/accelerated tectonic waves

Each Model-Ensemble contains **10 models** (different boundary conditions for tectonic waves), and each model allows for calculating **15 seismic/quantum states**, summing **150 states**. For each day, the Multi-Ensemble contains information on** 900 seismic/quantum states**.

For example, 10 days GLOBAL forecast contains information on 9000 seismic/quantum states in 64800 points (or quadrants/locations) on Earth.

Structure of the QEEFS multi-ensemble

## HYPER-ENSEMBLE

To accommodate different natural states, based on different physical parameters, Quantectum enables us to calculate various Multi-Ensembles. A group of such Multi-Ensembles is called a Hyper-Ensemble. For each time period (or "for each case") Quantectum calculates a minimum of 5 Multi-Ensembles, which results (in the case of five Multi-Ensembles) in 45,000 seismic/quantum states.

This is then the complete global earthquake forecast for some time period. It contains a virtually infinite amount of information on what can happen and where.

Structure of the QEEFS hyper-ensemble

Hyper-ensemble earthquake forecasting also allows for extensive statistical tests of earthquake predictability, which, however, cannot be done for one multi-ensemble only. Each model-ensemble member of a multi-ensemble is an independent and valid (but incomplete) description of the seismic activity of the Earth. Earthquakes happening on Earth each day are a direct consequence of the synchronizations of different subsystems of tectonic waves. At least one subsystem of tectonic waves should synchronize within some chosen region for that region to become seismically endangered. Even if other subsystems of tectonic waves did not predict/forecast any synchronization, an earthquake can happen due to the synchronization of only one subsystem. Therefore, it is not possible to make any statistical tests of differences between the model-ensembles within a multi-ensemble, since this has no physical meaning. The situation is, however, different at the level of the hyper-ensemble. Here, it is assumed that all multi-ensembles within a hyper-ensemble would predict/forecast an earthquake in some region. In this case, the probability of such an earthquake would be 100 %. In practice, not all multi-ensemble members predict/forecast all events, therefore, the probability of earthquakes is thus defined based on the number of multi-ensembles that actually do predict an event compared to the total number of multi-ensembles used in the hyper-ensemble. The difference between the forecasts by different multi-ensembles can then be used to describe the predictability of some events.

## Upgrading to Hyper-ensembles

One of our main future goals is to upgrade the Quantectum Ensemble Earthquake Forecasting System (QEEFS) to 64 days **hyper-ensemble forecasts** based on two reasons. First, the 64 days forecasts fall into the domain of the intermediate-range forecasts. Second, the hyper-ensembles are composed of numerous multi-ensembles, each multi-ensemble calculated based on slightly different physical parameters. *Logically, the question of the benefits and rationale behind such an approach arises*.

**The rationale of the 64-days forecasts**

Our past forecasting experiences indicate that moderate earthquakes with magnitudes close to 4 follow the synchronization field on a daily basis rather well. Large earthquakes, in contrast, occur at the beginning of large and long-lasting synchronizations. It is, therefore, crucial to intermediate-range forecasts to show long-range trends in the synchronization fields.

Calculation of the hyper-ensemble, however, demands great computing powers and data-storage capabilities. A 64-days multi-ensemble forecast consists of 6 model-ensembles each consisting of 10 models. This brings approximately 24 GB of data per multi-ensemble. A hyper-ensemble will at least be based on 10 multi-ensembles, which gives approximately 240 GB of data. This, in fact, is a minimum. In comparison, ECMWF produces 51 ensemble members. In the future, also Quantectum will work on the further development of the hyper-ensemble approach of earthquake forecasting.

**Hyper-ensemble and multi-ensembles**

As described above, one multi-ensemble forecast consists of 6 model-ensembles, each consisting of 10 models. Each model is based on different boundary conditions defining the propagation of tectonic waves through the Earth’s crust. The direction of tectonic waves and their velocity can be resolved based on the time-distance distribution of past large earthquakes. In our current multi-ensemble forecasts we use the EMSC catalog of M= 7.5+ earthquakes that happened after 01/01/2010. Based on these earthquakes it is possible to discover several thousands of tectonic waves with great efficiency. Nevertheless, by taking a different catalog, for example, M = 7+ earthquakes after 01/01/2016, the Quantectum would also be able to resolve other tectonic waves that are currently hidden or rather undiscovered. The future development of hyper-ensemble forecasts should, therefore, be based on different catalogs. This way, the efficiency of the forecast would be greatly improved.

**Conclusions**

During the year 2018, the Quantectum forecasting system has been upgraded to the level of multi-ensembles. At the beginning of the year 2020, one multi-ensemble is used based on the M = 7.5+ earthquakes that happened anywhere on Earth after 01/01/2010. Experiences show that this system of earthquakes and their time-distance relations that we currently use in our calculations define well the future M = 4+ earthquakes. In this way, we can say that almost all (but not all) current M = 4+ earthquakes are some kind of seismic echo of past large earthquakes. Approximately 90 % of M = 4+ events can be successfully predicted/forecasted based on this catalog. It is logical that Quantectum will never be able to use all options/combinations of catalogs, therefore, the description of the seismic activity of the Earth will always be incomplete. Nevertheless, based on a single multi-ensemble it is possible to correctly forecast 90 % of all M = 4+ earthquakes on Earth on a daily basis. In the future, the efficiency of the forecast could be significantly improved.