The seismic sequence in Central Italy (2016-2017) III - Heuristic seismic transmigration, and focal volume estimate

The seismic sequence in Central Italy that started in August 2016 - and is still in progress in February 2017- is investigated like a pilot study in order to focus on a multidisciplinary perspective for a realistic seismic hazard mitigation and management. A clear distinction has to be made with the "bottom-up" approach which is typical of a geologist or of a seismologist, who investigate phenomena after the occurrence of an earthquake, and upon consideration of a subset - of "all" known - phenomena that are available and that preceded every given shock. Statisticians, altogether with seismologists, apply a formally rigorous and careful approach, based on complicated algorithms etc. Their rigorous approach is certainly indicative and useful for hazard management, unlike every less rigorous statistical analysis that cannot be comparably reliable. In fact, the boundary is not always clearly stated between an "implicit suitable assumption" and logical rigor. A first paper ("paper I") in the present series was concerned with a real-time monitoring of crustal stress propagation, aimed to provide with new and physically more specific and precise observational information. It relies on acoustic emission (AE) monitoring of the crustal stress propagation and evolution before the occurrence of an eventual earthquake. That is, its focus is on the preliminary diagnosis of the state of the crust before the eventual occurrence of a seismic shock. The approach is from the viewpoint of the geophysicist ("top-down"), i.e. just apply the known laws of fundamental physics to the physical system and infer its evolution until an eventual catastrophe. A second paper ("paper II") was focused on a correct "top-down" and rigorous approach to the geodynamic interpretation. Its purpose was to show how the present standard way to approach geodynamics is unsuited for any real physical discussion. In fact, it relies on the "bottom-up" approach of geologists in terms of some more or less intuitive, certainly reasonable although often physically unreliable, arguments. The present paper ("paper III") completes the series. It is focused on the empirical evidence that is generally denoted as seismic (and eventually also volcanic) "transmigration". Two viewpoints are however to be distinguished. One approach deals with an analysis of single case histories. This is physically correct, as compared to all others every occurrence is a different case history. On the other hand, single case histories can allow for no statistical inference, hence with no "confidence limit" or error bar etc., which is the "dream" of every statistician (or of every experimenter). On the other hand, the alternative approach - which is formally applied to the seismic catalogues by means of the formal methods of statistics - has the drawback to manage a supposedly homogenous database that, in reality, is physically heterogeneous. Hence, every formal statistical result has the hazard to be only a mathematical exercise with no real physical correspondence to natural reality. Notwithstanding this warning and all logical constraints, this three-paper set shows how an earthquake appears to be a local response to a planetary paroxysm that somewhere is eventually manifested as a seismic shock, although in general it can even be associated to no earthquake. No "simple" "thumb rule", or no "magic" precursor, will ever be found. Similarly to every conscience-driven medical doctor who wants to take care of the health of his patient, the seismic hazard can be managed only by applying some suitable unprecedented objective monitoring of the natural system. In "paper I" it is shown that this effort can be optimized by a 4-level approach: (i) level 1 gets advantage from satellite monitoring; (ii) levels 2 and