Methods of short-term earthquake prediction and some results of mathematical modeling of fracturing processes in lithosphere are developed. General scienti c methodology of short-term prediction is formulated including two su cient conditions for increasing probability of the forecast of seismic event. Implementations of arti cial neural networks for interpretation of radon variations are proposed.
The goal of our research - construction of a methodology (including a model of the medium), which the key idea is to create an algorithm to determine the probability of seismic event occurrence. To provide short-term earthquake prediction, it is necessary to have an adequate model of the medium. In our case, we propose a multi-phase contrast model, which is a porous permeable water and gas saturated media with inclusions in a solid matrix of uraniumbearing minerals, such as Sierra-Nevada granite massif (Fig. 1). We assume that in the area of the proposed seismic event (during the preparation period) a nonuniform dilatant inclusion develops, which is a set interconnected by permeable channels. The dynamics of each dilatant inclusion depends on the ratio of the rate of tectonic stress increase and coe cients of the hydraulic di usion of dilatant inclusion area and host rocks. Depending on this rationing, dilatant inclusion boundary conditions may be draining or undraining. For undraining conditions in the dilatant inclusion area, the section of the pore uid reduced pressure occurs, which in the case of radon-bearing rock increases the radon content in the pores due to injection e ects. As a mathematical model of the inhomogeneous dilatant inclusion dynamics, we propose the arti cial neural networks.
In the investigation of variables matrix (radon variations) in real-time for a week before the earthquake, the perceptron with the independent variables is formed. We assume that by this time the tectonic energy relaxation process is completed and the interaction of dilatant mesoinclusions stopped. At each point of observation, only processes of uranium-238 radioactive decay occur and radon-222 appears. Therefore, at this moment the amount of emanation depends only on uranium-238 content. Thus, the beginning of the radon emanation independent process xed by arti cial neural networks is most likely a short-term earthquake precursor. Technique of the situation detection consists in the fact that the qualitative characteristics of the seismic hazard is de ned once a week. The rst rank of danger is the start and end of the stress relaxation process; the second rank of danger is the xation of independent spatial process of the radon emanation (maximum probability of earthquakes). 2
In paper, we propose a mathematical model of dynamics of tectonic processes
in the Earth's crust at various hierarchical levels and the relationship of these
levels to each other. Let us consider three mutually complementary
hierarchical levels that adequately describe the dynamics of the earth's crust. The rst
(lower hierarchical level) is a multiphase contrast model of the earth's crust,
which is a porous permeable moisture and gas-saturated medium with
inclusions in the solid matrix of uranium-containing minerals. The second
hierarchical level is where the inhomogeneous dilatant inclusion is replaced by clusters of
mesoinclusions interconnected by permeable channels. The third (the most high
hierarchical level) is the regional inhomogeneous dilatant inclusion in the eld
of variable tectonic stresses, the dynamics of which are described by the
RiceRudnicki model [
The paradigm of space-temporal point processes is particularly suited to
neural network analysis, which we previously applied to radon variations and their
relationship to tectonic processes. This approach proved to be useful in
describing the space-temporal dynamics of tectonic processes (regional shift stresses) in
Southern California [
At the same time, in our work, using the hypothesis of connectedness (in the physical sense) of dilatant inclusions, decomposition of the tectonic process into a set of successive (or parallel) acts was carried out. Each of them represents the process of development of the dilatant inclusion (the Rice-Rudnicki model) with certain space-temporal and energy scales. From our standpoint, the emerging physical chains linking the dilatant mesoinclusions are porous channels with permeability varying in time. Thus, the proposed model is a cluster of combined dilatant mesoinclusions interconnected by the permeable channels (Fig. 1).
As an example of analysis of space-time pattern of variations of radon
concentration, we considered the possibility of determining the time and place of tectonic
events. The problem of any forward-looking research is to determine the dynamic
parameters of the anomalous zone of the earth crust, which properties de ne the
conditions of tectonic events occurrence. Thus, we need to interpret the observed
data. Interpretation of the radon variations like any other physical eld has to
begin with its division into normal and anomalous components [
We conducted a study of radon exhalation eld variations from rock mass
obtained by King Chi-Yu on 12 boreholes in the vicinity of the San-Andreas
Fault (California, USA) in the period from 1975 to 1980 [
Based on the analysis of the space-temporal pattern of the radon concentration variation eld in Southern California, we studied both the structure of the earth's crust of the prospective indicator zone (the intersection of the SanAndreas and Calaveras faults) and the probability of determining the time and place of the tectonic event from these data. The goal of any predictive research is to determine the dynamic parameters of the investigated anomalous zone of the earth's crust, which determine the conditions for occurrence of a tectonic event. To create a system for forecasting earthquakes, it is necessary to have adequate both static and dynamic models of the earth's crust. To this end, we proposed a model of an inhomogeneous dilatant inclusion (Fig. 1). It is a volume lled with clusters of dilatant mesoinclusions connected by channels with time-varying permeability.
To provide short-term earthquake prediction it is necessary to have mentioned adequate both static and dynamic earth crust models. In our case, we propose a multiphase contrast model, there are a porous permeable water- and gas-saturated earth crust with the uranium-bearing minerals inclusions in a solid matrix. As a result of the proposed model of the medium at each point of observation in tectonically quiet periods, only processes of radioactive decay of the radium-226 isotope and the occurrence of radon-222 were considered. Therefore, at each point of observation the radon emanation amount should depend only from the radium-226 isotope content (Fig. 3).
The dynamic model of a medium is a high permeability dilatant inclusion
in the eld of variable tectonic stresses. The process of destruction is stabilized
at undraining conditions deformation of high permeable moisture saturating
inclusion. Such conditions involve signi cant deformation rate at a relatively low
rate of the liquid di usion. Stabilization of the fracture is associated with the
strengthening of a deformable object. In this regard, to explain the features of
radon eld variations, we use the Rice-Rudnicki model with dilatant
strengthening inclusion [
Since concentrations of the radioactive elements of the uranium-235 type
at the observation points are practically unchanged (with the exception of the
long-period decay process), it can be assumed that the time variations of the
radon concentration are related to the processes of gas transfer in the active
medium. The invariance of the position of the extrema of variations of the radon
concentration in space suggests that in these zones the sources (sinks) in the
earth's crust are stipulated by the redistribution of radon in space. It remains
to con rm presence of one more element(s), which is an integral part of the
model of the inhomogeneous dilatant inclusion. These are permeable channels
connecting dilatant mesoinclusions. Their presence is con rmed by analysis of
the long-period variations of the radon concentration (Fig. 4). This gure shows
the dynamics of variations of the radon concentration over a period of more than
4 years (averaged curve). From analysis of the presented data, it follows that,
apparently, there is a system of interconnected sources (sinks), i.e. presence of
permeable channels was proved. Thus, in the earth's crust in the zone of the
intersection of the San-Andreas and Calaveras faults in Southern California,
there is an inhomogeneous permeable dilatant inclusion, each element of which
obeys the laws described by the Rice-Rudnicki model and reacts to the change
in the dynamic situation of the investigation region [
In the article published in 1956, Tsuboi proposed to calculate the energy E of
the largest possible earthquake [
E = 1 ex2V; (1)
2 where the notations used have the following meanings: e is the e ective elastic constant of the crustal material, x is the ultimate strain of the crustal material, V is the earthquake volume.
Expression (1) amounts to mean that the material within the earthquake volume will be uniformly strained until this uniform strain reaches the value x everywhere at the same time within the volume. Further, at the time of earthquake occurrence, the stored energy E is sent out from the whole volume by some kinds of mechanism. Evidently, this uniform strain hypothesis cannot be strictly true, but the essential point of it, which the writers would like to emphasize, is that x is assumed not to di er notably from one part to another within the volume. The assumption that x uniform everywhere can be only the rst approximation in the formulation of the hypothesis.
Thus, local parts of the earthquake volume characterized by their x values store and emit according to (1) only a portion of the seismic energy. Consequently, they are sources of both foreshock and aftershocks. So, for example, we shall consider both foreshocks and aftershocks as a manifestation of dynamic processes in mesoinclusion previously, it was believed that the sources of both foreshocks and aftershocks are the entire volume of the earthquake preparation zone. Formalization of the dynamics of processes in the inhomogeneous dilatant inclusion and the construction of neural networks on this basis is a step forward to the theory of tectonic events forecasting and a new tool for analyzing the irregular structure of the tectonic eld in seismically dangerous regions. Perhaps, the proposed approach will lead to a new explanation of such established concepts as foreshocks and aftershocks.
We have formulated the following principles of arti cial intelligence for
automatically prediction of the earthquake time and place [
In the study of the matrix of variables in real-time for a week before the earthquake, the perceptron with independent variables is formed. I.e., at this time at each point of observation only processes of uranium-238 radioactive decay occur and radon-222 exhalation will be normally distributed. Therefore, at each point of observation, the emanation amount depends on the content of uranium-238 and does not depend on radon redistribution between points of observation. Thus, with the help of neural networks, complex dynamic processes are simulated that act in an inhomogeneous dilatant inclusion.
We have created a technique of rank recognition of a situation that occurred at any time in the vicinity of controlled earthquake source. On the basis of factor analysis, a technique of separation of radon signal at its normal and anomalous (predictive) components is developed that enabled us to formulate the principles of arti cial intelligence for automatical prediction the earthquake time and place. When approaching tectonic events are observed the space-temporal pattern of the eld variations of radon should not be related to changes in the structure of the pore space rock massif. Therefore, the study of the matrix of variables in real time with the help of neural networks for the week before the earthquake marked the formation of the perceptron with modi ed architecture that characterizes the independent of variables from each other. Apparently, this is a short-term earthquake precursor. 5
Conclusions 1. An original model of the crustal block at the intersection of the San-Andreas and Calaveras faults was constructed based on the hypothesis of the existence in the Earth's crust of Southern California of an inhomogeneous dilatant inclusion, which is a set of clusters of dilatant mesoinclusions, interconnected by permeable channels. 2. Analysis of the experimental data on the study of the space-temporal distribution of variations of radon concentration showed that the dynamic zones of the extrema apparently coincide spatially with the mesoinclusions that form the main dilatant volume. 3. The dynamic relationship of these mesoinclusions is derived from an analysis of the space-temporal characteristics of regional long-period variations of the radon concentration. 4. It has been suggested that the source of both foreshocks and aftershocks is not the entire volume of the earthquake preparation zone, but only the local sections of the volume (mesoinclusions). 5. On the basis of the factor analysis and neural network modeling, the basic principles of arti cial intelligence are formulated for automatical prediction of the time and place of possible earthquake. Two rank technique is developed for recognizing the situation that occurs at any time in the vicinity of the controlled section of the crust. The technique consists in the fact that once a week by the method of factor analysis the qualitative characteristics of seismic hazard are determined. In our case, the rst rank of danger is the beginning and end of the process of stress relaxation; the second rank of danger is xing the time of independent radon exhalation process at each point of observation by methods of neural network modeling (the maximum probability of an earthquake). 6
The study is supported by the Russian Science Foundation (project 14-27-00059 3D models of Urals region Nether-Polar zone deep structure construction based on new geophysical eld complex interpretation methods and modern computer grid modeling technologies) and is carried out in the Institute of Geophysics, UB RAS.