Y. Y. KAGAN

                      (UCLA, Los Angeles)

WHY DOES THEORETICAL PHYSICS FAIL TO EXPLAIN AND PREDICT EARTHQUAKE
OCCURRENCE? 

Several reasons can be proposed:

1. Multidimensional character of seismicity: time, space, and 
earthquake focal mechanism need to be modeled. The latter is a
symmetric second-rank tensor of special kind.

2. Intrinsic randomness of the earthquake occurrence, the need to 
apply the theory of stochastic point processes and appropriate 
complex statistical techniques.

3. Scale-invariant or fractal properties of earthquake process; the
theory of random stable or heavy-tailed variables is significantly more
difficult than that of Gaussian variables and is only being developed
at present. The earthquake process theory should be renormalizable. 

4. Statistical distributions of earthquake size, earthquake temporal
interaction, their spatial patterns and focal mechanisms are largely
universal with the values of major parameters similar for earthquakes
in various tectonic zones. The universality of these distributions
gives us some hope in creating foundations for earthquake process
theory. 

5. The quality of earthquake data statistical analysis is low, little 
or no study of random and systematic errors is usually performed, thus 
most of the published statistical results are artifacts.

6. Earthquake process does not operate as an isolated system. 
Scale-invariance of the process means that the largest inhomogeneity or 
earthquake fault system (defect) is comparable in size with the system
extent, same for the next largest defect, etc. Thus, in any seismic 
region we cannot separate the largest fault or fault system and treat 
the remainder as medium with uniform properties.

7. During earthquake rupture propagation focal mechanisms sometimes
undergo large 3-D rotations. This necessitates applying non-commutative
algebra (e.g., quaternions and gauge theory) to model earthquake
occurrence. We note that almost all field theories currently employed
in physics are based on complex numbers, i.e., use commutative algebra.

8. The phenomenological and theoretical difficulties are not limited to 
earthquakes; any fracture of brittle materials, tensile or shear, would 
encounter similar problems.