# What are the Omega-sequences?

## Elastic rebound theory and the Omega-sequences

**Introduction**

In the classical seismology, the elastic-rebound theory is an explanation of how energy is accumulated and then released from the rock during an earthquake. The model was formulated by Reid in 1910. Due to the slow and constant movements of the tectonic plates, the rocks on the opposing sides of faults are subjected to the shear stress. They deform slowly until their internal rigidity is exceeded. When the actual earthquake nucleates, the rock is split with a rupture along the fault partially releasing the accumulated energy. The rocks around the fault snap back toward their original shape.

Elastic rebound model by Reid, 2010

**Problem**

The problem with the Reid rebound model is that it is based on a single fault, thus excluding any possible interactions among them. The advantage of the Omega-Theory is that it expands and upgrades the Reid rebound model with the incorporation of a minimum of two and usually multiple faults. This extended model also accounts for potential interactions among faults and block rotations between the fault planes. In structural geology, such rotations are well known to occur within the systems of interacting sub-parallel faults, where they are referred to as the domino-type rotations.

**Solution**

To obtain a solution, we need to analyze, how the elastic rebound model is applied to a system of two interacting parallel faults. In their initial state, the rocks are un-deformed. Due to the increase of shear stress, the rocks are elastically sheared and rotated. After the internal rigidity of the rock is exceeded, the earthquake occurs, first as the mainshock along one fault, followed by the aftershock along the second fault. During this process, the block of rock between both fault planes rotates back toward the original position.

Careful mathematical examination of this process within the Omega-Theory shows that the parallel-faults interaction can happen between equal and also non-equal sized parallel faults. Let L1 be the length of the first fault, while L2 is the length of the second fault. The Omega-Theory shows that the ratio, B, between L1 and L2 is a parameter of the rock itself and depends on the frictional properties of the rocks and their geological settings. The theory also shows that the reactivation time is linearly proportional to the length of the fault. This means that larger faults will need more time to reactivate and produce an earthquake compared to smaller faults. In nature, there is a considerably larger number of small earthquakes in comparison to larger earthquakes.

Elastic rebound model in the Omega-Theory

In the case of several interacting sub-parallel faults, this leads to the development of either periodic or geometric series of interacting faults.

When the fault series is periodic, all interacting faults have the same lengths and the distance between them is also equal.

When the fault series is geometric, the length of each subsequent fault is B times larger compared to the previous one. Also, the distance to each subsequent fault is B times longer compared to the previous one.

The existence of such periodic and geometric series of faults is most evident at the mid-ocean ridges. These have segmented structure, composed of long sub-parallel transform faults and fracture zones separated by ridge segments, where the Earth’s crust is pulled apart. Careful measurements of these structures clearly show that the series of both, the transform faults as well as ridge segments tend to be geometric.

Periodic series of faults

Geometric series of faults

Analysis of the seismic activity of such series of faults shows that they produce cascades of earthquakes, which are also periodic or geometric. This is well in accordance with the Omega-Theory. Such cascades of earthquakes are generally referred to as the Repeating Earthquake Series, and in the Omega-Theory they are called the Omega-sequences. Within the Omega-sequences, the seismic activity is systematically transferred from one fault to all subsequent parallel faults.

The easiest and the most effective way of illustrating how the Omega-sequences work is an example of the falling dominoes. If all dominoes are of equal size the sequence of events is periodic. But if the dominoes form a geometric series, the sequence of events is also geometric. Thousands of such periodic and geometric Omega-sequences are constantly occurring in the Earth’s crust in all seismic zones along tectonic plate boundaries.

Geometric and periodic series of transform faults and ridge segments in the Atlantic

**Types of the Omega-sequences**

There are four basic types of the Omega-sequences.

Decreasing Seismicity Rate sequences or DSR sequences are characterized by the systematic transfer of the seismic activity from smaller to larger faults. The average rate of earthquakes decreases according to Omori’s law.

Increasing Seismicity Rate sequences or ISR sequences are just the opposite. Here, the seismic activity is systematically transferred from larger to smaller faults. The average rate of earthquakes increases according to inverse Omori’s law.

DSR-I sequences are those DSR sequences that transform into the ISR sequences.

ISR-D sequences are those ISR sequences that transform into the DSR sequences.

DSR Omega-sequence

ISR Omega-sequence

DSR-I Omega-sequence

ISR-D Omega-sequence

**Can Omega-sequences be found in nature?**

Careful mathematical analysis of the seismic activity of the Earth, as well as earthquake series worldwide, shows that the Omega-sequences can occur everywhere, not just at the mid-ocean ridges. Seismic catalogs were long thought to be composed of random events. Yet, the Omega-Theory showed that these supposedly random catalogs are actually composed of a multiplicity of the Omega-sequences, which represent a concealed order within the seismic activity of the Earth and as such, being far from random processes.