To be clearer, I am not interested in general assessment of seismic hazards (i.e. magnitude distribution for the next 25-50 years), but rather in short-term forecasts precise enough to order evacuation. I am aware that evacuation is a contentious issue...

In fact, the basic physical mechanism responsible for earthquakes is understood to be elastic rebound . It's really the details of that mechanism that are still the subject of study.

If you are asking whether it will be possible, in the future, to forecast earthquakes sufficiently well to justify the evacuation of a major city, I would say yes. However, that is also going to depend upon municipal emergency evacuation capacity.

The prediction of an earthquake has consequences in and of itself, and seismologists have been: Sent to Jail for Being Too Flippant.

If I had to guess where the future breakthroughs in seismology leading to better earthquake forecasting will come from - I would guess real-time remote sensing of crustal deformation from space platforms. This will produce large amounts of data about fault-zones, in real-time and computer-accessible format, that can be interpreted in terms of our present understanding of earthquake physics.

Stress

These stresses are also pretty difficult to measure. These methods include (Source World Stress Map):

• Earthquake focal mechanisms
• Well bore breakouts and drilling-induced fractures
• In-situ stress measurements (overcoring, hydraulic fracturing, borehole slotter)
• Young geologic data (from fault-slip analysis and volcanic vent alignments)

These may sometimes give contradictory stress tensors. One of these reasons is that in-situ measurements are often more localized than focal mechanisms (as an example). But when we look at the map, we do have a lot of data (27.000 data points). Here another big problem comes into play:

Material

While geophysicists like to assume that the ground is homogeneous, it really isn't. A rupture may occur when the material at a fault fails under pressure. Yet the material is highly diverse and includes cracks and fractures that make it virtually impossible to make an accurate assessment. The material may act elastic, ductile or brittle and that may be location-dependent. From this you cannot say if a small rupture triggers a larger earthquake due to stress transfer or if it stays a small earthquake.

What would be to improve

This would make a simulation highly chaotic and the prediction would have a high probability to be false positive or false negative, therefore, decreasing the reliability significantly.

In the end we would have to improve our understanding of:

• Stress fields
• Stress-Strain relations
• Rupture mechanisms
• Material science and location

Early Warning in California

Nevertheless, an earthquake early warning (EEW) system is being implemented in California (and tested). It's called CISN ShakeAlert. They can use the trick that so-called P-waves of earthquakes are faster (and less destructive) than surface waves. This can give valuable time to safety-relevant systems like nuclear plants or high speed trains. But this is in a very early stage, when an earthquake already happened and is bound to arrive somewhere.

(I would have loved to put down more links, but my rep is too low, so see Wikipedia for Rupture Mechanics, Stress-Strain relations, the World Stress Map website and the CISN ShakeAlert website.)

It is like predicting failure of a wooden (e.g., balsa) stick by bending the two sides with your hands, i.e., you know it will break more or less somewhere near the center, where the strain is highest (assuming homogeneity in properties and geometry) but getting the timing right is significantly harder and very difficult to reproduce. It is even harder in case of earthquakes, given the heterogeneity, non-linearity in the system.

So with time it will get easier to predict location of large earthquakes, as we monitor strain accumulation using modern tools like GPS, InSAR etc., but getting the timing right to even within a few years will be much harder. For example, we know that Southern San Andreas is due to for an earthquake (just based on the amount of slip deficit) as the last major earthquake was in 1857. But will this earthquake occur, today, in five years or within next 50 years, is unknown. Having said that additional faults in SoCal (e.g., San Jacinto and Elsinore) make the situation even more complex. Same goes for the North Anatolian fault near Istanbul, i.e., we know that an earthquake will occur there soon, as the entire plate boundary except the part near Istanbul had ruptured at least once in the last hundred years. See here for more details.

But getting the timing right for short term forecasts right now (and IMHO even in the next few decades) is impossible. Your only hope is alarms based on P-wave arrivals but then the earthquake has already started and heading towards you. Note: P waves arrive faster than surface waves, which cause most of the destruction so you might have a few seconds (depending on how far you are from the hypocenter) to take cover, automatically shutdown crucial stuff like gas flow in underground pipelines, subways, power plants etc.

According to the article Radon as an Earthquake Precursor – Methods for Detecting Anomalies (Gregorič et al.), the radon isotope $\ce{^222Rn}$ originates from the radioactive decay of $\ce{^226Ra}$ as part of the $\ce{^238U}$ decay chain that occurs naturally in varying degrees in the Earth's crust. Due to the relatively short half-life of the $\ce{^222Rn}$ isotope.

Gregorič et al. explains that the altered stress-strain dynamics before an earthquake alters the transport of "geogas", which consists of carrier volatiles (e.g. $\ce{CO2}$, $\ce{CH4}$) and rarer gases within (including $\ce{Rn}$) via grounwater (liquid-phase advection), gas flow through cracks and fissures (gas-phase advection), or by quick 'bubble flow' via being carried on buoyant 'bubbles' through aquifers and water filled fractures.

Of course, this method is highly dependent on he amount of the amount of the radiogenic source already present, and factors such as soil grain size and meteorological parameters (e.g. soil moisture, rainfall, air pressure and temperature) can affect the concentrations of $\ce{^222Rn}$ at the surface, research is ongoing to determine the seismic source vs meteorological sources of radon emissions.

Observations presented in the paper Radon Monitoring in Soil Gas and Ground Water for Earthquake Prediction Studies in North West Himalayas, India (Singh et al. 2010) found some correlation between surface measurements of radon and he occurrences of earthquakes, but confirmed that these were significantly affected by meteorological events and also stated that monitoring of other carrier (and rare) gases is required to potentially more accurately predict an earthquake.

In a very recent paper, Detecting precursory patterns to enhance earthquake prediction in Chile (Florido et al. 2015) also state that in Chile, one of the recognised precursors are radon gas fluctuations occurring in the soil, groundwater and air.