In this paper, G. A. Smith and A. Frank discuss the chances and evidence that an industrial civilization might have arisen on planet Earth before humans.

Summary

Relevance to the Drake equation

If industrial civilizations has arisen more than once on planet Earth that would mean the chances of having extraterrestrial civilizations in the Milky Way galaxy (represented by the Drake equation) would be greatly multiplied.

Limitations of the Geological Record

Why are we even asking this question? Isn't it obvious that if there was any advanced previous advanced civilization on Earth that collapsed we would be able to find their fossils and objects left behind?

The authors argue:

The fraction of life that gets fossilized is always very small.
Civilizations older than about 4 Ma, the chances of finding direct evidence of their existence via objects or fossilized examples of their population is small:

weathering
tectonic activity

(Pause for recovering from the striking realization that most traces left by humankind would be erased after 4 Ma).

So any evidence would have to be gathered from the atmosphere, ice core samples, etc.

The Geological Footprint Of The Anthropocene

Golden quote:

There is an interesting paradox in considering the Anthropogenic footprint on a geological timescale. The longer human civilization lasts, the larger the signal one would expect in the record. However, the longer a civilization lasts, the more sustainable its practices would need to have become in order to survive.

Here are the main anthropogenic impacts considered by the authors:

Stable isotope anomalies of carbon, oxygen, hydrogen and nitrogen

Carbon: Biological processes preferentially take up the C12 isotope instead of C13, by consequence the atmosphere has a larger ratio of C13 than bio-organisms. Because one of the features of the anthropocene is an increase in biomass burning (fossil fuels, deflorestation) the ratio of C13 to C12 is decreasing in the atmosphere (Suess Effect).

Oxygen: Due to the increase in greenhouse gases, we see an increase in temperature-related formation of carbonates. (TODO: understand better this process).

Nitrogen: Nitrogen in the soil usually was the bottleneck for plant growth in the preindustrial era. The discovery of the Haber–Bosch process gave way to artificial nitrogen fertilizers and had a profound effect on the nitrogen cycle.

Sedimentological records

Increase in soil erosion due to agriculture and deflorestation.
Canalization of rivers increases oceanic deposition of sediment.
Upper ocean acidification
Ocean anoxia ("dead-zones")
Higher movement of rare earth minerals.

Faunal radiation and extinctions

Wild chances in animal populations due to extinction, invasive species, etc.

Non-naturally occurring synthetics
Plastics
Transuranic elements

There are no known natural sources of Pu244 outside of supernovae.

Abrupt Paleozoic, Mesozoic and Cenozoic Events

The authors hipothesis is that industrialization has an impact on many different geological variables so we should look for an abrupt and simultaneous change on the geological records. The authors go over available records of the Paleozoic, Mesozoic and Cenozoic eras looking if there's any match to this model and find 4 matches.

Discussion and Testable Hypotheses

Almost all changes proposed to the Antropocene can be found on previous geological events. Which is to be expected if any of these events was caused by a massive output of biogenic CO2 that would have caused global warming (such as major volcanic events lighting up shale/petroleum reservoirs). So these are not enough to prove or disprove the existence of a previous industrial civilization.
Current changes seem to be happening faster than paleoclimatic records but there's no way to be sure because our dating methods are not precise enough at short timescales.
Posing a so intriguing question about previous industrial civilizations of Earth can offer new perspectives on other problems regardless of the answer (which is probably "No" according to the authors of the paper).