Step 1: Understand what the sentence is describing.
It talks about modern scientific methods studying earthquakes, and explains that quakes are the periodic release of a certain kind of energy, rather than random freak events.
Step 2: Choose the word for the first blank.
The whole point of studying the pattern of accumulation and discharge of energy is to anticipate future earthquakes. "Predicting earthquakes" is the standard phrase used for this branch of seismology, forecasting when and where a quake might occur based on patterns of stress build-up.
Step 3: Choose the word for the second blank.
Earthquakes are caused by the build-up and release of energy within the earth itself, which is called "seismic" energy, the term directly associated with earthquakes and ground vibrations.
Step 4: Eliminate the other options.
"Identifying ..... iconic" does not fit, earthquakes are not normally described using the word iconic, which means widely recognised as a symbol, not related to energy type. "Locating ..... cosmic" is wrong because cosmic energy refers to energy from outer space, not the energy stored within the earth's crust that causes quakes. "Watching ..... heavenly" fails for a similar reason, heavenly energy again points to celestial sources, unrelated to geologic processes, and watching earthquakes does not capture the scientific, analytical sense the sentence needs. "Prevailing ..... acerbic" makes no sense at all, acerbic means sharp or bitter in tone, it has nothing to do with physical energy.
Step 5: Conclude.
The pair that correctly matches both the scientific method and the type of energy involved is Predicting ..... seismic, option (c).