verb-ing modifier trouble

Question

I'm unexplainably confused about this topic.

1. What does the following verb-ing clause modify? (noun) researchers or (action) have sent?
2. How do we decide that? --> very important for me
3. Is there any source by which we can study over the topic?

Searching for signs of life on Mars, researchers have sent many probe rovers to the planet.

Answer 1

Searching for signs of life on Mars, researchers have sent many probe rovers to the planet.

searching for sign of life on Mars is a participle phrase that describes the researchers and is adjectival.

The sentence can be written as:

Researchers, searching for signs of life on Mars, have sent many probe rovers to the planet.

It can also be written as:

Researchers have searched for signs of life on Mars and have sent many probes to the planet.

Very often, participle phrases are used for style purposes to avoid a compound sentence.

"Thinking he would win the race, the racer did not hesitate to take risks."
is the same as:

"The racer thought he would win the race and did not hesitate to take risks."

participle phrases

Answer 2

"Searching for signs of life" explains why the researchers have sent probes to the planet, so in that sense, it modifies the action. For example, "Needing food, John drove his car to the store." The reason that John took the action (going to the store) was because he needed food. Similarly, the researchers sent probes to Mars to search for signs of life.

Answer 3

1.(By reason of) searching for signs of life on Mars--->an adverbial clause modifies "have sent"

2.Researchers are the understood subject of this adverbial clause,irrelevant to modification.

3.https://en.wikipedia.org/wiki/Dangling_modifier