I’m afraid that there is no adverbial clause in this sentence. Let’s see that together.
{}= entire sentences
[]= independent clauses
()= dependent clauses (noun/adjective/adverb clauses + phrases)
{[Some researchers say] = first independent clause
((that) the results constitute compelling evidence) = noun clause
(that telepathy is genuine).} = adjective clause (defining which evidence)
{[Other parapsychologists believe] = independent clause
((that) the field is on the brink of collapse) = noun clause
(, having tried to produce definitive scientific proof and failed).} = MISPLACED PARTICIPLE PHRASE.
The participle phrase is a reduced adjective clause when it is placed AFTER the noun/subject WITHOUT commas, and it acts as an adjective.
When it is placed BEFORE it, it is just a participle phrase WITH commas, and it acts as an adjective modifying a subject or a noun.
The participle phrase can either be placed at the beginning, in the middle or at the end of a sentence.
Here are four easy examples:
Beginning: Eating their food, (COMMA) the cats are happy.
It means that WHILE THE CATS ARE eating their food, they are happy.
It is a participle phrase here.
In the middle (non-defining): The cats, (COMMA) eating their food, (COMMA) are happy.
It means that cats IN GENERAL, are happy when they eat their food.
It is a participle phrase here, as well.
In the middle (defining): The cats eating their food are happy. (NO COMMA)
It means that some specific cats THAT ARE eating their food (now) are happy.
It is a reduced adjective clause acting as a participle phrase here.
End: I saw the happy cats eating their food. (NO COMMA)
It means that I saw the happy cats THAT WERE eating their food.
It is a reduced adjective clause acting as a participle phrase here, as well.