1. Scientists are puzzled as to why the whale had swum to the shore.

1-2. Scientists are puzzled as to why the whale has swum to the shore.

2. Scientists are puzzled about why the whale had swum to the shore.

3.Scientists are puzzled concerning why the whale had swum to the shore.

4. Scientists are puzzled regarding why the whale had swum to the shore.
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Do we have to use 'had swum' or 'has swum'? Can we use 'about' etc. instead of 'as to'?

2 answers

Yes to all your questions. "has" or "had" do not quite mean the same thing, though. "has" is present tense, meaning the whale is still near the shore. "had" is past tense, so it means the whale may no longer be near the shore.
Maybe she swam away again. :)
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