1. all arrayOopDesc tests use arrayOopDesc::header_size_in_bytes which depends on a jvm state, it reads HeapWordSize and UseCompressedClassPointers and furthermore has an assert which checks that their values haven't changed.
2. all utilities/json tests use tty variable (as JSON::_st field), tty initialization is a port of jvm initialization.
3. SymbolTable.temp_new_symbol calls JavaThread::current()
4. LogFileOutput tests use ResourceMark which calls JavaThread::current()
5. LogDecorations.level, uptime, tags and timestamps tests directly or indirectly call os::javaTimeNanos() which assumes that some structures, e.g. Bsd::_timebase_info, are inited
6. LogConfigurationTest tests require ResourceMark or os::javaTimeNanos

mentioned problems are the first which a test bumps into, there can be other problems in the same tests as well.