The "best way" depends on the situation at each point in the cavern. You can get good video/pics with and without artificial light.
When facing towards the entrance light, use natural light.
When shooting with the entrance light to your back, you may or may not need extra light.
If you're near the entrance, then there may be enough natural light for some nice photos/video using only natural light.
If you're back in the darker areas of the cavern, and shooting towards the darkness, then you will require a light source.
You may issues with autofocus in low light. In that case, fire up your Kraken.
Experiment with the camera above the surface and the Kraken light underwater, illuminating cavern below. You can get some great glowing effects that way. If the cavern ceiling is low, pay attention to the cool light reflections on the ceiling.
The beauty of digital is that you can see the effects of your lighting live on the camera screen.
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