Namaste.
It isn't all that clear-cut or easy to understand all this and a lot of confusion arises. It also depends on the Jyotisha (natal astrology).
The Root Chakra, Muladhara is linked to our association with the Earth and the Earth represents it. It is reddish-brown in colour, like the soil and the gemstones relating to it include carnelian, smoky quartz and red agate.
The second Chakra, Swadhisthana is linked to the fluids within the body and the regulation of the lunar cycle which promotes menstruation in women and thus, it is associated with the moon and the image of it includes the moon (see below). It is also the abode of Makara, the half crocodile/fish thing. Gemstones associated with Swadhisthana include moonstone, aquamarine and opal.
The third Chakra, Manipura is linked to the digestive function and the heat within the body. The source of our inner heat is also the Sun and it's like the 'solar powerhouse' for our system, residing in the solar plexus. People with an overactive Manipura chakra are often very proud, egotistical and fiery, suffering with a lot of digestive complaints and are of the Pitta Dosha. The gemstones corresponding to Manipura are sunstone, tiger-eye and citrine quartz.
The fourth Chakra, Anahata has to do with our place in society, feeling gratitude, love, compassion and humility. It is ruled by the planet Venus, as indicating the receptive nature and the need to 'open up' our emotional side over the rational one. It is green in colour, and the gemstones associated with it are rose quartz and aventurine.
I could go on and will at a later date, but all this comes from my study of the Tantras and I have tried to re-locate where I have learned it, not being able to remember it right now (it was so long ago), but so far, it all escapes me.
Om Namah Shivaya