Radeon HD 7970 requires 30 Amps on the 12v rail, a 500W PSU minimum with 1x 8pin & 1x 6pin PCIE
By the looks of it, it is a cheap no-name brand PSU , the fact it only has 1x 6pin for 850W is absurd for this rating, it should have 4 or more. If that PSU puts out it's advertised wattage i'd eat your 7970 with some liver beans & a nice chianti.
It's fine for an entry level card like what you have been using it for. But i wouldn't contemplate using it for a high end card like the 7970. Replace the PSU with a decent, branded 550W-650W PSU.
XFX Pro 550W:
http://uk.pcpartpicker.com/part/xfx-power-supply-p1550sxxb9
XFX XXX 650W: http://uk.pcpartpicker.com/part/xfx-power-supply-p1650xxxb9