More of an economic answer than historical, but yet...
The answer is that it would change very little.
Silver and gold are not consumed, so the amount available the previous year was still available the current year.
Silver and gold are scarce and difficult to mine (from it their value), so at any given period its production would have been small compared with the already circulating bullion. And what would change their relative value would be the difference in production rate, which would be even smaller.
To put an example, imagine that there are circulating 1000 tons of gold and 10000 tons of silver. If each year 1 ton of gold and 10 tons of silver were mined, their relative value would not have changed.
Now double silver production. To get a 1% change in the exchange ratio (1 gold sheckels = 10.1 silver schekels).
This can be expressed as1
1000 + 1*years = Tg
10000 + 20*years = Ts
Tg = 10.1Ts
which gives a result of 497.5 years. For these timescales, the effects of supply of bullion pale with other effects (debasing, wars, economic developments).
Now, for the first assertion, there are a few things to consider:
Bullion could be lost by several ways; for example in shipwrecks and the like. But with few exceptions, those events would be few and would mean the loss of bullion in proportion to the circulating quantities.
Other ways of getting gold was through plunder and tributes. But you would more likely be plundering your neighbours which, due to trade, would likely have a similar proportion of bullion to yours.
Historically, changes in the relationship between metals have been mostly been caused by colonizers getting to new territories with easy to mine resources (Potosí, Gold and Silver rushes) and improved trade with other regions of the world with a different proportion of gold and silver (Far East), but those events were few and their effects are very documented.
Yes! I got to write equations on a history.SE answer!