This paper explores the structural driving sources of oil market volatility and correlation dynamics using our derived volatility impulse response and correlation decomposition functions. A focal point of this paper is to conduct hypothesis tests for the observed diverging dynamics of oil market volatilities (a steady decline in oil production volatility and a concurrent increase in oil price volatility). In order to circumvent the restriction of uncorrelated disturbances in traditional structural models with stochastic volatility, we specify a time-varying level-volatility transmission matrix that allows for time-varying correlations between level and volatility innovations. Our model generalization hence captures transmissions of unexpected changes in oil levels to oil volatilities, and proves more adequate than traditional models for estimating oil market dynamics. Our results reveal several new useful insights for policy-makers, firms and investors. First, we find that a decrease in oil price persistence is at the origin of the diverging pattern of oil volatilities. Second, decreased variability of flow supply shocks is responsible for about 32% of the reduction in oil production volatility, while increased variability of demand-side shocks explains almost 60% of the increase in oil price volatility. Lastly, we find a near-zero correlation between oil production and oil price since the mid-1980s – a result that supports the theoretical prediction that oil production is inelastic to oil price changes.