System and method for determining a value of information metric from a posterior distribution generated through stochastic inversion

A computer system for determining a value of information, the computer system comprising:

• a computer readable memory configured to store well locations and existing well data;
• and
• a processor in communication with the computer readable memory, the processor being configured to:
• draw a plurality of synthetic prior earth models from one or more prior distributions for a plurality of well locations and generate from each prior distribution synthetic data;
• draw a plurality of posterior earth models from a posterior distribution for the plurality of well locations, wherein the posterior distribution is generated through stochastic inversion from the synthetic data and the plurality of posterior models are drawn from each of the plurality of prior earth models;
• calculate, from the plurality of prior earth models and posterior earth models, a well production at a plurality of proposed well locations using a relationship between the earth parameters and the well production for both the prior earth models and the posterior earth models;
• calculate a prior well cost using a relationship between the prior well cost and the earth parameters and calculate a posterior well cost using a relationship between the posterior well cost and the earth parameters;
• calculate a value prior using the prior cost and the prior production and calculate a value posterior using the posterior cost and the posterior production;
• calculate a weighted prior value and calculate a weighted posterior value using, respectively, the value prior and the value posterior;
• and
• calculate a difference or a ratio between the weighted value prior and the weighted value posterior and calculate a sum over a plurality of well locations of the difference or the ratio to obtain the value of information.