Systems and methods for forward modeling of well logging tool responses

A method for forward modeling to produce synthetic tool responses for a well logging tool for an earth formation having a plurality of layers, the wellbore logging tool in a wellbore in the earth formation and generating wellbore logging data for a particular part of the earth formation from the group consisting of electrical resistivity data, acoustic data, vertical seismic profiling data, magnetic data, gravimetric data, temperature data, and nuclear data, the method comprising

• producing an input earth model of the particular part of the earth formation based on the wellbore logging data,
• inputting the input earth model to a primary trained artificial neural network,
• processing the input earth model with the primary trained artificial neural network to produce an output model that includes a set of synthetic tool responses for the wellbore logging tool for a plurality of points in the earth formation,
• the primary trained artificial neural network produced by training a first artificial neural network with an input training set producing a first trained artificial neural network, producing a first output set of synthetic tool responses for the well logging tool with the first trained artificial neural network, and inputting to a second artificial neural network both the input earth model training set and the first output set of synthetic tool responses for the well logging tool, producing a second trained artificial neural network which serves as the primary trained artificial neural network.