Rapid Inversion of Resistivity

Measurements Using Deep Learning

Mostafa Shahriari, Software Competence Center Hagenberg, Austria.

In geosteering, it is necessary to invert (interpret) borehole resistivity measurements in real-time. Recently, Deep Neural Networks (DNNs) have arisen as an alternative to performing such a complex task due to their strong ability to approximate different unknown functions.

Here, we shall explore the main advantages and limitations of applying DNNs to the rapid inversion of borehole resistivity measurements. Mathematically speaking, we divide the problem of inversion of the resistivity measurements into two: (a) the forward problem F, which is governed by Maxwell's equations. For a given subsurface properties P, it produces a set of measurements M (i.e.,F(P) = M) [1]; (b) the inverse problem, in which for given measurements M, it evaluates the subsurface properties P (i.e., I(M) = P) [2].

Herein, using a DNN, we approximate the inverse operator I [3]. Using this approach, we overcome the limitations of traditional inversion techniques, which only evaluate the inverse operator at a given set of measurements. However, DNNs construct an approximation to the full inverse operator, which can be rapidly evaluated for any set of measurements [4]. On the other side, since the inverse operator is not well-defined (it may have multiple solutions), using a DNN requires to design proper loss functions that are different from the traditional mist used in most DNNs. We propose the use of an encoder-decoder type loss function.

In this presentation, we shall describe the use of DNNs for the rapid inversion of borehole resistivity measurements. Moreover, we describe the use of different loss function and their corresponding DNN architecture.