Page 231 - Machine Learning for Subsurface Characterization

Deep neural network architectures Chapter 7 201

FIG. 7.6 Schematic for training the LSTM architecture. The number of hidden layers in each
network and the number of neurons in each hidden layer are determined by hyperparameter
optimization.

In this study, we use the LSTM network for sequence-to-sequence modeling
(i.e., many-to-many mapping), wherein for each sequence of one feature vector,
the LSTM network learns an intermediate vector that can be decoded to
generate a distinct sequence of one target vector. LSTM first encodes the
relationships between the various combinations of inversion-derived logs and
the amplitudes of various combinations of T2 bins into an intermediate
vector. Consequently the use of LSTM frees us from knowing any of the
mechanistic rules that govern the multitude of physical relationships between
the various logs and those between the logs and physical properties of the
formation. LSTM-based sequence-to-sequence model generally contains
three components, namely, encoder, intermediate vector, and decoder. The
encoder is tasked with learning to generate a single embedding (intermediate
vector) that effectively summarizes the input sequence, and the decoder is
tasked with learning to generate the output sequence from that single
embedding.
Unlike the three other neural network architectures discussed in the previous
sections, LSTM training requires only one stage. LSTM excels other deep
neural network architectures for data that have long-term dependencies and
unfixed lengths of input/target vectors. LSTM sequence-to-sequence
modeling has been successful in language translation. Language translation
relies on the fact that sentences in different languages are distinct
representations of one common context/theme. In a similar manner, different
subsurface logs acquired at a specific depth are distinct responses to one
common geomaterial having specific physical properties. We implement
LSTM to capture the dependencies among the various T2 bins in the T2
distribution and also to capture the dependencies between various
combinations of inversion-derived logs and the amplitudes for various
combinations of T2 bins.