Page 232 - Machine Learning for Subsurface Characterization

202 Machine learning for subsurface characterization

For each depth in the training dataset, the encoder network receives, one at a
time, each element (i.e., one log) of the input sequence of 10 inversion-derived
logs. Encoder updates the intermediate vector based on each element and
propagates the updated intermediate vector for further updates based on the
subsequent elements of the input sequence. Intermediate vector (also referred
as encoder vector or context vector) is the final hidden state produced by
encoder network. The intermediate vector contains information about the
input sequence in an encoded format. Decoder learns to process the
intermediate vector to compute an internal state for generating the first
element of the output sequence constituting the 64-dimensional NMR T2.
For generating each of the subsequent elements in the output sequence, the
decoder learns to compute the corresponding internal states by processing
the intermediate vector along with the internal state calculated when
generating the previous element in the output sequence.
The encoder and decoder networks of the LSTM network architecture are
collections of LSTM modules. The encoder and decoder networks comprise
10 and 64 chained LSTM modules, respectively. Each module has gates
controlling the flow of data. Controlled by various gates the LSTM can
choose to forget or update the information flowing through the modules. The
encoder compresses the seven formation mineral logs and three fluid
saturation logs into a single intermediate vector. Then the decoder
sequentially decodes the intermediate vector to generate the 64 elements of
the target NMR T2 sequence. The 10 inversion-derived logs are taken as
sequence, and the encoder processes one of the 10 logs at each timestep to
generate an internal state. After processing all the 10 input inversion-derived
logs, the encoder generates the 15-dimensional intermediate vector v in the
last step. The intermediate vector v is fed to each module in the decoder.
The decoder modules sequentially generate each element of the output NMR
T2 sequence. Each decoder module processes the 15-dimensional
intermediate vector v along with the internal state from the previous module
to construct a corresponding element of the output sequence. The full
synthesis of NMR T2 for a single depth requires 64 timesteps. The loss
function used for the LSTM model is mean squared error function, like the
second training steps of the previous three neural network architectures. The
optimizer used to train the LSTM model is RMSprop that updates the
weights of neurons based on the loss function during the backpropagation.

4.6 Training and testing the four deep neural network models
NMR T2 distribution log and inversion-derived mineral content and fluid
saturation logs are split randomly into testing and training datasets. Data
from 460 depths were used as the training data, and other data from 100
depths were used as the testing data. In a more realistic application, the
dataset should be of larger size for robust development of the deep neural