Comparison of PCA and Autoencoder Compression for Telemetry of Logging-While-Drilling NMR Measurements

Compression is an essential aspect of real-time operations as the bandwidth of transmitted information is very limited during logging while drilling. Processing of nuclear magnetic resonance (NMR) data involves the inversion of echo trains (ET), which are compressed downhole and transmitted via telemetry. The performance of individual NMR ET compression techniques also needs to be evaluated on the input signal level because the comparison of inversion results is highly dependent on regularization. Improved compression is key to properly encoding and decoding rate of penetration (ROP)-dependent motion effects with the goal of improving the accuracy of NMR T2 distribution at increased ROP in real time. The value of information of an ET differs over its range. First, early echoes have a large impact on the total porosity. They require a large contribution to the computation of, i.e., root-mean-squared error, used for comparing compression techniques. Secondly, non-exponential motion artifacts have a non-negligible impact on the inversion for cutoff-dependent volumetrics with increasing ROP. We propose a logarithmic weighting of the error contribution when comparing different compression implementations. Principal component analysis (PCA) is a linear transformation and is, therefore, very robust. It can reduce the dimensionality of data even given highly clustered inputs. In a previous implementation of PCA, ROP motion effects were neglected in developing the basis set of vectors at the low ROP used in earlier drilling operations. However, neglecting ROP motion effects may have noticeable effects on inversion results for porosity and volumetrics at increased ROP. Therefore, new PCA basis vectors are developed to account for these motion effects. Parallel with the development of the enhanced PCA basis vectors, an alternative denoising and compression concept utilizing a neural network autoencoder was developed and evaluated. The autoencoder first encodes the input data to a lower-dimensional representation. The original input is reconstructed from this compact latent space encoding using a decoding block. The autoencoder is trained on a synthetic data set comprising different subsurface properties and acquisition parameters learning the salient features. With the aim of implementing the encoding block on a low latency/memory device downhole, optimization of the network topology involved both the size of the network and the accuracy of the decompressed signals for real-time NMR inversion. Validation of the PCA and autoencoder compression is performed using inverted volumetrics of the encoded and decoded ETs. A new PCA basis for NMR data compression was developed to properly encode and decode ROP-related motion effects. Its performance was compared to a conventional compression technique. In addition, results of a denoising and compression algorithm for NMR ET based on a fully connected neural network autoencoder are presented. Tests show an improvement in the axial motion effects introduced by increasing ROP. By using a weighted error metric to compare individual compression implementations, it is possible to focus on the value of information on the early echoes. Accounting for ROP motion effects in the development of a new PCA basis, as well as using the autoencoder in training, improves the inversion of movable and irreducible fluid components. In addition, a reduction in the amount of data to be transmitted allows for a further decrease in the telemetry footprint of the NMR measurement. Both approaches increase the amount of transmitted information while improving the evaluation of the subsurface environment.