One-Dimensional Seismic Inversion using Machine Learning techniques

Abstract:

Seismic inversion is a non-linear, multimodal, high-dimensional problem that suffers from non-uniqueness, i.e.; several models may match the observation equally well. In the present work, we have used an Artificial Neural Network (ANN) model and a Random Forest Regressor (RFR) model to find the unknown parameters (velocity and thickness of each layer), assuming four-layered earth. Seven test cases were analyzed to check the robustness of the Machine Learning (ML) models. These test cases are representative of different possible scenarios for four-layered earth. The objective of the study is to solve the inverse problem using the ANN and RFR models.

The ML models were trained over 90,000 and validated over 10,000 datasets. The seismogram data was generated by convolving the reflection coefficient series with Ricker wavelet of central frequency 27 Hz. As we are interested in velocity variations in the near-surface, we have assumed a constant density for all the layers, and the inversion was performed to obtain P-wave velocity profiles.

The ANN model developed here is a seven-layered Deep Neural Network. The input layer contains 512 input nodes, and the output layer consists of seven nodes (4 for velocity and 3 for thickness). The backpropagation approach used in the ANN model is based on the Adam Optimization Algorithm to train over the generated data. Here, data normalization played an essential role in improving the accuracy of the model.

The RFR model consisted of 100 decision trees. The mean of the values from all the trees gave the final result. No pruning was performed, and the Gini index was used to measure impurity. The output variables were scaled on a logarithmic scale while regressing to achieve higher accuracy.

For all the seven test cases, both ANN and RFR models were successfully able to delineate the nature of each case (with and without noise). Overall, ANN has performed better by estimating model parameters close to the true value, while RFR predictions seem to be underestimated.