The project is mainly based on improvement of uncertainty quantification methods used for probabilistic geo-statistical/geophysical inversion and reservoir modeling. Inverse problem approaches in earth science are used for discovering subsurface structure and making models that can present rock and mineral properties in desired areas such as a reservoir. We work on developing these methods in order to generate improved models or accelerate the process.
In a common geological structure, there are patterns at different resolutions generated by various geological processes. Normally, the same statistical information is considered for all different scales in the simulation process.
In this project, we consider different statistics for large and small patterns in our model. A multi-resolution training image is used that shows a specific geological structure and provides patterns and statistics in our prior model.
By the means of wavelet transformation this training image can be decomposed into high and low frequency parts called approximation and details. The wavelet coefficients in each category can be simulated and used as prior in a seismic inverse problem.
Using this method, we will have the prior model at two different scales while choosing to simulate both parts or keep one constant and simulate the other part. In this study, direct sampling has been used which is a multiple point simulation algorithm and suitable for simulating non-categorical images.
This prior model along with some synthetic seismic data is used for setting up a Metropolis_Hastings algorithm to sample the posterior. The forward function is G=WR where R represents 2D inverse wavelet transform and W is the convolution operator with seismic wavelet.
One limitation in this method is the fact that wavelet coefficients in approximation and details are correlated and need to be simulated conditioned to each other.
Co- supervisor: Thomas Mejer Hansen