Centre for Geophysical Forecasting 

By Jo Eidsvik, Department of Mathematical Sciences, NTNU 

Research Director, Centre for Geophysical Forecasting

The Centre for Geophysical Forecasting (CGF, https://www.ntnu.edu/cgf) is one of the Norwegian centres for research-based innovation, funded by the research council of Norway and 13 industry partners. The goal of CGF is to become a world-leading research and innovation hub for the geophysical sciences, creating innovative products and services in Earth sensing and forecasting domains. Norway is already at the forefront of global exploration geophysics. CGF intends to leverage that expertise to catalyse a new wave of geophysical capabilities, using disruptive technologies in the transition from hydrocarbon geophysics to the new blue economy, in addition to important terrestrial geohazard risk and CO2 storage monitoring. Mathematical modelling and statistical methodologies play important roles here, enabling reliable predictions and uncertainty quantification that aid decision support. We next present two examples where applied mathematics and statistics are key components for driving innovative solutions. 

Åknes rock slope monitoring

The Åknes rock slope is located in Western Norway (Fig. 1). The Norwegian Water Resources and Energy Directorate (NVE), a partner in CGF, has instrumented the rock slope with eight three-component (x,y,z) geophones that register seismic activity. Data are streamed to a computer server, and this hence forms a continuous-time monitoring system for detecting seismic events which are indicative of various movements on the rock slope. When there is a seismic signal above an amplitude threshold, a window of 16 seconds of geophone data is stored. The current practice then relies on expert opinion to manually label this event among classes of rock fall. A database of events provides an excellent test case to understand and try out new machine learning methods for classifying rock slope events (Langet and Silverberg, 2022). By building an automatic classifier of geophone data events, one enables low-cost valuable decision-support tools in the context of geohazard warning systems. 

Figure 1: (a) The location of the Åknes rock slope. (b) If the unstable rock slope collapses into the fjord it causes a tsunami. (c) Eight three-component geophones are placed in the slope to monitor seismic activity. (Fig. from Lee et al., 2022.)

Examples of (x,y,z) components data recorded at one geophone for two particular events are shown in Fig. 2 (left). A slopequake (Fig. 2(a)) is characterized by a shearing or fracture opening in the slope, while a tremor (Fig. 2(b)) is water (thawing) in existing cracks. These data represent non-stationary time series, where the amplitude and frequency content clearly change over the time interval. It is not obvious how to summarize the data by simple statistics (mean, variance, correlation, dominating frequency, etc). A useful data analysis technique is to compute spectrograms and power spectral densities (PSD) (Fig. 2, right). This involves a (rolling window short-time) Fourier transform of the data. The magnitudes for each frequency and time displayed in the spectrogram indicate the signal characteristics.

Figure 2: (a) Geophone time series data (left) from a slopequake event. The spectrogram (right) indicates high energy and frequency early in the signal. (b) Geophone time series data (left) from a tremor event. The spectrogram indicates a longer-lasting signal. (Fig. from Lee et al., 2022.)

With CGF partner NORSAR, we are developing algorithms (Lee et al., 2022) to improve on existing classification results. A convolutional neural network encoder and classifier works as a benchmark. We benefit from leveraging self-supervised learning for this purpose of limited labeled training data. The accuracy of using the new classification methods increases from 0.80 to 0.88 for the defined set of eight rock fall types. Additional improvement in accuracy (0.92) is achieved by splitting the multiple geophone data to create a committee vote, rather than aggregating all data prior to classification. Such ensemble learning approaches also aid uncertainty quantification. Future research includes mathematical modeling of the slope subsurface properties and Bayesian hierarchical models for borrowing information in time and space.

CO2 storage risk evaluation

There is growing attention in sequestration and storage of CO2 in the subsurface as a possible mitigation strategy to reduce the greenhouse gas concentration in the atmosphere. With CGF partner Equinor, we are developing mathematical-physical models to predict the dynamic behavior of CO2 during injection and migration. Such models entail complex differential equations for flow in porous media, or simpler invasion-percolation rules where the pressure build-up in the relatively homogeneous layers are modelled together with the capillary thresholds of the cap rock formation. Fig. 3 illustrates the latter concept with CO2 being injected in the bottom layer. There is a probability that the injected volume of CO2 gives a pressure that exceeds the capillary threshold of the cap formation. CO2 then leaks into the layer(s) above. We describe the leakage process by a Markov chain with a special transition structure (Santi et al., 2022).  

Figure 3: When storing CO2 in subsurface aquifers, there is a probability that pressure build-up in one layer (t1) exceeds the capillary threshold of the cap (T1), leading to migration of CO2 to the layer above. Subsequent leakage to shallower layers will again depend on the properties in these layers. Leakage event probabilities can be modelled via a Markov chain structure. (Fig.from Santi et al., 2022).

For the Sleipner CO2 injection project, we train Markov transition probabilities using simulations of input parameters and realizations of pressure build-up and capillary threshold properties. The leakage probability from the injection layer to the above layer is then computed to be 0.06, while the leakage probability up to the fourth layer of the Sleipner formation is as small as 1/30.000.000. Future research includes more nuanced physical modeling of the CO2 migration and evaluation of various geophysical monitoring plans. As geophysical monitoring surveys have a substantial cost, quantitative analysis of various designs adds decision support tools in this context. 

New directions

During an 8-year period 25 PhDs are planned in CGF. To spark research development and innovation, CGF is relying on recent sensor technologies and current developments in enabling sciences such as high-performance computing, AI and statistical machine learning. Early-stage researchers work in an inter-disciplinary team developing and using new tools for the analysis of geophysical data. The above cases are just two interesting examples among many exciting applications: For deep Earth understanding, we are inverting seismic and electromagnetic data for characterizing ocean ridges (Johansen et al., 2019). Of technological advances, there is much focus on using fiber-optical sensing data for diverse situations such as imaging near-surface properties (Taweesintananon et al., 2022) and for detecting marine mammals (Bouffaut et al., 2022).


Bouffaut, L., Taweesintananon, K., Kriesell, H. J., Rørstadbotnen, R. A., Potter, J. R., Landrø, M., Johansen, S.E., Brenne, J.K., Haukanes, A., Schjelderup, O. & Storvik, F. (2022). Eavesdropping at the speed of light: Distributed acoustic sensing of baleen whales in the Arctic. Frontiers in Marine Science, 994.

Johansen, S. E., Panzner, M., Mittet, R., Amundsen, H. E., Lim, A., Vik, E., … & Arntsen, B. (2019). Deep electrical imaging of the ultraslow-spreading Mohns Ridge. Nature567(7748), 379-383.

Langet, N., & Silverberg, F. M. J. (2022). Automated classification of seismic signals recorded on the Åknes rockslope, Western Norway, using a Convolutional Neural Network. Earth Surface Dynamics Discussions, 1-50.

Lee, D., Aune, E., Langet, N., & Eidsvik, J. (2022). Ensemble and Self-supervised Learning for Improved Classification of Seismic Signals from the Åknes Rockslope. Mathematical Geosciences, 1-24.

Santi, A.C., Ringrose, P., Eidsvik, J., & Haugdahl, T. A. (2022). Assessing CO2 Storage Containment Risks Using an Invasion Percolation Markov Chain Concept. Available at SSRN 4282992.

Taweesintananon, K., Landrø, M., Brenne, J. K., & Haukanes, A. (2021). Distributed acoustic sensing for near-surface imaging using submarine telecommunication cable: A case study in the Trondheimsfjord, Norway. Geophysics86(5), B303-B320.

Mathematics in Technology -Strategic Research Area at NTNU
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