Coupled poroelastic waves and electromagnetic fields in layered media: Theory, Modeling, and Interferometric Synthesis

In this thesis, I study coupled poroelastic waves and electromagnetic fields in layered media. The focus is two-fold:
1. Increase the theoretical and physical understanding of the seismo-electromagnetic phenomenon by analytically-based numerical modeling.
2. Investigate the potential of seismo-electromagnetic interferometry.

After presenting the governing equations that form the basis of the theoretical framework, I capture this system into a matrix-vector representation of the wave equation. I first use literature eigenvector sets, which I normalize with respect to power-flux. I then derive new, alternative power-flux normalized eigenvector sets that I prove to be numerically more stable and accurate. The eigenvector sets form the basis of the analytically-based numerical modeling code `ESSEMOD' that I developed to model seismo-electromagnetic wave/field propagation/diffusion in layered-Earth media. The alternative eigenvector set models scenarios with no seismo-electromagnetic coupling correctly, where the literature eigenvector sets fail. In addition, the alternative set properly deals with scenarios where both small amplitude signals and large amplitude signals occur in the record, whereas the literature eigenvector sets result in noise levels masking the small events. The same holds for scenarios with a small seismo-electromagnetic coupling coefficient. I design an effective global reflection scheme that properly describes the primary and multiple reflections in the models. I implement the correct boundary conditions to account for scenarios with a free-surface, and also for scenarios containing fluid/porous medium/fluid transitions.
To transform all the seismo-electromagnetic source-receiver combinations in a numerically effective way back from the horizontal wavenumber-frequency domain to the space-frequency domain, I derive and implement explicit Fourier-Bessel transformations.

I then validate the developed modeling code in numerous ways. First of all, I compare the results of seismo-EM layer-code modeling in a homogeneous medium with explicit homogeneous space Green's function expressions. This comparison provides a clear validation that the layer-code models the dynamic responses in homogeneous scenarios correctly. Next, I check numerical consistency by carrying out reciprocity checks. I study homogeneous space models, models containing a free-surface and models with interfaces.
As a next step, I validate the modeling results of seismo-EM layer-code modeling for typical seismo-electromagnetic laboratory configurations, i.e. models containing fluid/porous medium/fluid transitions. I first compare the purely electromagnetic part of the seismo-EM layer-code with an independently developed purely electromagnetic layered-Earth code. The results match perfectly in both phase and amplitude for full transmission and pure reflection experiments, as well as for a combination of both. I then carry out a seismo-electromagnetic reciprocity test for a fluid halfspace overlying a porous medium halfspace, proving that the coupled poroelastic and electromagnetic fields are modeled consistently and yield the expected results.
As a final validation step, I compare ESSEMOD with an independently developed seismo-electromagnetic layered-Earth modeling code. The results display an almost perfect match in both phase and relative amplitudes, and a constant amplitude correction factor of 4 needs to be applied to let the absolute amplitudes match.

I then carry out a small feasibility test to study the potential of the seismo-electromagnetic effect for exploration purposes. I investigate different source-receiver combinations for the same model, and focus on the signal strength recorded at different distances from the target depth level. I conclude that for the source-receiver combinations studied, the electric field due to a volume injection monopole source, as well as the magnetic field due to a seismic bulk force source, yield the strongest converted signals. The receiver-distance from the target of interest plays an important role in the signal measurability. The closer the receivers to the target, the higher the signal strengths. However, when the receivers are located too close to the target, the coseismic reflected fields can mask the interface response fields that we are mainly interested in.

Next, I study if nature itself can help us to overcome the very low signal-to-noise ratio of seismo-electromagnetic converted fields, by investigating the effects of thin-bed geological structures on the seismo-electromagnetic signal.
To investigate the effects of bed-thinning on the seismo-electromagnetic interference patterns, I numerically
simulate seismo-electromagnetic wave propagation through horizontally layered media with different amounts and thicknesses of thin-beds. I demonstrate seismo-electromagnetic sensitivity to changes in medium parameters on a spatial scale much smaller than the seismic resolution. By simulating moving oil/water contacts during
production, where the oil layer is gradually being thinned, seismo-electromagnetic signals are proven very sensitive to oil/water contacts.

I now explore the application of interferometric techniques to the seismo-electromagnetic system, which might eventually lead to an improved signal-to-noise ratio of the weak converted fields.
I derive the theory for interferometric retrieval of 2D SH-TE seismo-electromagnetic Green's functions.
Using both a circular source configuration and a line source configuration, I show that it is possible to correctly retrieve the dynamic seismo-electromagnetic 2D SH-TE response in a homogeneous medium, using seismic boundary sources only. Using seismo-EM layer-code data, I then show that it is also possible to correctly retrieve the direct shear wave-related causal coseismic field in a homogeneous medium, in both phase and amplitude. To obtain a perfect match in absolute amplitudes, I apply a single linear scaling factor. I finally carry out interferometric experiments in a model containing a single interface at 800 m depth, proving that it is possible to correctly
retrieve all 2D SH-TE causal seismic-related direct and reflected coseismic fields, as well as interface response fields, by cross-correlation interferometry, using seismic boundary sources only.
These results are promising for the application of 3D seismo-electromagnetic interferometry using seismo-EM layer-code modeling, and later on, in the field.

Next, I present an alternative way to effectively decompose fields into their up- and downgoing components and different field types, using recordings at multiple depth levels. I present the theory of this MDL decomposition scheme, followed by successful decomposition of synthetic elastodynamic data sets. I additionally study the implications of laterally-varying media on the horizontal wavenumber-frequency domain MDL decomposition scheme.
I demonstrate successful decomposition, using an acoustic approximation and applying a combined multi-component / MDL decomposition approach, of a field data set recorded in Annerveen, in the North of the Netherlands. I address how to effectively use the MDL decomposition scheme in a unified fashion, applied to all wave phenomena including seismo-electromagnetic phenomena.

I then make a step towards seismo-electromagnetic inversion, presenting an effective way to carry out a seismo-electromagnetic sensitivity analysis using resolution functions. I start by explaining the theory of resolution functions using a seismo-electromagnetic example. I define the seismo-electromagnetic resolution function for inversion for a bulk density perturbation. I demonstrate the effectiveness of this method by first carrying out a purely electromagnetic sensitivity analysis for a point perturbation in conductivity, located in an isotropic homogeneous half-space. These results are compared with literature results based on analytical homogeneous space Green's function expressions. The result using the seismo-EM layer-code is nearly identical to the literature result. The position of the scatterer is correctly resolved. At the end of this section, I present the results of the fully-coupled seismo-electromagnetic senstivity analysis for a bulk density contrast for a specific source-receiver combination, using single-frequency multi-component line data. I show that the coupled seismo-electromagnetic system is sensitive to a perturbation in bulk density and that the position of the perturbation can be correctly recovered.

I finalize this thesis by discussing potential seismo-electromagnetic applications, as well as by providing a brief outlook for future research.