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 numericallysimulate 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 duringproduction, 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 correctlyretrieve 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.Applied Geophysics and Petrophysic

Seismoelectric interface response signal behaviour in thin-bed geological settings

Increasing industrial and societal challenges demand a continuous need for improved imaging methods. In recent years, quite some research has been performed on using seismoelectric phenomena for geophysical exploration and imaging. Like the other methods, the seismoelectric technique also has its drawbacks. Besides the fact that the physical phenomenon is very complex, one of itsmain challenges is the very low signalto- noise ratio of the coupled signals, especially the secondorder interface response fields. From seismics, it is wellknown that anonamously high amplitudes can arise due to amplitude-tuning effects which can occur when a seismic signal travels through a package of thin-layers with appropriate amplifying thickness. Using numerical seismoelectric wave propagation experiments through packages of thin-beds, we show that thin-bed geological settings can improve the signalto-noise ratio of the interface response fields. Whether a certain package of thin-beds results in a net strengthening or weakening of the signal, is determined by the contrast in and the order of the coupling coefficients of the different thin-layer media. Formulated differently, we show that the seismoelectric method is sensitive to the medium parameters of thin-bed geological structures far below the seismic resolution, and that due to natural strengthening of the seismoelectric interface response signal, the method might be already suitable for certain geological settings.Geoscience & EngineeringCivil Engineering and Geoscience

Seismo-Electromagnetic Thin-Bed Responses: Natural Signal Enhancements?

We study if nature can help us 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, we numerically simulate seismo-electromagnetic wave propagation through horizontally layered media with different amounts and thicknesses of thin beds. We distinguish two limits of bed thickness. Below the upper limit, the package of thin beds starts acting like an “effective” medium. Below the lower limit, further thinning does not affect the seismo-electromagnetic interface response signal strength anymore. We demonstrate seismo-electromagnetic sensitivity to changes in medium parameters on a spatial scale much smaller than the seismic resolution. Increasing amounts of thin beds can cause the interface response signal strength to increase or decrease. Whether constructive or destructive interference occurs seems to be dependent on the seismo-electromagnetic coupling coefficient contrasts. When the combined result of the contrast, between upper half-space and package of thin beds and the internal thin-bed contrast, is positive, constructive interference occurs. Destructive interference occurs when the combined contrast is negative. Maximum amplitude tuning occurs for thicknesses of thin-bed packages similar to the dominant pressure and shear wavelengths. Artifacts due to model periodicity are excluded by comparing periodic media with random models. 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. An oil layer with a thickness of <1% of the dominant shear wavelength is still recognized.Applied Geophysics and Petrophysic

Validation of an electroseismic and seismoelectric modeling code, for layered earth models, by the explicit homogeneous space solutions

We have developed an analytically based, energy fluxnormalized numerical modeling code (ESSEMOD), capable of modeling the wave propagation of all existing ElectroSeismic and SeismoElectric source-receiver combinations in horizontally layered configurations. We compare the results of several of these modeled source-receiver combinations in a homogeneous medium with explicitly derived homogeneous space Green’s function solutions, in order to be able to validate the results of ESSEMOD both in arrival times and amplitudes. Especially the amplitudes are important due to the fact that the main reason seismoelectric phenomena are not yet used in industry, are the weak amplitudes of these phenomena. Here we show that ESSEMOD correctly models the wave propagation of components of the electric field generated by different components of bulk forces, as well as the particle velocity fields generated by a bulk force source and an electric current source. We are capable of validating both amplitudes and arrival times of the results of ESSEMOD for all electroseismic and seismoelectric source-receiver combinations in homogeneous media. Herewith, we reduce uncertainty in our modeling results (also for heterogeneous scenarios) and can get better insights in which parameters affect the amplitudes most. In addition, we show that ESSEMOD is capable of modeling reciprocal source-receivers combinations correctly, implicitly indicating correct modeling of both geometrical configurations (source located above or below the receiver level). ESSEMOD can now be used for comparison with and validation of existing seismoelectric layered earth numerical modeling codes. Afterwards, ESSEMOD can be used for validation of existing seismoelectric finite-element and finite-difference codes.Geoscience & EngineeringCivil Engineering and Geoscience

Seismoelectric wave propagation modeling for typical laboratory configurations: A numerical validation

The seismoelectric effect can be of importance for hydrocarbon exploration as it is complementary to conventional seismics. Besides enabling seismic resolution and electromagnetic sensitivity at the same time, the seismoelectric method can also provide us with additional, high-value information like porosity and permeability. However, very little is still understood of this complex physical phenomenon. Therefore, it is crucial to be able to perform numerical modeling experiments to carefully investigate the effect and the parameters that play a role. Over the last couple of years, several seismoelectric laboratory experiments have been carried out in an attempt to validate the underlying theory of the phenomenon and to better understand this complex physical phenomenon. We have recently extended our analytically based, numerical seismoelectric modeling code ’ESSEMOD’ to be able to model seismoelectric wave propagation in arbitrarily layered Earth geometries with fluid / porous medium / (fluid) interfaces. In this way, we are capable of effectively simulating full seismoelectric wave propagation, i. e. all existing seismoelectric and electroseismic source-receiver combinations, in typical laboratory configurations. We present the underlying theory that is required for the extension towards arbitrary fluid / porous medium / (fluid) geometries and an effective way to incorporate this in a general seismoelectric layered Earth modeling code. We then validate the underlying global reflection scheme by comparing it with an independently developed layered Earth modeling code for purely electromagnetic fields. The results show a perfect match in both amplitude and phase, indicating that ESSEMOD is correctly modeling the electromagnetic parts of the seismo-electric wave propagation in horizontally layered media with fluid / porous medium / fluid transitions. We finalize with a seismoelectric reciprocal modeling experiment, proving that also the full seismoelectric wave propagation through fluid / porous medium transitions is modeled consistently.Geoscience & EngineeringCivil Engineering and Geoscience

Data-driven spatiotemporal assessment of the event-size distribution of the Groningen extraction-induced seismicity catalogue

For induced seismicity, the non-stationary, heterogeneous character of subsurface stress perturbations can be a source of spatiotemporal variations in the scaling of event sizes; one of the critical parameters controlling seismic hazard and risk. We demonstrate and test a systematic, statistical, penalized-likelihood approach to analysing both spatial and temporal variations in event size distributions. The methodology used is transferable to the risk analysis of any subsurface operation, especially for small earthquake catalogues. We explore the whole solution space and circumvent conventional, arbitrary choices that require a priori knowledge of these variations. We assess the effect of possible bias in the derivation, e.g., due to tapering of the earthquake-size distribution, correlation between the b-value and the magnitude of completeness and correlation between the b-value and the largest magnitude observed. We analyse the spatiotemporal variations in the earthquake-size distribution of the Groningen induced seismicity catalogue (December 1991–November 16, 2021). We find statistically significant spatial variations without any compelling, statistical evidence of a temporal variation. Furthermore, we find that the largest magnitudes observed are inconsistent with the sampling statistics of an unconstrained earthquake-size distribution. Current risk assessment models likely overestimate the probability of larger magnitude events (M ≥ 3.0) and thus the risk posed.Applied Geolog

ESSEMOD - electroseismic and seismoelectric flux-normalized modeling for horizontally layered, radially symmetric configurations

Geoscience & EngineeringCivil Engineering and Geoscience

Comparison of Eigenvectors for Coupled Seismo-Electromagnetic Layered-Earth Modeling

We study the accuracy and numerical stability of three eigenvector sets for modelling the coupled poroelastic and electromagnetic layered-Earth response. We use a known eigenvector set, its flux-normalized version and a newly derived flux-normalized set. The new set is chosen such that the system is properly uncoupled when the coupling between the poroelastic and electromagnetic fields vanishes. We carry out two different numerical stability tests: the first test focuses on the internal system, eigenvector and eigenvalue consistency; the second test investigates the stability and preciseness of the flux-normalized systems by looking at identity relations. We find that the known set shows the largest deviation for both tests, whereas the new set performs best. In two additional numerical modelling experiments, these numerical inaccuracies are shown to generate numerical noise levels comparable to small signals, such as signals coming from the important interface conversion responses, especially when the coupling coefficient is small. When coupling vanishes completely, the known set does not produce proper results. The new set produces numerically stable and accurate results in all situations. We therefore strongly recommend to use this newly derived set for future layered-Earth seismo-electromagnetic modelling experiments.Applied Geophysics and Petrophysic

Towards Seismoelectric Inversion: Sensitivity Analysis using Resolution Functions

Applied Geophysics and Petrophysic

Electromagnetic and seismoelectric sensitivity analysis using resolution functions

For multi-parameter problems, such as the seismoelectric system, sensitivity analysis through resolution functions is a low-cost, fast method of determining whether measured fields are sensitive to certain subsurface parameters. We define a seismoelectric resolution function for the inversion of a bulk density perturbation. The synthetic data and Green’s functions required to construct the resolution function are computed using the seismoelectric modelling code ESSEMOD. First, we consider the purely electromagnetic problem with a conductivity perturbation at a single point in an isotropic homogenous half-space. The result is nearly identical to a published result based on analytical Green’s functions. It correctly maps the position of the scatterer. Next, we perform an electromagnetic sensitivity analysis for the case of a layered background medium. Again, the resolution function is capable of correctly mapping the scatterer when it is above as well as below a layer of increased conductivity; although in the latter case with less resolution. Finally, we generate multi-component synthetic data with our forward modelling code and compute the seismoelectric resolution function for inversion of a bulk-density perturbation. We find that the seismoelectric system is sensitive to a perturbation in bulk density and that the position of the perturbation can be correctly recovered.Geoscience & EngineeringCivil Engineering and Geoscience