This work investigates surface electromagnetic wavefields generated by a finite fault due to electrokinetic effect with Pride's theory as the governing equations. A finite fault is discretized into a ...series of small subfaults, each of which is taken as a point source with different initiation time. The wavefields generated by the whole fault are then synthesized by stacking those generated by all the subfaults. Numerical simulations of a vertical strike‐slip fault with a constant rupturing velocity are then conducted on the basis of the derived formalism. Simulation results show that the rupturing fault generates observable permanent ground motions and electromagnetic field disturbances. Two types of electric field characters are observed in simulations: the coseismic oscillatory variation and the postseismic decaying variation. When the fault rupturing stops and the seismic waves pass far away, the magnetic field vanishes while the electric field remains, decaying slowly and lasting for hundreds of seconds. Adjacent to the free surface the vertical electric field is about 100 times larger than the horizontal one. When the receiving depth increases, the amplitudes of the horizontal electric fields in both the oscillatory and decaying components increase while those of the vertical electric fields decrease. It is also shown that there is no horizontal electric field remnant right at the free surface after the seismic perturbations decay away. The near‐fault electric fields simulated in this paper hold similar features to some field observations in literature.
Key Points
There are electromagnetic perturbations accompanying the seismic waves
There is remnant electric field decaying with time near the fault
The horizontal electric fields are smaller than the vertical one near the surface
SUMMARY
In this study, we present a semi-analytical method to simulate the propagation of seismic waves in horizontally stratified double-porosity media. We solve the governing equations in the ...frequency–wavenumber domain and then compute the time–space domain solutions by Hankel and fast Fourier transforms. We conduct numerical simulations to study the properties of the seismic waves in the double-porosity media. The results show the existence of three P waves, one fast P wave and two slow P waves. The two slow P waves are highly attenuated and can be observed by assuming a low fluid viscosity. By comparing the fast P wave in a single-porosity medium and that in a double-porosity medium, we find that the double-porosity model predicts much higher attenuation of the fast P wave due to the local fluid flow between the background medium and the inclusions. We also study the parameters affecting the attenuation, such as the radius of the spherical inclusions, the viscosity of the pore fluid, the permeability of the background medium and the porosity of the inclusions. Finally, we present a cross-well survey model to investigate the seismic responses in the double-porosity media and compare them with the responses in the single-porosity media. We find that both the amplitude and velocity of the fast P wave decrease with the increase of the volume ratio of the inclusions.
Studied in this paper are the properties of seismoelectromagnetic waves radiated by a double couple in a saturated porous medium arising from the electrokinetic effect. First, using the Pride's ...equations, we derive the Green's function of the magnetic field due to a single point force as a complement of previous authors' works, in which only the Green's functions of the solid displacement, the relative fluid–solid displacement and the electric field were expressed. Furthermore, we extend these Green's functions to cater for the moment tensor sources. Then we derive the Green's functions of the solid displacement, the electric and magnetic fields in the frequency-space domain excited by a double couple source, which is frequently used in earthquake seismology. To visualize these fields, the radiation patterns are calculated and displayed. The results illustrate that the radiation pattern of the electric far field for the longitudinal (or transverse) wave is the same in shape as that of the far field of the P (or S) wave in elastodynamics. For a transverse wave, the electric and magnetic far fields share the same radiation patterns in shape, while the electric and magnetic near fields do not. For each of the four body waves, the far, intermediate and near fields are compared at different receiver-to-source distances, respectively. The electromagnetic (EM) wave has a much longer near-field-dominating distance than the seismic waves. We calculate the waveforms in the time–space domain by numerically Fourier transforming the Green's functions into the time domain. In order to validate these Green's functions and the waveforms, we calculate the waveforms again by another method. The main idea of the method is regarding the source as a displacement–stress–EM discontinuity vector. The result shows that the waveforms from those two methods are in excellent agreement. In the waveforms, there are the electric fields accompanying both the P and S waves, as well as the magnetic field accompanying the S wave. We testify that the S wave generally has a weaker capacity than the P wave in inducing an electric field. In the waveforms, there is also an independently propagating EM wave, which has a much higher speed than the seismic waves, and reaches the observation point immediately after the source launched. By comparing the waveforms at different receiving locations, we find that waveforms differ at different observation orientations.
SUMMARY
Seismoelectric measurements are conducted with a synthetic porous rock sample to model an ocean exploration. Two kinds of seismoelectric coupling signals, that is, the interfacial EM wave ...signal and the coseismic electric signal, have been recorded by the electrodes buried inside a rock sample instead of those located in the fluid or in the solid region near the interface as performed in previous works. These seismoelectric signals are clearly observed and identified with a high signal-to-noise ratio. The characteristics of the measured interfacial EM wave and coseismic electric signals are analysed with the experimental data. We also simulate the seismoelectric conversion fields and make a comparison between the measured and simulated seismoelectric signals. The result shows that the simulated and measured signals match well for both the interfacial EM wave and the coseismic electric fields accompanying the fast P wave. Our results also show that the amplitudes of seismoelectric signals are in the order of tens to hundreds of microvolts with our experimental system. This confirms that the seismoelectric signals are measurable in the interior of the rocks with current measurement techniques, suggesting the seismoelectric measurement to be a potential method for studying characteristics of the material beneath the seafloor.
This paper is concerned with a modified Leslie-Gower and Holling-type II two-predator one-prey model with Lévy jumps. First, we use an Ornstein-Uhlenbeck process to describe the environmental ...stochasticity and prove that there is a unique positive solution to the system. Moreover, sufficient conditions for persistence in the mean and extinction of each species are established. Finally, we give some numerical simulations to support the main results.
Summary
Movement of the conductive earth medium in the ambient geomagnetic field can generate an electromotive force and a motional induction current, which further cause the disturbances of the ...electromagnetic (EM) fields. Such a mechanoelectric coupling is known as the motional induction (MI) effect and has been proposed to be a possible mechanism for the generation of the observed EM signals during earthquakes. In this paper, we study the EM responses to an earthquake source due to such a MI effect in a 2-D horizontally layered model. First we transform the governing equations that couple the elastodynamic equations and Maxwell equations into a set of first-order ordinary depth-dependent differential equations. Then we solve the seismic and EM responses to a moment tensor source. Finally, we transform the 2-D seismic and EM responses to 3-D responses using a simple amplitude correction method. We conduct several numerical examples to investigate the properties of the EM signals generated by the earthquake source. The results show that two types of EM signals can be observed. The first one is the coseismic electric/magnetic field that accompanies the seismic P and S waves as well as the Rayleigh wave. The second one is the early EM signal which arrives before the P wave. The numerical results show that the EM signals change with the inclination angle of the geomagnetic field, the azimuth angle between the wave propagation plane and the geomagnetic vertical plane, and the medium conductivity. Increase in the conductivity can enhance the coseismic electric and magnetic signals. Our simulation also shows that an EM wave can be generated by a seismic wave at the interface separating two different media. The radiation pattern of the interface EM wave generated by a P wave is similar to that of a horizontal electric dipole located on the interface.
In this paper, we use a mean-reverting Ornstein-Uhlenbeck process to simulate the stochastic perturbations in the environment, and then a modified Leslie-Gower Holling-type II predator-prey ...stochastic model in a polluted environment with interspecific competition and pulse toxicant input is proposed. Through constructing V-function and applying
formula, the sharp sufficient conditions including strongly persistent in the mean, persistent in the mean and extinction are established. In addition, the theoretical results are verified by numerical simulation.
SUMMARY
When a seismic wave propagates in a fluid-saturated porous medium, a relative movement forms between the solid and the fluid and induces an electric current due to the electronic double ...layer. As a result, two kinds of seismoelectric coupling responses are generated in this procedure: the localized electric/magnetic field and interfacial electromagnetic wavefield. One important potential application of these two seismoelectric conversions is used for measuring formation P and S waves in well logging. Considering that the strong collar wave seriously affects the velocity measurements of formation P and S waves in current acoustic logging while drilling (LWD), the seismoelectric LWD method, which combines seismoelectric conversion and acoustic LWD technique, was suggested to be a novel method in oil and gas exploration. The collar wave cannot induce any seismoelectric signal on the metal collar since there is no double layer formed on a metal surface. In this paper, acoustic and seismoelectric LWD measurements are conducted in the laboratory. We build a scaled multipole acoustic LWD tool to conduct acoustic measurements in a water tank and a sandstone borehole model. We also build a multipole seismoelectric LWD tool and record the seismoelectric signals induced with the same acoustic source. Then, we compare the recorded acoustic and seismoelectric signals by using the experimental data. The result indicates that the apparent velocities of seismoelectric signals are equal to the formation P- and S-wave velocities and the collar waves do not induce any visible electric signal in the full waveforms. We further analyse the mechanism of seismoelectric LWD by a quantitative comparison of the amplitudes between the inner collar wave and outer collar wave. The results show that the amplitude of outer collar wave decreases significantly when it radiates out of the tool, so that the seismoelectric signals induced by collar waves are too weak to be distinguished in the full waveforms of seismoelectric LWD measurements. Thus, the formation P- and S-wave velocities are detected accurately from the recorded seismoelectric LWD data. These results verify the feasibility of the seismoelectric LWD method for measuring acoustic velocities of the borehole formation.
SUMMARY
At 04:14:45 UT on 2022 January 15, a powerful eruption of the submarine Hunga Tonga–Hunga Ha'apai volcano occurred at about 30 km south of the Ha'apai Islands in the Kingdom of Tonga (at ...−20.55° N, −175.39° E). This eruption caused atmospheric waves that spread worldwide. In this study, we investigate the the total electron content (TEC) variation over China using the BeiDou Navigation Satellite System. The particularly interesting feature of the data set compared to other ground-based TEC data is the exclusive use of the BeiDou geostationary satellites, which monitor the TEC variations for fixed ionospheric piercing points and can provide more accurate calculations of the travelling speed of the disturbance. For comparison, atmospheric pressure records were examined, which show that the Lamb wave passed by the same stations four times with a constant speed of 310 m s−1. However, the TEC results show that the ionospheric disturbances passing over China four times with different speeds within four days after the eruption, two travelling along the short-path direction and two along the long-path direction. The primary front of the first short-path event travels with a speed of 340 m s−1, which is higher than the Lamb wave. The faster speed suggests that the primary front cannot be fully attributed to the Lamb wave, and further studies need to explore its mechanism. The second short-path and first long-path events travel with speeds of 301 and 310 m s−1, respectively, close to the speed of the Lamb wave, and they may be caused by upward energy leakage during the propagation of the Lamb wave. The second long-path event travels with a speed of 264 m s−1, possibly induced by the gravity waves.
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