The basin environment is a widely studied subject in both geology and geophysics for its economic significance in energy and mineral explorations. However, the estimation of the basement depth is often a challenging task given the complexity of the basement relief and lateral physical property change. Previous works simplify the problem by only inverting for the depth to the basement, and more recent studies have suggested the need to incorporate the variation of physical properties to improve basement structure imaging. In this study, we develop an inversion method with the associated workflow to simultaneously recover both the depth to a magnetic basement and a laterally varying magnetic susceptibility in the basement rock. To achieve this, we employ a set of constraints on the inverse problem. Particularly, both the recovered susceptibility and basement depth models are bounded below a possible maximum value, and the depth model is guided by a few depth points obtained from the resistivity models that are obtained from the one-dimensional blocky inversions of magnetotelluric (MT) data. In addition, we apply the fuzzy C-means (FCM) clustering to the susceptibility model during the inversion and use the inverted cluster centers to differentiate for different geological units in the basement. To show the effectiveness of our work, we compare the existing approaches and our method using two test inversions on one synthetic model resembling the basin–basement environment before demonstrating our method on a field data example with magnetic data collected by the U.S. Geological Survey (USGS) over the Illinois Basin. Our results show improved recovery in both basement relief and susceptibility in the basement rock, and inversion with field data is able to identify three different susceptibility zones in basement rock below the Illinois Basin.
The fractal formalisms are well known for providing new understandings regarding the geometrical, spatial, and temporal behaviour of seismicity. Particularly, the fractal dimensions give information about the seismic events self-organization and self-similarity. On the other hand, the Gutenberg–Richter value, known as the b-value, has shown through the years to give handy information regarding the statistical distribution of earthquakes, on-site physical parameters, and geomechanical inputs. The Gutenberg–Richter value (b) and the capacity and correlation fractal dimensions, (D0 and D2), of the spatial distribution of earthquake hypocentres interact mathematically for micro- and macro-events. From this interaction, it is possible to obtain new insights into the fracture network development and the microseismicity source characterization in terms of single fractures, fault planes, or densely fractured volumetric spaces. Here we show this interaction for the open-source Decatur CO2 project seismicity catalogue, comparing it with the results obtained for a natural earthquake catalogue of Illinois, in the United States. The fractal dimension D0 is calculated using two different methodologies: box-counting and correlation integral partitioning. This last method is also used to calculate D2. The results presented in this study allow us to describe how the fracture network geometry influences the earthquake complexity. Together with the calculation of the b-value, we present clear indications which show that seismicity recorded in the Illinois tectonic environment partially follows the Aki relationship D0 ∼ 2b, which is not the case for induced events. In addition, the induced earthquake dataset shows that D2 > D0, an anomalous behaviour in terms of the fractal formalisms. All these facts might be used to establish spatial fracture network control techniques and seismicity-type distinctions in CO2 injection sites located in highly active tectonic areas, respectively.
To enhance the 3D numerical simulation of the induced polarization method within anisotropic media, our study employs the 2D Fourier transform technique. This technique is utilized to convert the 3D integral of the abnormal potential from the space domain into a 1D integral in the wave number domain. Subsequently, we apply the shape function integration method, which is founded on quadratic interpolation, to resolve the 1D integral equation effectively. This methodology significantly decreases the necessary computational resources and storage while simultaneously harnessing the high efficiency and accuracy of the 1D shape function integration method, as well as the high efficiency of the fast Fourier transform, optimizing the numerical simulation process of the induced polarization method. We validate the accuracy of our algorithmic approach using an equivalent uniform layered model. Furthermore, by employing the sphere model, we conduct a comparison of computation time with the finite element method, thereby demonstrating high efficiency of the proposed algorithm. Utilizing the OpenMP parallel algorithm, we confirm that the proposed algorithm has a high degree of parallelism. We also analyse the differences in the equivalent apparent resistivity and apparent polarizability for various electrical parameters, using a prismatic model as the basis for our analysis. Our results clearly indicate that the anisotropy of the polarizability exerts substantial influence on the observe data. Consequently, the implications of polarizability anisotropy are deemed critical and not be disregarded in the field detection applications.
Acoustic logging is an important method used to determine formation velocities near boreholes. However, in practice, determining accurate formation velocities from acoustic logging data is challenging because of the presence of various noise interferences. Accordingly, a method to increase the amplitudes of refracted waves in open boreholes is proposed herein on the basis of the directional radiation technology of pulse compression signal–driven linear phased array acoustic transmitters. The waveforms generated by a Ricker monopole acoustic transmitter, linear frequency modulation monopole acoustic transmitter and pulse compression signal–driven linear phased array acoustic transmitter in a fluid-filled open borehole are numerically simulated by employing the finite-difference method. The effects of the pulse compression signal–driven linear phased array parameters on the amplitudes of the refracted compressional and shear waves are studied. Results show that borehole mode waves with the same velocities and dispersion characteristics can be determined using the pulse compression signal–driven linear phased array acoustic and Ricker monopole acoustic transmitters in fluid-filled open boreholes. Pulse compression signal–driven linear phased array acoustic transmitters leverage the advantages of pulse compression and phased array technologies, ensuring that a single element can radiate more acoustic energy, whereas pulse compression signal–driven linear phased array parameters can be modulated to further increase the amplitudes of the refracted compressional and shear waves. Compared with Ricker and linear frequency modulation monopole acoustic transmitters, pulse compression signal–driven linear phased array acoustic transmitters can provide downhole received waveforms of better quality and improved a signal-to-noise ratio of the mode wave dispersion curves obtained using the downhole received waveforms. Because pulse compression signal–driven linear phased array acoustic transmitters use linear frequency modulation drive signals of longer duration, the recording time required for the received waveforms is also longer and the amount of data generated is larger, presenting new challenges for downhole data processing and high-speed data transmission.