Post-seismic crustal internal deformation in a layered earth model

Summary The present study introduces a novel method for computing post-seismic crustal internal deformation in a layered earth model. The surface dislocation Love number (DLN) calculated by the reciprocity theorem was implemented as the initial value. Furthermore, numerical integration of the value from the Earth's surface to the interior was undertaken to obtain the internal DLN. This method does not require a combination of the general solution and particular solution for the calculation of internal deformation above the seismic source, thus avoiding the loss of precision. When the post-seismic deformation within a certain period is calculated, the particular solutions at the beginning and end of the considered period cancel each other. This simplifies the calculation of post-seismic internal deformation. The numerical results depict that as the degrees increase, the post-seismic DLN reaches stability in a shorter interval of time. Thus, for improved efficiency of the post-seismic internal deformation calculation, the post-seismic DLNs should be calculated within 2000 degree and integrated with the co-seismic results. As an application, the post-seismic Coulomb failure stress changes (ΔCFS) induced by the 2011 Tohoku-Oki earthquake in the near field around the Japanese archipelagos and two major faults in Northeast China were simulated. The results exhibit that the ΔCFS values in the near field agree well with those simulated by the method in a half-space layered earth model, thus verifying the present method. The co-seismic ΔCFS on the Mishan-Dunhua fault in Northeast China, as an example, is only 0.094–0.668 KPa. However, the ΔCFS caused by the viscoelastic relaxation of the mantle within 5 years following the 2011 Tohoku-Oki event on the same fault exceeds the co-seismic results. Therefore, the cumulative effect of the viscoelastic relaxation of the mantle is deserving of attention.

Core–mantle topographic coupling: a parametric approach and implications for the formulation of a triaxial three-layered Earth rotation

SUMMARY We propose a parametric approach to the topographic (TOP) coupling between the mantle and outer core for refinement of the latest triaxial three-layered Earth rotation theory. Based on three models of the core–mantle boundary (CMB) topography, we obtain the axial components of the TOP torque as −2.08 × 1019, −2.72 × 1018 and −1.97 × 1017 N m, respectively. Under the frame of the triaxial three-layered Earth rotation theory, we solve the corresponding periods of free core nutation as −(329.83 ± 28.12), −(457.54 ± ∼) and −(428.23 ± 1.09) mean solar days (d), respectively. The other three normal modes, namely, Chandler wobble, inner core wobble and free inner core nutation, are almost not affected by the TOP coupling of the CMB, their period values being 433.24, 2718.69 and 934.02 d, respectively. Calculations show that the TOP torque is highly sensitive to the adopted model of the topography, which is known to be robust. Taking into account the normal modes of the triaxial three-layered Earth rotation, the results of the CMB topography obtained by seismic tomography can be constrained in the future to a certain extent. In this study, considering the TOP coupling with the appropriate topography model, the estimates for the dynamic ellipticity ef of the fluid core lie between 0.0026340 and 0.0026430, values that are 3.56 % higher than the hydrostatic equilibrium value.

A point dislocation in a layered, transversely isotropic and self-gravitating Earth Part IV: Exact asymptotic solutions of dislocation Love numbers for the special case of isotropy

Summary We derive exact asymptotic solutions for the static deformation due to a concentrated or point-like dislocation in a spherical, layered, elastic, isotropic and self-gravitating Earth. The exact asymptotic solutions are quite general and can provide the dislocation Love numbers on the Earth's surface, near the dislocation or ‘source’, and close to any layer interface or boundary. We also discuss the special case where both the source and field points are located on the Earth's surface. We compare our exact asymptotic solutions with previous results obtained from the analytical dual variable and position (DVP) method via curve fitting. Our comparison confirms that the analytical DVP results converge to the exact asymptotic solutions. These new exact asymptotic solutions are particularly helpful when evaluating slowly convergent series of Green's functions using a Kummer transformation, anywhere within the layered Earth, especially for field points located very close to the point dislocation or source.

An Approximate Inversion Scheme for Surface-Borehole EM in the Presence of Steel Casing. 1D Implementation

An approximate inversion scheme for Surface-Borehole EM data is proposed. The method aims at reducing the computational burden arising by the fine discretization required to accurately solve for the field distribution in the full complexity of the borehole system together with the reservoir medium. I first analyze numerical simulations of the surface-borehole response performed for a 1D layered earth, incorporating also realistic complexity of the borehole system. The analysis brings useful insight on the requirement of incorporating fluid and mud/cement electrical properties when implementing an inversion by numerically simulating the full complexity of the system. Subsequently, the synthetic dataset was used to test an inversion method which uses the data dominated by the casing effect to approximately describe the casing secondary fields. A scaling factor is then introduced to account for the the current induced in the well as the exciting source is placed further below the casing shoe. The method is found to recover fairly well the known 1D resistivity strata, still some bias is expected for the resistivity close below the casing shoe, where the data is anticipated to be most distorted by the casing effect.

Inductive sounding of layered earth

Research aim. The research results in the development of a technology of continuous multi-frequency induction profiling measuring magnetic field components on long survey routes and detailed elaboration of sections by means of remote induction soundings. Research methodology. Theoretical and experimental studies of magnetic field components change patterns of harmonic vertical magnetic dipole over non-uniform layered earth. Mathematical simulation of harmonic vertical magnetic dipole magnetic field in non-uniform layered earth. Analysis of results. Information value of harmonic vertical magnetic dipole magnetic field components characteristics in low-frequency induction zone has been shown when studying non-uniform geoelectric sections together with the obtained results correspondence to the type of the non-uniform section when carrying out remote inductive sounding. 30 "Izvestiya vysshikh uchebnykh zavedenii. Gornyi zhurnal". No. 4. 2020 ISSN 0536-1028 Scope of results. for extended sections of route research (road and railway, oil and gas pipelines, power transmission lines, etc.) process sequence of vertical magnetic dipole magnetic field characteristics measurement has been determined to determine geoelectric properties of a layered section by means of continuous multi-frequency profiling and determination of homogeneous sections of medium structure with their detailing by discrete analysis by the method of remote inductive sounding.

Co-seismic internal deformations in a spherical layered earth model

SUMMARY Using a numerical integral method, we deduced a set of formulae for the co-seismic internal deformation in a spherically symmetric earth model, simultaneously taking self-gravitation, compressibility and realistically stratified structure of the Earth into account. Using these formulae, we can calculate the internal deformation at an arbitrary depth caused by an arbitrary seismic source. To demonstrate the correctness of our formulae, we compared our numerical solutions of radial functions with analytical solutions reported by Dong & Sun based on a homogeneous earth model; we found that two sets of results agree well with each other. Our co-seismic internal Green's functions in the near field agree well with the results calculated by the formulae of Okada, which also verifies our Green's functions. Finally, we calculated the Coulomb stress changes on the Japanese Islands and Northeast China induced by the Tohoku-Oki Mw 9.0 earthquake using the methods described above. We found that the effect of layered structure plays a leading role on the near field, while curvature occupies a dominant position on the deep region of the far field. Through a comparison of the Coulomb stress changes at a depth of 10 km on a layered earth model calculated by our method along with the corresponding results of Okada, we found that the discrepancy between them in near field was ∼31.5 per cent, and that of far field was >100 per cent of the signals.