Norberto Flores-Guzmán

Scholte waves on fluid-solid interfaces by means of an integral formulation

The present work shows the propagation of Scholte interface waves at the boundary of a fluid in contact with an elastic solid, for a broad range of solid materials. It has been demonstrated that by an analysis of diffracted waves in a fluid it is possible to infer the mechanical properties of the elastic solid medium, specifically, its propagation velocities. For this purpose, the diffracted wave field of pressures and displacements, due to an initial wave of pressure in the fluid, are expressed using boundary integral representations, which satisfy the equation of motion. The source in the fluid is represented by a Hankel’s function of second kind and zero order. The solution to this wave propagation problem is obtained by means of the Indirect Boundary Element Method, which is equivalent to the well-known Somigliana representation theorem. The validation of the results is carried out by using the Discrete Wave Number Method and the Spectral Element Method. Firstly, we show spectra of pressures that illustrate the behavior of the fluid for each solid material considered, then, we apply the Fast Fourier Transform to show results in time domain. Snapshots to exemplify the emergence of Scholte’s waves are also included.

Diffractions due to P and SV waves on irregular bathymetries

Diffractions of P and SV waves on irregular bathymetries are studied using the indirect boundary element method. This allows us to evaluate the complete displacement field by the superposition of a free field plus a diffracted one. Six elemental bathymetries are analyzed in the frequency domain and normalized displacement spectra are obtained. Hence, synthetic seismograms are generated in order to get a better perspective on the effects caused by the bathymetries. Results in the frequency domain suggest that the absolute value of normalized displacement is amplified almost four times in a sinusoidal bathymetry for incoming P-waves. For the incidence of SV-waves on a semi-circular bathymetry, the amplification reaches a value of five times. Moreover, several kinds of materials for the semi-circular bathymetry are used for comparison purposes, these are: sandstone, limestone and granite. Results for these materials reveal that sandstone produces an amplification of almost 3.5 times an incident P-wave. Therefore, seismic amplifications should be taken into account when marine foundations or pipelines are designed.

Near shore seismic movements induced by seaquakes using the boundary element method

This study quantifies seismic amplifications in near-shore arising from seaquakes. Within the Boundary Element Method, boundary elements are used to irradiate waves and force densities obtained for each element. Huygens´ Principle is implemented since the diffracted waves are constructed at the boundary from which they are radiated, which is equivalent to Somigliana´s theorem. Application of boundary conditions leads to a system of integral equations of the Fredholm type of second kind and zero order. Several numerical configurations are analyzed: The first is used to verify the present formulation with ideal sea floor configurations to estimate seismic amplifications. With the formulation verified, simple slope configurations are studied to estimate spectra of seismic motions. It is found that P-waves can produce seismic amplifications from 1.2 to 3.9 times the amplitude of the incident wave. SV-waves can generate seismic amplifications up to 4.5 times the incident wave. Another relevant finding is that the highest amplifications are at the shore compared to the ones at the sea floor.

SEISMIC PRESSURES IN OFFSHORE AREAS: NUMERICAL RESULTS

THE PURPOSE OF THIS STUDY IS TO OBTAIN NUMERICAL ESTIMATIONS OF SEISMIC PRESSURES IN OFFSHORE AREAS CONSIDERING THE EFFECT OF SEABED CONFIGURATIONS AND MATERIALS. ACCORDING TO THE BOUNDARY ELEMENT METHOD, BOUNDARY ELEMENTS ARE USED TO IRRADIATE WAVES AND FORCE DENSITIES ARE DETERMINED. FROM THIS HYPOTHESIS, HUYGENS´ PRINCIPLE IS IMPLEMENTED SINCE THE DIFFRACTED WAVES ARE CONSTRUCTED AT THE BOUNDARY FROM WHICH THEY ARE RADIATED. APPLICATION OF BOUNDARY CONDITIONS ALLOWS US TO DETERMINE A SYSTEM OF INTEGRAL EQUATIONS OF FREDHOLM TYPE OF SECOND KIND. VARIOUS MODELS WERE ANALYZED, THE FIRST ONE IS USED TO VALIDATE THE PROPOSED FORMULATION. OTHER MODELS OF IDEAL SEABED CONFIGURATIONS ARE DEVELOPED TO ESTIMATE THE SEISMIC PRESSURE PROFILES AT SEVERAL LOCATIONS. THE INFLUENCE OF P- AND SV-WAVE INCIDENCE WAS ALSO HIGHLIGHTED. IN GENERAL TERMS, MATERIALS WITH HIGHER WAVE PROPAGATION VELOCITIES GENERATE A LESSER PRESSURE FIELD. THE DIFFERENCE BETWEEN THE MAXIMUM PRESSURE VALUES OBTAINED FOR A MATERIAL WITH SHEAR WAVE VELOCITY OF I²=3000 M/S IS APPROXIMATELY 9 TIMES LOWER THAN THOSE OBTAINED FOR A MATERIAL WITH I²=90 M/S, FOR THE P WAVE INCIDENCE, AND 2.5 TIMES FOR THE CASE OF SV WAVES. THESE RESULTS ARE RELEVANT BECAUSE THE SEABED MATERIAL HAS DIRECT IMPLICATIONS ON THE PRESSURE FIELD OBTAINED.

Extracting the elastodynamic 2D Green's tensor from noise correlations: a numerical study

The correlation of the coda of seismic records and the measurement of seismic noise are nowadays important as they can be used to obtain the physical characteristics of the medium. The extraction of Greens tensor between two points is possible by averaging the cross correlation of the records at those points. We explore numerically Greens tensor retrieval in the time domain using canonical 2D elastic cases in order to evince the recovery of body waves under controlled circumstances. To this end, parametric analyses are performed using up to 5000 random sources. The isotropy of the illumination and attenuation are modified with noticeable effects on the retrieved signals. Several source distributions are used and reveal the importance of isotropy of illumination on the retrieved Greens tensor.

Spectral Ratios for Crack Detection Using P and Rayleigh Waves

We obtain numerical results to help the detection and characterization of subsurface cracks in solids by the application of P and Rayleigh elastic waves. The response is obtained from boundary integral equations, which belongs to the field of elastodynamics. Once the implementation of the boundary conditions has been done, a system of Fredholm integral equations of the second kind and order zero is found. This system is solved using the method of Gaussian elimination. Resonance peaks in the frequency domain allow us to infer the presence of cracks using spectral ratios. Several models of cracked media were analyzed, where effects due to different crack orientations and locations were observed. The results obtained are in good agreement with those published in the references.