Alejandro Rodríguez-Castellanos

Multiple Scattering of Elastic Waves by Subsurface Fractures and Cavities

Comprehensive studies in geophysics and seismology have dealt with scattering phenomena in unbounded elastic domains containing fractures or cavities. Other studies have been carried out to investigate scattering by discontinuities located near a free surface. In this last case, the presence of fractures and cavities significantly affects wave motion and, in some cases, large resonant peaks may appear. To study these resonant peaks and describe how they can be affected by the presence of other near-free-surface fractures or cavities we propose the use of the indirect boundary element method to simulate 2D scattering of elastic P and SV waves. The geometries considered are planar and elliptic cracks and cavities. This method establishes a system of integral equations that allows us to compute the diffracted displacement and traction fields. We present our results in both frequency and time domains. In the planar cracks located near the free surface, we validate the method by comparing results with those of a previously published study. We develop several examples of various fractures and cavities to show resonance effects and total scattered displace- ment fields, where one can observe conspicuous peaks in the frequency domain and important wave interactions in the time domain. Finally, we show how our dimen- sionless graphs can be used to deal with materials like clay, sand, or gravel and compare the response with finite-element analysis of elastic beams.

Two perspectives on equipartition in diffuse elastic fields in three dimensions.

The elastodynamic Green function can be retrieved from the cross correlations of the motions of a diffuse field. To extract the exact Green function, perfect diffuseness of the illuminating field is required. However, the diffuseness of a field relies on the equipartition of energy, which is usually described in terms of the distribution of wave intensity in direction and polarization. In a full three dimensional (3D) elastic space, the transverse and longitudinal waves have energy densities in fixed proportions. On the other hand, there is an alternative point of view that associates equal energies with the independent modes of vibration. These two approaches are equivalent and describe at least two ways in which equipartition occurs. The authors gather theoretical results for diffuse elastic fields in a 3D full-space and extend them to the half-space problem. In that case, the energies undergo conspicuous fluctuations as a function of depth within about one Rayleigh wavelength. The authors derive diffuse energy densities from both approaches and find they are equal. The results derived here are benchmarks, where perfect diffuseness of the illuminating field was assumed. Some practical implications for the normalization of correlations for Green function retrieval arise and they have some bearing for medium imaging.

Rayleigh-wave scattering by shallow cracks using the indirect boundary element method

The scattering and diffraction of Rayleigh waves by shallow cracks using the indirect boundary element method (IBEM) are investigated. The detection of cracks is of interest because their presence may compromise structural elements, put technological devices at risk or represent economical potential in reservoir engineering. Shallow cracks may give rise to scattered body and surface waves. These waves are sensitive to the cracks geometry, size and orientation. Under certain conditions, amplitude spectra clearly show conspicuous resonances that are associated with trapped waves. Several applications based on the scattering of surface waves (e.g. Rayleigh and Stoneley waves), such as non-destructive testing or oil well exploration, have shown that the scattered fields may provide useful information to detect cracks and other heterogeneities. The subject is not new and several analytical and numerical techniques have been applied for the last 50 years to understand the basis of multiple scattering phenomena. In this work, we use the IBEM to calculate the scattered fields produced by single or multiple cracks near a free surface. This method is based upon an integral representation of the scattered displacement fields, which is derived from Somiglianas identity. Results are given in both frequency and time domains. The analyses of the displacement field using synthetic seismograms and snapshots reveal some important effects from various configurations of cracks. The study of these simple cases may provide an archetype to geoscientists and engineers to understand the fundamental aspects of multiple scattering and diffraction by cracks.

Fuzzy logic and image processing techniques for the interpretation of seismic data

Since interpretation of seismic data is usually a tedious and repetitive task, the ability to do so automatically or semi-automatically has become an important objective of recent research. We believe that the vagueness and uncertainty in the interpretation process makes fuzzy logic an appropriate tool to deal with seismic data. In this work we developed a semi-automated fuzzy inference system to detect the internal architecture of a mass transport complex (MTC) in seismic images. We propose that the observed characteristics of a MTC can be expressed as fuzzy if-then rules consisting of linguistic values associated with fuzzy membership functions. The constructions of the fuzzy inference system and various image processing techniques are presented. We conclude that this is a well-suited problem for fuzzy logic since the application of the proposed methodology yields a semi-automatically interpreted MTC which closely resembles the MTC from expert manual interpretation.

Numerical Simulation of Multiple Scattering by Hidden Cracks under the Incidence of Elastic Waves

In this paper, the scattering of P-waves by hidden cracks located near to a free surface is investigated. The Indirect Boundary Element Method was used in order to study the wave propagation phenomenon in a halfspace considering various crack models. A near free-surface crack generates scattered surface waves whose amplitude spectra show conspicuous resonance peaks. Such effect has been attributed to local resonances of a virtual layer formed by the free surface and the up crack´s face. For the case of two-near-free-surface cracks the amplitude spectra show additional peaks, which can be associated to the presence of the second crack. Given similar sizes between these two cracks, the characteristic resonance frequency measured at the free surface corresponds mainly to the equivalent layer formed by the shallowest crack and the free surface. However, when the deepest crack becomes sufficiently large with respect to the shallow crack, two characteristic resonance frequency peaks appear. To illustrate the response and multiple scattering effects due to the presence of a second crack, results in frequency domain are provided. For the case of a near free-surface crack, results obtained by means of the formulation shown here have been verified against those obtained by using an analytical solution and good agreement was obtained.

A genetic algorithm for filter design to enhance features in seismic images

ABSTRACT We present a novel method to enhance seismic data for manual and automatic interpretation. We use a genetic algorithm to optimize a kernel that, when convolved with the seismic image, appears to enhance the internal characteristics of salt bodies and the sub‐salt stratigraphy. The performance of the genetic algorithm was validated by the use of test images prior to its application on the seismic data. We present the evolution of the resulting kernel and its convolved image. This image was analysed by a seismic interpreter, highlighting possible advantages over the original one. The effects of the kernel were also subject to an automatic interpretation technique based on principal component analysis. Statistical comparison of these results with those from the original image, by means of the Mann‐Whitney U‐test, proved the convolved image to be more appropriate for automatic interpretation.

Numerical Formulation to Study Fluid-Solid Interfaces Excited by Elastic Waves

In this paper, the scattering of elastic waves in a fluid-solid interface is researched. The Indirect Boundary Element Method (IBEM) was used to study this wave propagation phenomenon in a 2D fluid-solid model. The source, represented by a Hankel´s function of the second kind, is always applied in the fluid. This approximate boundary integral technique is based upon the integral representation for scattered elastic waves using single-layer boundary sources. The approach presented is usually called IBEM as the sources’ strengths should be obtained as an intermediate step. This indirect formulation can give a deep physical insight to the analyst on the generated diffracted waves, because it is closer to the physical reality and can be regarded as a realization of Huygens’ Principle, which mathematically is fully equivalent to the classical Somigliana’s representation theorem. In order to gauge accuracy, the method was tested by comparing it to an analytical solution. A near interface pulse generates scattered waves that can be registered by sensors located in the fluid. Results are presented in time domain, where several aspects related to the different wave types that emerge from this kind of problems are pointed out.

Seismic data interpretation using the Hough transform and principal component analysis

In this work two novel image processing techniques are applied to detect and delineate complex salt bodies from seismic exploration profiles: Hough transform and principal component analysis (PCA). It is well recognized by the geophysical community that the lack of resolution and poor structural identification in seismic data recorded at sub-salt plays represent severe technical and economical problems. Under such circumstances, seismic interpretation based only on the human-eye is inaccurate. Additionally, petroleum field development decisions and production planning depend on good-quality seismic images that generally are not feasible in salt tectonics areas. In spite of this, morphological erosion, region growing and, especially, a generalization of the Hough transform (closely related to the Radon transform) are applied to build parabolic shapes that are useful in the idealization and recognition of salt domes from 2D seismic profiles. In a similar way, PCA is also used to identify shapes associated with complex salt bodies in seismic profiles extracted from 3D seismic data. To show the validity of the new set of seismic results, comparisons between both image processing techniques are exhibited. It is remarkable that the main contribution of this work is oriented in providing the seismic interpreters with new semi-automatic computational tools. The novel image processing approaches presented here may be helpful in the identification of diapirs and other complex geological features from seismic images. Conceivably, in the near future, a new branch of seismic attributes could be recognized by geoscientists and engineers based on the encouraging results reported here.

Shot Peening Effect on Fatigue Crack Repaired Weldments

Fracture mechanics calculations are required to validate the safety level defined in design codes to prevent a fatigue failure. The periodic inspection-assessment cycle can lead to the implementation of a fatigue crack repair by crack removal. To improve the fatigue performance of the crack repair, residual compressive stresses induced by peening can be considered. This paper is in relation to the peening effect estimation on stress intensity factors in fatigue crack repaired weldments, since the stress intensity factor is a key parameter in fracture mechanics calculations. A set of T-butt specimens were experimentally fatigue tested and crack propagation data was gathered for the calculation of stress intensity factors. The experiments were designed to estimate the residual compressive stress depth layer and its effect on crack propagation inhibition. Experimental estimation of the peening effect on stress intensity factors in fatigue crack repaired weldments was validated by comparison against an analytical weight function solution. Experimental stress intensity factors determined from a set of fatigue tested T-butt specimens allowed estimating preliminarily that peening has a limited effect on fatigue crack propagation inhibition for edge repaired T-butt weldments subjected to bending loading.

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.