J. J. S. de Figueiredo

Estimating fracture orientation from elastic‐wave propagation: An ultrasonic experimental approach

[1]xa0Elastic-wave propagation in fractured and cracked media depends on the dominant spatial orientation of the discontinuities. Consequently, compressional and shear-wave velocities can give valuable information about the orientation of the cracks. The main goal of this work is to estimate the preferential fracture orientation based on an analysis of cross-correlated S-wave seismograms and Thomsen parameters. For this purpose, we analyzed ultrasonic measurements of elastic (P and S) waves in a physical-modeling experiment with an artificially anisotropic cracked model. The solid matrix of the model consisted of epoxy-resin; small rubber strips simulate cracks with a compliant fill. The anisotropic cracked model consists of three regions, each with a different fracture orientation. We used the rotation of the S-wave polarizations for a cross-correlation analysis of the orientations, and P- and S-wave measurements to evaluate the weak anisotropic parametersγ and e.The shear and compressional wave sources had dominant frequencies of 90xa0kHz and 120xa0kHz. These frequencies correspond to long wavelengths compared to the spacing between layers, indicating a nearly effective-media behavior. Integrating the results from cross-correlation with anisotropic parameter analysis, we were able to estimate the fracture orientation in our anisotropic cracked physical model. Theγparameter showed good agreement with the cross-correlation analysis and, beyond that, provided additional information about the crack orientation that cross-correlation alone did not fully resolve. Moreover, our results show that the shear waves are much more strongly influenced by, and can thus contain more information about, crack orientation than compressional waves.

A study of ultrasonic physical modeling of isotropic media based on dynamic similitude.

For decades, seismic and ultrasonic physical modeling has been used to help the geophysicists to understand the phenomena related to the elastic wave propagation on isotropic and anisotropic media. Most of the published works related to physical modeling use physical similitudes between model and field (geological environment) only in the geometric and, sometimes, in the kinematics sense. The dynamic similitude is approximately or, most of the time, not obeyed due to the difficulty to reproduce, in laboratory, the forces and tensions excited inside the earth when elastic waves propagate. In this work, we use expressions for dynamic similitude related to the ratio between stiffness coefficients or Lamé parameters. The resulting expression for dynamic similitude shows that this type of similitude has multiple solutions in the context of dynamic stress (non-uniqueness problem). However, the regularization of this problem can be reached by controlling porosity and clay content. Ultrasonic measurements (elastic) as well as petrophysical measurements (density, porosity and clay content) in synthetic sandstone rocks show how difficult it is to reproduce experimentally the three physical similarities studied in this work.

A Computer Library for Ray Tracing in Analytical Media

Ray tracing technique is an important tool not only for forward but also for inverse problems in Geophysics, which most of the seismic processing steps depends on. However, implementing ray tracing codes can be very time consuming. This article presents a computer library to trace rays in 2.5D media composed by stack of layers. The velocity profile inside each layer is such that the eikonal equation can be analitically solved. Therefore, the ray tracing within such profile is made fast and accurately. The great advantage of an analytical ray tracing library is the numerical precision of the quantities computed and the fast execution of the implemented codes. Although ray tracing programs already exist for a long time, for example the seis package by Cervený, with a numerical approach to compute the ray. Regardless of the fact that numerical methods can solve more general problems, the analytical ones could be part of a more sofisticated simulation process, where the ray tracing time is completely relevant. We demonstrate the feasibility of our codes using numerical examples.

Diffraction imaging point of common-offset gather: GPR data example

SUMMARY Hydrocarbon traps are generally located beneath complex geological structures. Such areas contain many seismic diffractors that carry detailed structureinformation in theorder of theseismic wavelength. Therefore, the development of computational resources capable of detecting diffractor points with a good resolution is desirable, but has been a challenge in the area of seismic processing. In this work, we present a method for the detection of diffractor points in the common-offset gathers domain. In our approach, the diffraction imaging is based on the diffraction operator, which can be used in both the time and depth domains, in accordance with the complexity of the area. This method, which does not require any knowledge apart from the migration velocity field (i.e., rms velocities or interval velocities) applies pattern recognition to the amplitudes along the diffraction operator. Numerical examples using synthetic and real data demonstrate the feasibility of the technique.

Physical modeling of anisotropic domains: Ultrasonic imaging of laser‐etched fractures in glass

Physical modeling, using ultrasonic sources and receivers over scaled exploration structures, plays a useful role in wave propagation and elastic property investigations. This paper explores the anisotropic response of novel fractured glass blocks created with a laser-etching technique. We compare transmitted and reflected signals for Pand Swaves from fractured and unfractured zones in a suite of ultrasonic experiments. The unaltered glass velocities are 5801 m/s and 3448 m/s for P and S waves, respectively, with fractured zones showing a small decrease (about 1%). Signals propagating through the fractured zone have decreased amplitudes and increased coda signatures. Reflection surveys (zero-offset and variable polarization and offset gathers) record significant scatter from the fractured zones. The glass specimens with laser-etched fractures display a rich anisotropic response.

Velocity analysis on CMP sections based on the smearing paradigm

Techniques that use Common Mid-Point (CMP) data, such as NMO correction, stacking and velocity analysis are the core of seismic processing. They are combination of procedures that relies on the physics, signal processing and basic laws of statistcs. In general, they all use a underlying velocity model, which gives a traveltime expression, and numerical schemes to acomplish their goals. For instance, the construction of coherence panels in spectral velocity domain are traditionally made by summing up amplitudes along auxiliary hyperbolae, which are parameterized by zero-offset time and velocity. In this work we insvestigate how some of these methods could benefit of smearing procedures instead of stacking ones.

Analytical ray tracing system: Introducing art, a C-library designed for seismic applications

Abstract Ray tracing technique is an important tool not only to forward but also for inverse problems in Geophysics, which most of the seismic processing steps depend on. However, implementing ray tracing codes can be very time consuming. This article presents a computer library to trace rays in 2.5D media composed by a stack of layers. The velocity profile inside each layer is such that the eikonal equation can be analytically solved. Therefore, the ray tracing within such profile is made fast and accurate. The great advantage of an analytical ray tracing library is the numerical precision of the quantities computed and the fast execution of the implemented codes. Even though ray tracing programs exist for a long time, for example the seis88 package by Cervený, most of those programs use a numerical approach to compute the ray. Regardless of the fact that numerical methods can solve more general problems, the analytical ones could be part of a more sophisticated simulation process, where the ray tracing time is completely relevant. We demonstrate the feasibility of our codes using several examples (Miqueles etxa0al., 2013)xa0 [1] . The library can also be used for other applications besides seismic, e.g., optics and tomography. Program summary Program title: art Catalogue identifier: AEQK_V1_0 Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEQK_V1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 149519 No. of bytes in distributed program, including test data, etc.: 2609188 Distribution format: tar.gz Programming language: C. Computer: Workstations and PCs. Operating system: Linux and Windows. RAM: ≥ 2 Mb Classification: 2.9. External routines: LibConfuse ( http://www.nongnu.org/confuse/ ). To run the examples included in the distribution file, gengetopt ( http://www.gnu.org/software/gengetopt/gengetopt.html ), Seismic Unix ( http://www.seismicunix.com/w/Main_Page ), gnuplot ( http://www.gnuplot.info/ ) and SU. Nature of problem: Fast ray tracing algorithms for Seismic simulation and problems related to Wave propagation and/or Optics. Solution method: Method of characteristics for the eikonal equation, at a layered media, with analytical velocities. Running time: Milliseconds to 3 min, depending on the data size