Chih-Hsiung Chang

Reliable estimation of virtual source position for SAFT imaging

The synthetic aperture focusing technique (SAFT), employing a scanned focused transducer as a virtual source, is commonly used to image flaws in immersion testing. The position of a virtual source is estimated from rays emitted from the rim of a focused transducer. However, it is often found that the virtual source position cannot be uniquely determined because of severe focal spot aberration at the focal zone. Based on an analysis of the energy radiated from the focused transducer and the refracted energy varied with the incident angle of ultrasound, we propose that paraxial rays emitted from the focused transducer are the best for estimating the position of a virtual source for incorporation into SAFT. This study results also shows that by using this simple virtual source position estimation for SAFT, the axial resolution and SNR of the reconstructed image can be greatly improved. This new approach minimizes the effect of such factors as refraction at high-velocity-contrast interfaces, distance of the transducer to the couplant-specimen interface, and the focal length of a focused transducer, which may cause focal spot aberration resulting in decreased sensitivity in SAFT imaging.

Laboratory results for the features of body-wave propagation in a transversely isotropic media

Much of the earth’s crust appears to have some degree of elastic anisotropy (Crampin, 1981; Crampin and Lovell, 1991; Helbig, 1993). The phenomena of elastic wave propagation in anisotropic media are more complex than those in isotropic media. Shear‐wave propagation in an orthorhombic physical model is most complex when the direction of the wave is close to the neighborhood of the cusp on the group velocity surfaces (Brown et al., 1991). The first identification of singularities in wave propagation through sedimentary basins occurred in the examination of shear‐wave splitting in multioffset vertical seismic profiles (VSPs) at a borehole site in the Paris Basin (Bush and Crampin, 1991), where large variations in shear‐wave polarizations in propagation directions close to point singularities were observed. Computation of synthetic seismograms for layer sequences showed that the shear‐wave polarizations and amplitudes were irregular near point singularities (Crampin, 1991).

Azimuthal variation of converted-wave amplitude in a reservoir with vertically aligned fractures − a physical model study

ABSTRACT The existence of fractures not only provides space for oil and gas to reside in but also creates pathways for their migration. Accurate description of a fractured reservoir is thus an important subject of exploration for geophysicists and petroleum engineers. In reflection seismology, a reservoir of parallel vertical fractures is often considered a transversely isotropic medium with its symmetry axis horizontally oriented and its physical properties varying in azimuth on the horizontal symmetry‐axis plane. In the history of fractured reservoir exploration, azimuthal variation in the P‐wave amplitude, velocity, and fractional difference of the split S‐waves have been popular seismic attributes used to delineate characteristics and extract information from the reservoir. Instead of analysing the reflection signatures of P‐wave and S‐wave, the objective of this study is to demonstrate the azimuthal variation of the converted wave (C‐wave) amplitude in a fractured reservoir. To facilitate our objective, both common offset and end‐on shooting reflection experiments were conducted in different azimuths on the horizontal symmetry‐axis plane of a horizontal transverse isotropic model. In the acquired profile, reflections of P‐wave, PS1‐wave (C1‐), and a mixture of PS2‐ (C2‐) and S1‐waves were observed and identified. Thereafter, the laboratory observations were Hilbert transformed to compute the reflectivity strength of the relative events. Results show that the reflectivity strengths of both P‐ and C1‐waves are consistently weakened from the direction of the layering strike to the layering normal. However, the azimuthal variation of the C1‐wave amplitude is more significant than that of the P‐wave and can be considered another effective seismic attribute for orienting the fracture strike of a reservoir that consists of vertically aligned fractures.

Ultrasonic Synthetic Aperture Focusing Technique With Finite Source Element for Focused Transducers

A spherically focused transducer (SFT) can concentrate the ultrasounds to a focal zone that yields a better lateral resolution at a certain axial range. Unfortunately, this result is always accompanied by a loss of resolution outside the focal zone. The synthetic aperture focusing technique (SAFT) is a type of digital signal processing technique that is commonly based on the point-source wavefront backpropagation (WFBP) theory to improve the axial resolution of the image. However, the ultrasound is refracted when it propagates through the couplant–specimen interface to detect the flaws in specimens; thus, the capability of a virtual point-source SAFT in refocusing ultrasonic energy is deteriorated caused by the phase aberration by an SFT. Therefore, in this study, the finite source element (FSE) refraction corrected WFBP SAFT imaging method will be introduced to reduce the phase aberration effect when refocusing a defocused ultrasonic image. Study results show that the axial resolution of the image is largely improved by this technique, but improvement is not yet attained in the lateral resolution. In addition, the signal-to-noise ratio of the image is enhanced. Therefore, for cases with a strong phase aberration, the proposed method is recommended for obtaining better image resolution.

A physical model study of the travel times and reflection points of SH-waves reflected from transversely isotropic media with tilted symmetry axes

In reflection seismology, detailed knowledge of how seismic waves propagate in anisotropic media is important for locating reservoirs accurately. The SH-wave possesses a pure mode polarization which does not convert to P- and SV-waves when reflecting from a horizontal interface, and vice versa. The simplicity of the SH-wave thus provides an easy way to view the details of SH-wave propagation in anisotropic media. In this study, we attempt to inspect the theoretical reflection moveouts of SH-waves reflected from transversely isotropic (TI) layers with tilted symmetry axes and to verify the reflection point, which could be shifted away from the common midpoint (CMP), by numerical calculations and physical modelling. In travel time-offset analyses, the moveout curves of SH-waves reflected from horizontal TI media (TIM) with different tilted angles of symmetry axes are computed by the TI modified hyperbolic equation and Fermat’s principle, respectively. It turns out that both the computed moveout curves are similar and fit well to the observed physical data. The reflection points of SH-waves for a CMP gather computed by Fermat’s principle show that they are close to the CMP for TIM with the vertical and horizontal symmetry axes, but they shift away from the CMP for the other tilted angles of symmetry axes. The shifts of the reflection points of the SH-waves from the CMP were verified by physical modelling. The reflection moveouts of SH-waves reflected from a transversely isotropic layer with tilted symmetry axis computed by the modified hyperbolic equation and Fermat’s principle fit well to the physical data. Their reflection points will shift away from the common midpoint when the symmetry axes are not vertical and horizontal.

Traveltimes and conversion-point positions for P-SV converted wave propagation in a transversely isotropic medium: numerical calculations and physical model studies

This study uses ultrasonic physical modelling to test the accuracies of numerical calculations of traveltimes and conversion-point (CP) positions for P-SV wave propagation in a horizontal transversely isotropic (TI) medium. Study results show that the traveltimes and CP positions for P-SV wave propagation on the isotropic plane of a TI medium computed using Fermat’s minimum-time principle are the same as those of using the isotropic non-hyperbolic moveout equation and the isotropic CP equation. However, for P-SV wave propagation on the symmetry-axis plane of a TI medium, the arrival times and CP positions of SV-waves are difficult to determine by any ray methods when the propagation directions of SV-waves are within the cuspoidal SV-wave group velocities zone. But the first arrival times and the propagation of the dominant energy of P-SV waves can still be analysed by ray methods. Based on the calculation of Fermat’s minimum-time principle, if the source-receiver offset is greater than a critical distance, the reflection angles of the converted SV-waves are fixed at a specific angle with a local maximum SV-wave group velocity of the neighbourhood area. This is because the converted SV-waves prefer to propagate along the cuspoidal directions with larger amplitude and higher velocity. Verified by the physical modelling, the Fermat’s minimum-time principle used to calculate traveltimes of P-SV waves is better than the anisotropic non-hyperbolic moveout equation. The physical modelling for the CP position experiment can give a clearer visualisation of the variations of CP positions in the profile, and the feasibility of using Fermat’s minimum-time principle to determine CP positions is also better than that of the anisotropic CP equations. Therefore, in the seismic data processing, Fermat’s minimum-time method is recommended to accurately determine the arrival times and CP positions of P-SV wave propagation in TI media. This study uses ultrasonic physical modelling to verify that Fermat’s minimum-time principle is better than the anisotropic non-hyperbolic moveout and conversion-point (CP) equations for calculating the traveltime and CP position of a P-SV wave reflected from a strong vertical transversely isotropic medium.

Effects of the symmetry axis orientation of a TI overburden on seismic images

In active tectonic regions, the primary formations are often tilted and subjected to the processes of folding and/or faulting. Dipping formations may be categorised as tilted transverse isotropy (TTI). While carrying out hydrocarbon exploration in areas of orogenic structures, mispositioning and defocusing effects in apparent reflections are often caused by the tilted transverse isotropy of the overburden. In this study, scaled physical modelling was carried out to demonstrate the behaviours of seismic wave propagation and imaging problems incurred by transverse isotropic (TI) overburdens that possess different orientations of the symmetry axis. To facilitate our objectives, zero-offset reflections were acquired from four stratum-fault models to image the same structures that were overlain by a TI (phenolite) slab. The symmetry axis of the TI slab was vertical, tilted or horizontal. In response to the symmetry axis orientations, spatial shifts and asymmetrical diffraction patterns in apparent reflections were observed in the acquired profiles. Given the different orientations of the symmetry axis, numerical manipulations showed that the imaged events could be well described by theoretical ray paths computed by the trial-and-error ray method and Fermat’s principle (TERF) method. In addition, outputs of image restoration show that the imaging problems, i.e. spatial shift in the apparent reflections, can be properly handled by the ray-based anisotropic 2D Kirchhoff time migration (RAKTM) method. Benefitting from the forward modelling studies, the phenomenon of spatial mispositioning in apparent reflections caused by the symmetry axis orientation of the TI overburden was demonstrated. Numerical manipulations show the imaging problems can be well described by the TERF method and properly handled by the RAKTM method.

Experimental observation of qS‐wave propagation in an orthorhombic anisotropic medium

We are now working on the propagation of qS-wave in an orthorhombic anisotropic medium (OAM) through laboratory work. The aim of this work is trying to get a close view of the degenerate of quasi-shear (qS-) wave in the OAM. To perform the objective of this work, a pulsetransmission experimental setup was designed to measure the direct arrivals of the elastic energy. The transmission experiments were done from one principal (symmetry) axis to another. Our laboratory data clearly demonstrate the degeneration of the qS-wave propagation in the OAM. Compare to transversely isotropic media (TIM), the splitting phenomenon of the qS-wave, which was not shown along the axis of an infinite-fold of symmetry planes in a TIM, was observed in all three principal axes of the OAM.