Douglas R. Schmitt

Repeatability of multimode Rayleigh‐wave dispersion studies

Rayleigh‐wave dispersion is used to study the near‐surface elastic properties of a thick, lacustrine clay to approximately 10 m depth. Ten repeated sets of Rayleigh dispersion curves were obtained through late spring to early fall. A variety of methodologies were used to extract the dispersion curves, but a modified frequency–ray parameter (f − p) method most successfully yields dispersion curves for the first three Rayleigh modes. The Rayleigh‐wave velocities varied from 100 to ∼350 m/s with frequency over the band from 75 to 10 Hz. Over this band, these velocities did not measurably vary during the study period. The observed phase velocity curves were inverted with P‐wave and density values obtained from shallow coring to obtain the shear‐wave velocity structure at the site down to > 14 m. This case study highlights the robust, repeatable, nature of surface wave dispersion methods when care is taken in the acquisition of field data.

Poroelastic effects in the determination of the maximum horizontal principal stress in hydraulic fracturing tests—A proposed breakdown equation employing a modified effective stress relation for tensile failure

Abstract In a hydraulic fracturing stress measurement, the greatest horizontal principal compressive crustal stress S Hmax must be calculated using a breakdown equation which relates the fracture initiation pressure to in situ stress, tensile strength, pore pressure, and, for permeable formations, the Biot poroelastic parameter α. Using laboratory-derived α from core, S Hmax magnitudes have been calculated with breakdown equations for impermeable, permeable and nonporous materials published by Hubbert and Willis [1] ( Trans AIME 210 , 153–163), Haimson and Fairhurst [2] ( Soc. Petrol. Engrs J. Sept , 310–318) and Pine et al. [3] ( Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. 20 , 63–72), respectively. Not surprisingly, there are major differences between computed values for S Hmax associated with the different breakdown equations, especially for low compressibility rocks at great depth. This is illustrated with data from two field experiments in crystalline rock. Another problem is that while the published breakdown equations accurately estimate breakdown pressures in many laboratory hydraulic fracturing experiments in relatively high α rocks, in some cases with low α rocks, breakdown pressures are not predicted by any of the breakdown formulae. To resolve these problems we propose a breakdown equation based on a modified effective stress failure relation in which the tensile strength is dependent on a non-Terzaghi effective stress law. This proposed breakdown equation needs experimental validation in the laboratory and the field.

Physical properties and seismic imaging of massive sulfides

Laboratory studies show that the acoustic impedances of massive sulfides can be predicted from the physical properties (Vp, density) and modal abundances of common sulfide minerals using simple mixing relations. Most sulfides have significantly higher impedances than silicate rocks, implying that seismic reflection techniques can be used directly for base metals exploration, provided the deposits meet the geometric constraints required for detection. To test this concept, a series of 1-, 2-, and 3-D seismic experiments were conducted to image known ore bodies in central and eastern Canada. In one recent test, conducted at the Halfmile Lake copper‐nickel deposit in the Bathurst camp, laboratory measurements on representative samples of ore and country rock demonstrated that the ores should make strong reflectors at the site, while velocity and density logging confirmed that these reflectors should persist at formation scales. These predictions have been confirmed by the detection of strong reflections from...

Seismic attributes for monitoring of a shallow heated heavy oil reservoir; a case study

In production geophysics, detecting the zones of production or constraining the in-situ conditions within a reservoir are often of greater importance than obtaining highly resolved seismic structural images. Standard seismic data processing distorts the signal and limits the potential for extracting additional information, especially for shallow targets. An alternative “shift-stack” procedure is applied in the processing of a shallow 12-fold, 1-m common midpoint (CMP) spacing reflection profile acquired over a heated Athabasca heavy oil sand reservoir. The shift-stack involves summing of CMP traces which have been flattened to an appropriate reference event. Simple modeling confirms that the prestack waveforms are better preserved by this process. Amplitude and frequency attributes are extracted from the reflection profile. Amplitudes of a continuous reservoir event vary by 600% over 35-m intervals along the profile. Bright spots correlate with heated regions. Apparent frequencies, as measured by the instantaneous frequency and by short time-window power spectral estimates of the subreservoir event are 20‐30 Hz lower in these same regions. These diminished apparent frequencies most probably result from interference of the subreservoir reflection with events related to structural changes within the reservoir. A complete interpretation of the results has not been attempted as knowledge of the in-situ conditions is incomplete. However, changes in the seismic response at the well locations suggest that these attributes are useful in detection and mapping of heated zones. The shiftstack procedure may also be useful in environmental and geotechnical applications.

Amplitude and AVO responses of a single thin bed

The seismic reflection characterizations of a thin layer are important for reservoir geophysics. However, discussions on the reflection for a thin layer are usually restricted to precritical angle incidence. In this work, an exact analytical solution is derived to model the reflection amplitude and amplitude variation with offset (AVO) responses of a single thin bed for arbitrary incident angles. The results show that the influence of an ultra-thin bed is great for opposite-polarity reflections and is small for identical-polarity reflections. Opposite-polarity precritical reflection amplitudes first decrease in magnitude with the wavelength/thickness ratio to a local minimum, then increase to a maximum, and finally decrease gradually to zero as the layer vanishes. Opposite-polarity postcritical reflections monotonically decrease from near unity to zero, proportional to the thickness of the layer. Identicalpolarity precritical reflection amplitudes first increase in magnitude with the wavelength/thickness ratio to a local maximum, then decrease to a minimum, and finally increase to the amplitude of a single bottom reflection when the layer vanishes. Identical-polarity postcritical reflections have magnitudes near unity. The AVO responses for both opposite and identical-polarity acoustic thin beds gradually increase with angle. The influence of the Poisson’s ratio of the thin bed is small for either small incidence angles or thicknesses less than 7% of the seismic wavelength, but is large for high incidence angles or thicknesses greater than 13% of the wavelength. A decrease of Poisson’s ratio causes a pronounced AVO response that reaches its maximum at the quarter-wavelength tuning thickness.

First-break timing: Arrival onset times by direct correlation

In attenuating media, pulse characteristics evolve with propagation distance and saturation or pressure‐dependent changes in rock properties. This nonstationarity of the waveform complicates determination of meaningful traveltimes. As a result, depending on the time‐picking criteria used, substantially different values of interval velocity can be obtained. This problem is particularly severe in high‐frequency laboratory time‐of‐flight measurements on porous rock. A potentially less ambiguous measure of wave speed is the signal velocity that is calculated using the pulse onset time. Here, a semiautomated method is developed to determine this onset time in high‐fidelity, pressure‐dependent core measurements. The greatest value of Pearson’s correlation coefficient between segments of observed waveforms near the pulse onset and at an appropriate reference serves as the time determination criterion. Tests of the method on artificial data suggest the signal velocity may be determined to better than 0.3% for −60...

Diminished pore pressure in low‐porosity crystalline rock under tensional failure: Apparent strengthening by dilatancy

Rupture tests on internally pressurized, thin-walled hollow cylinders of Westerly granite with impermeable inner membranes suggest that the conventional, or Terzaghi, effective stress law does not describe tensile failure at high internal pressurization rates near 6 MPa/s. Unjacketed and saturated samples, with an initial pore pressure and for which the inner cavity pressure was increased rapidly with respect to the diffusivity, display substantially increased apparent tensile strengths and deformational moduli much higher than similarly configured but more slowly pressurized tests. Alternatively, the properties of completely dry test pieces with no pore pressure show little, if any, dependence on pressurization rate. Further, the behavior of the rapid unjacketed tests was similar to that for completely dry samples. These observations cannot be explained by the predicted undrained response, but they provide indirect evidence for diminished pore pressure effects reminiscent of dilatant hardening observed in compressive failure experiments. Calculated pore pressure diffusion rates support this suggestion as pore pressure perturbations cannot be damped out on the time scale of the rapidly pressurized tests. It is not clear if these effects are produced by elastic microcrack dilatancy, of which the nonlinear stress-strain curve of granites is symptomatic, or the irreversible production of new porosity as in compressive shear failure tests.

Drilling-induced core fractures and in situ stress

The relationship between the shapes of drilling-induced core fractures and the in situ state of stress is developed. The stress concentrations at the well bore bottom are first determined using a complete three-dimensional finite element analysis. Existing in situ compressional stresses generate large tensions in the immediate vicinity of the bottom hole which are sufficient to rupture the rock. Tensile fracture trajectories within these concentrated stress fields are predicted using a simple model of fracture propagation. These modeled fracture trajectories resemble well the observed shapes of drilling-induced core disking, petal, and petal-centerline fractures. Further, this agreement suggests that both the shape of the drilling-induced fracture and the location at which it initiates depends on the in situ stress state existing in the rock mass prior to drilling; the core fractures contain substantial information on in situ stress conditions. In all faulting regimes the coring-induced fractures initiate near the bit cut except for most cases under thrust faulting regime where the fracture initiates on the well bore axis. Further, under thrust faulting conditions only disk fractures appear possible. Both petal and disking fractures can be produced in strike-slip and normal faulting regimes depending upon the relative magnitudes between the least compressive horizontal principal stress and the vertical overburden stress. The predicted fracture shapes are in good qualitative agreement with observations of drilling-induced fractures described in the literature from laboratory experiments and field programs in which in situ stresses are measured by other means. The relationship of the morphology of coring induced fractures and in situ stresses suggests that the fractures can be used as independent complementary indicators in identifying stress regimes.

Inherent transversely isotropic elastic parameters of over-consolidated shale measured by ultrasonic waves and their comparison with static and acoustic in situ log measurements

In terms of elastic anisotropy, sedimentary shales may be considered to have transverse symmetry. Experimentally determining the five independent elastic constants required for this case remains challenging. This paper proposes the use of ultrasonic waves in determination of the five constants. Arrays of specially constructed transducers with different modes of vibration were mounted on samples trimmed from natural cores to measure ultrasonic P-waves and S-waves along the horizontal, vertical and 45 ◦ -inclination axes on the samples. The elastic constants calculated from these wave velocities were compared to those determined from static tests and acoustic in situ logs. The static tests included drained triaxial compression and confined torsion tests. The acoustic logs were conducted in an open hole using monopole compressional and dipole shear transmitters and receivers. It was found that the elastic constants determined by the static tests were much lower than those determined from the ultrasonic tests and acoustic logs. Discrepancies among the elastic constants determined from these three different methods are discussed and explained.

Compressional-wave velocities in attenuating media : A laboratory physical model study

Elastic-wave velocities are often determined by picking the time of a certain feature of a propagating pulse, such as the first amplitude maximum. However, attenuation and dispersion conspire to change the shape of a propagating wave, making determination of a physically meaningful velocity problematic. As a consequence, the velocities so determined are not necessarily representative of the materials intrinsic wave phase and group velocities. These phase and group velocities are found experimentally in a highly attenuating medium consisting of glycerol-saturated, unconsolidated, random packs of glass beads and quartz sand. Our results show that the quality factor Q varies between 2 and 6 over the useful frequency band in these experiments from ∼200 to 600 kHz. The fundamental velocities are compared to more common and simple velocity estimates. In general, the simpler methods estimate the group velocity at the predominant frequency with a 3% discrepancy but are in poor agreement with the corresponding phase velocity. Wave velocities determined from the time at which the pulse is first detected (signal velocity) differ from the predominant group velocity by up to 12%. At best, the onset wave velocity arguably provides a lower bound for the high-frequency limit of the phase velocity in a material where wave velocity increases with frequency. Each method of time picking, however, is self-consistent, as indicated by the high quality of linear regressions of observed arrival times versus propagation distance.