ALBERT

Notes: Abstract —We investigate a new nonlinear inversion method for low frequencies to determine the bulk and shear modulus as well as the material density and the location of subsurface inhomogeneities. The solution is a direct exact nonlinear inversion of single scattered waves containing near- and far-field terms for incident P and scattered P and S waves, allowing for inversion of parameters in the vicinity and at distance from the sources and receivers. Because the approach is based on single scattering theory, the range of application includes single strong scattering anomalies of various sizes like magma chambers, gas- or fluid-filled cavities, or buried near-surface obstacles. The replacement of the material properties by a new set of parameters, referred to as scattering factors, allows the inverse problem to be solved analytically. The nonlinear nature of the scattering problem is investigated and implications for the inversion process are discussed. The deviations in the elastic parameters as a function of the scattering factors show a strong asymmetry about zero, and therefore linearized approximations will perform differently, depending on the sign of the perturbation. Based on the low frequency (Rayleigh) approximation, we introduce and evaluate a pair of approximations (Mie) derived by numerical and analytical integration of the Rayleigh approximation. Both approximations are based on the underlying principle of subdividing the inhomogeneities into a number of small noninteracting parts and subsequent integration over the total volume, thus increasing the Rayleigh limit and producing better resolution of the parameter estimates during the inversion. The two Mie approximations, when evaluated as a function of scattering angle and distance, produce similar results in the mid- and far-field of the inhomogeneity and reveal better resolution than the Rayleigh approximation. For three anomalies of ± 50% in bulk modulus, shear modulus, and density, the relative error between the exact solution and the two Mie approximations remains below 10%, 20%, and 30%, respectively, for values of k p R 〈 3.0, where R is the radius of the heterogeneity. However, smaller errors for individual cases are found for values up to k p R≈ 4.5. The performance of the inversion based on the analytically and the numerically integrated Mie approximation is tested for single parameter perturbations, revealing reliable and stable inversion results for the bulk and the shear modulus, reasonable results for the density, and crosstalk between the shear modulus and the density. The results show well-defined locations of the anomalies and slight deviations in the estimates of their magnitudes, which can be explained by amplitude and phase deviations between the analytical solution used for forward modeling and the approximations used for the inversion. The analytical Mie approximation provides a fast means to estimate elastic parameters compared to the more time consuming numerically integrated approximation, while the latter can be applied to more arbitrarily shaped inhomogeneities.

Notes: The traditional method of exciting channel waves in coal deposits underground consists of firing explosive sources in a mid-seam position generating seam waves of the Rayleigh and Love type. We investigate various source positions and excitation mechanisms within the bedrock structure surrounding the seam to evaluate the effects of source positions adjacent to the seam. The investigation is based on analogue and numerical modelling of half- and full-space cases, for which the excitation and the nature of Rayleigh channel waves are examined.In the analogue modelling, sources, located from mid-seam out into the bedrock, along the edge of a 2D plate model, excited channel waves through a conversion of the free surface Rayleigh wave at the edge of the plate. The excited channel wave belongs to the normal mode range. Frequency-wavenumber analysis shows that the symmetric 2nd mode of the channel wave is excited with frequencies comparable to the forcing frequency of the source signal. The polarization changes from retrograde to prograde, as the wave develops from the front to the rear of the seam, respectively. The amplitude-depth distribution resembles that of an ordinarily excited seam wave, for the symmetric component. However, the antisymmetric component does not show the characteristic change of sign in amplitudes across the mid-seam axis.Numerical modelling with sources located in the bedrock (full-space case) shows that relocating the source away from the seam lowers the frequency content of the excited channel wave. Based on these investigations, the influence of a lower-frequency source signal on the excitation of the channel wave is examined in an analogue experiment. Sources are sited in the bedrock adjacent to the seam at three locations. A lower-frequency wavelet is calculated for each source location from the results obtained in the numerical analysis. For comparison, a higher-frequency wavelet is also used which is known to be optimal for this model geometry when excited by a mid-seam source location. It is found that in two cases the use of the lower-frequency wavelet improves the channel wave excitation, while no amplification is achieved in one case.

Notes: A series of time-lapse seismic cross-well and single-well experiments were conducted in a diatomite reservoir to monitor the injection of CO2 into a hydrofracture zone, based on P- and S-wave data. A high-frequency piezo-electric P-wave source and an orbital-vibrator S-wave source were used to generate waves that were recorded by hydrophones as well as 3-component geophones. During the first phase the set of seismic experiments was conducted after the injection of water into the hydrofractured zone. The set of seismic experiments was repeated after a time period of seven months during which CO2 was injected into the hydrofractured zone. The questions to be answered ranged from the detectability of the geological structure in the diatomic reservoir to the detectability of CO2 within the hydrofracture. Furthermore, it was intended to determine which experiment (cross-well or single-well) is best suited to resolve these features.During the pre-injection experiment, the P-wave velocities exhibited relatively low values between 1700 and 1900 m/s, which decreased to 1600–1800 m/s during the post-injection phase (−5%). The analysis of the pre-injection S-wave data revealed slow S-wave velocities between 600 and 800 m/s, while the post-injection data revealed velocities between 500 and 700 m/s (−6%). These velocity estimates produced high Poisson's ratios between 0.36 and 0.46 for this highly porous (∼50%) material. Differencing post- and pre-injection data revealed an increase in Poisson's ratio of up to 5%. Both velocity and Poisson's ratio estimates indicate the dissolution of CO2 in the liquid phase of the reservoir accompanied by an increase in pore pressure.The single-well data supported the findings of the cross-well experiments. P- and S-wave velocities as well as Poisson's ratios were comparable to the estimates of the cross-well data.The cross-well experiment did not detect the presence of the hydrofracture but appeared to be sensitive to overall changes in the reservoir and possibly the presence of a fault. In contrast, the single-well reflection data revealed an arrival that could indicate the presence of the hydrofracture between the source and receiver wells, while it did not detect the presence of the fault, possibly due to out-of-plane reflections.