Each time signal is corrected by the amplification and sensitivity factors used in the field for each accelerometer. The corrected data is used to calculate the attenuation factor. However, the data is also normalized to the maximum response of each trace to enhance the interpretation of time traces and Fourier spectra. Time signals are significantly affected by noise after the eighth receiver because of the attenuation properties of the sidewall. Therefore, the responses of the accelerometers located in the first four meters of the array are given more weight in the data analysis. The arrival times are used to compute the corresponding group velocities (VP and VR). The arrival of compressional waves is weak because of the low amplitude of the generated p-waves and the attenuation properties of the sidewall.
The Fourier spectra indicate that after the first receiver the energy is mostly distributed between 250 Hz and 2,500 Hz; these frequencies correspond to wavelengths equal to X=1.45 m and X=0.30 m respectively. Therefore, the measured properties of the sidewall are representative of depths of 10 cm to 50 cm. Frequencies between 1 kHz and 4.5 kHz attenuate faster than frequencies below 1 kHz. Phase wave velocities change with distance because of the different conditions of the sidewall. Phase velocities are computed by curve fitting the change in phase angle with distance (Eq. 1) for each frequency component. A decrease of phase velocities with frequency indicates that the condition of the inside sidewall (0.50 m to 1.0 m) is better than the condition at the surface (0.0 to 0.25 m). Phase velocities give an indication of the relative condition of the sidewall with depth; however, the results should be interpreted carefully because wave reflections influence significantly the results. Cracks and voids reflect and diffract the wave front, thus relatively higher wave attenuation is expected in weaker sections than in sound sections. The attenuation or absorption coefficient (a, Eq. 3) can be computed in terms of the maximum response in time, frequency, or the area of the Fourier spectra. The attenuation information confirms previous observations that after the first 3.5 m of the array signals are drastically affected by the noise and wave reflections because the wave amplitude does not continue to decrease with distance in the second half of the array.
Two-dimensional Fourier transforms indicate wave velocities (VR and VP) that are closed to the measured group velocities. Energy peaks for negative wavenumbers indicate spatial aliasing for frequencies higher than 1300 Hz. The spatial aliasing is produced by the selected receiver spacing (Ax= 0.5 m). Spatial aliasing can be reduced by using a smaller spacing; however, this solution requires an
increased number of measurements and thus more time for testing and data processing. The surface-wave group velocity (Vr), range of phase velocities (Vph1 to Vph2), attenuation coefficient (a), and the frequencies of higher spectral energy (f1) for all sections are summarized in Table 1. The average values for these variables are shown at the bottom of the table. Results for the right-hand side and the left-hand side of the sections are denoted by the letters R and L, respectively. The condition of the sidewall could change in a distance of few meters; therefore, it is possible to have consecutive sections with completely different conditions (e. g. sections 1L and 2R, Table 1).
Дх = 0.5m
(Accelerometers) -4 re
Receivers at different locations
Side wall (top view)
Figure 2. Test configuration of a multiple-channel seismic measurement
A fuzzy model is developed to assess the relative structural condition of different sections of the brick sidewall using seismic wave properties. The fuzzy model summarizes the results of nondestructive measurements in a quantitative parameter named condition index (CI). The most straightforward fuzzy modeling method is the direct approach in which expert knowledge is used to specify input and output variables (e. g. group velocity, phase velocity, wave attenuation, and condition index). Specific steps are:
(a) to label the partitions of the input and output variables with linguistic terms (e. g. low, medium, high);
(b) to define a set of linguistic rules (IF-THEN) that represent the relationships between the variables; (c) to select an appropriate reasoning method; and (d) to verify the model. A condition index CI = 0 indicates a section in relatively very good condition; whereas, CI = 1 refers to a damaged section. The input variables are partitioned into three fuzzy numbers low (L), medium (M), and high (H). The output is expressed using five partitions: very good (VG), good (G), moderate (M), deteriorated (DT), and damaged (DG). A fuzzy expert system (Najjaran et al. 2004) is used to develop the fuzzy model and evaluate the condition indices for the different sections. The results are summarized in the last two columns of Table 1. The condition index shows that Sections 1L, 6R, 8R, 9L, 10R, 10L, 11R and 11L are the relatively weaker sections. Visual inspection of these sections revealed that surface conditions are fine for most of them; however, voids and cracks are evident close to the line of measurement. In addition, low velocity and high attenuation could be the result of internal cracks and weaker conditions of the brick and mortar that could not be evident on the surface.