Machine learning regression implementation for high-frequency seismic wave attenuation estimation in the Aswan Reservoir area, Egypt
Sayed S. R. Moustafa, Gad-Elkareem A. Mohamed, Mahmoud El-Hadidy, Mohamed S. Abdalzaher
Abstract
Abstract Attenuation characteristics have been estimated to understand the effect of the heterogeneity in the tectonically active Aswan Reservoir, the southern part of Egypt using data collected by a ten-station local seismological network operating across the reservoir. The quality factor was estimated from 350 waveform spectra of P- and S-waves from 50 earthquakes. By applying a spectral ratio technique to bandpass-filtered seismograms, obtained results show variations in both P-waves attenuation ( $$Q_\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>α</mml:mi> </mml:msub> </mml:math> ) and corresponding S-waves ( $$Q_\beta$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>β</mml:mi> </mml:msub> </mml:math> ) as a function of frequency, according to the power law $$Q=Q_0 \times f^n$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>Q</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>Q</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>×</mml:mo> <mml:msup> <mml:mi>f</mml:mi> <mml:mi>n</mml:mi> </mml:msup> </mml:mrow> </mml:math> , with n ranging between 0.85 and 1.19 for P-waves and between 0.92 and 1.18 for S-waves. A supervised machine learning algorithm known as Orthogonal distance regression was utilized to fit the attenuation power law functions. Estimates of $$Q_\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>α</mml:mi> </mml:msub> </mml:math> and $$Q_\beta$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>β</mml:mi> </mml:msub> </mml:math> show a clear dependence on frequency. The frequency-dependent attenuation is found to be $$Q_\alpha = (11.22 \pm 2.2) \times f^{(1.09 \pm 0.07)}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>α</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>11.22</mml:mn> <mml:mo>±</mml:mo> <mml:mn>2.2</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>×</mml:mo> <mml:msup> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1.09</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.07</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> and $$Q_\beta = (9.89 \pm 1.89) \times f^{(1.14 \pm 0.07)}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>β</mml:mi> </mml:msub> <mml:mo>=</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>9.89</mml:mn> <mml:mo>±</mml:mo> <mml:mn>1.89</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> <mml:mo>×</mml:mo> <mml:msup> <mml:mi>f</mml:mi> <mml:mrow> <mml:mo>(</mml:mo> <mml:mn>1.14</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.07</mml:mn> <mml:mo>)</mml:mo> </mml:mrow> </mml:msup> </mml:mrow> </mml:math> for P- and S-waves, respectively. The average ratio $$Q_\alpha /Q_\beta$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>α</mml:mi> </mml:msub> <mml:mo>/</mml:mo> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>β</mml:mi> </mml:msub> </mml:mrow> </mml:math> is higher than unity, which is commonly observed in tectonically active regions characterized by a high degree of heterogeneity of the crustal structure of the area. Final results indicate that seismic wave attenuation in the AHDR region is highly frequency-dependent. Moreover, estimated low values of $$Q_0$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>Q</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:math> clearly highlight the heterogeneity of the AHDR with considerably high seismic activity. These findings will be useful in any future assessment of seismic hazards and the damage pattern of earthquakes.