Machine learning regression implementation for high-frequency seismic wave attenuation estimation in the Aswan Reservoir area, Egypt

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 ($Q_\alpha$) and corresponding S-waves ($Q_\beta$) as a function of frequency, according to the power law $Q=Q_0 \times f^n$, 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 $Q_\alpha$ and $Q_\beta$ show a clear dependence on frequency. The frequency-dependent attenuation is found to be $Q_\alpha = (11.22 \pm 2.2) \times f^{(1.09 \pm 0.07)}$ and $Q_\beta = (9.89 \pm 1.89) \times f^{(1.14 \pm 0.07)}$ for P- and S-waves, respectively. The average ratio $Q_\alpha /Q_\beta$ 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 $Q_0$ 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.

Introduction

Egypt is a land with observable aridity and the Nile River is its primary source of water. To preserve the available surface water resources, Egypt began the construction of the Aswan High Dam (AHD) on the Nile in 1959. The chosen location of the AHD is about 17 km south of Aswan city (square in Fig. 1a). In terms of social, agricultural, and electrical energy generation, it is Egypt’s most important initiative. The significance of this dam stems from the fact that it is a one-of-a-kind situation in the world in which a single dam dominates nearly an entire country in its downstream.

Annual accumulation of the massive amount of water behind the dam creates one of Africa’s largest man-made lakes known as Nasser Lake (NL) and huge reservoirs known as the Aswan High Dam Reservoir (AHDR) (Shahin 1985; Sutcliffe 2009). The reservoir stretches from Egypt’s southern border to Sudan’s northern border and is about 500 km long in total ($\approx$ 350 km inside Egypt).

Following the occurrence of the 1981 earthquake, detailed investigations of regional seismicity and local faults on the AHD were initiated, and a final report was submitted in 1985 by Woodward Clyde Consultants (Consultants 1985), which indicated a possible association of the 1981 earthquake with the NL behind AHD.

The attenuation of the seismic ground motion amplitude is critical in determining the likelihood of heavy ground shaking. When a seismic wave travels across the earth, it loses energy (attenuation). This occurrence is linked to the dispersion of seismic energy as a function of source-receiver spatial distance (Jackson and Anderson 1970; Ghamry et al. 2021). To continuously update seismic hazard estimates, a proper definition of hazard parameters is needed relying on different technologies (Abdalzaher et al. 2020; Abdalzaher and Elsayed 2019). In its most general form, deterministic seismic hazard analysis identifies the seismic source or sources that may have an effect on the AHD location and calculates the highest potential earthquake magnitude for any of these sources (Elhadidy et al. 2021; Moustafa et al. 2022b).

In seismic hazard analysis, both seismic wave attenuation and site effects are important. In particular, they can have a significant impact on the appearance and spectral form of seismograms, influencing the low-frequency level and obstructing the determination of the corner frequency. To mitigate and continuously update (AHD) seismic hazard estimates, a proper definition of hazard parameters in particular attenuation is needed. This issue is exacerbated in the analysis of microearthquakes since the higher frequencies used to identify the smaller seismic sources are heavily influenced by seismic wave attenuation and near-surface site impact (Reiter 1991; Moustafa and Takenaka 2009; Moustafa et al. 2016). Therefore, proper knowledge of these mechanisms is required for the appropriate determination of source dimensions (Stirling et al. 2013; Thingbaijam et al. 2017; Moustafa et al. 2021a).

Some previous studies have examined crustal attenuation in the Aswan area. Investigations on attenuation of seismic waves were performed by using both coda waves (Mohamed et al. 2010; Mukhopadhyay et al. 2016) and direct P- and S-waves (Mohamed 2019a). These studies showed that the effect of attenuation on seismic radiation at the Aswan reservoir is considerable. Hence, the evaluation of seismic attenuation is the main goal of the current study for the quantitative estimate of the seismic source parameters which control the propagation of elastic waves and the source processes acting inside the (AHD) reservoir. Attenuation characteristics have been estimated to understand the effect of heterogeneity in the tectonically active Aswan Reservoir region of Egypt.

In the present work, attenuation characteristics considering P- and S-spectra are obtained for the Aswan region based on recorded ground motions using data collected by Aswan Local Seismological Network (ALSN) operating across the reservoir to understand the attenuation characteristics as well as the tectonic activity beneath the (AHDR) region. These characteristics will serve as an integral part of developing a synthetic ground motion model for better assessment of future seismic hazards. It has to be highlighted here that the study area of Aswan has experienced numerous damaging earthquakes in the recent past both from nearby and far sources as in Fig. 1a, b (Deif et al. 2009; Consultants 1985). Thus, the development of a regional synthetic ground motion model for Aswan based on proposed seismic wave attenuation can definitely help towards assessment of future seismic hazards which may help in controlling damages during future earthquakes.

Recently, machine learning (ML) techniques have been developed to address a variety of research issues (Abdalzaher et al. 2021a, 2022b; Moustafa et al. 2021b). This has increased interest in using different (ML) techniques to solve a variety of difficult research challenges. Due to the limitations of traditional techniques’ models, (ML) tools can be used to generate extremely complicated relational models (Abdalzaher et al. 2021b; Hamdy et al. 2022). Varieties of (ML) techniques have been employed to solve several problems in seismology such as location and magnitude determinations (Abdalzaher et al. 2021c) as well as corresponding homogenization (Moustafa et al. 2021c) and discrimination between earthquakes and man-made explosions (Abdalzaher et al. 2022).

To improve our understanding of seismic attenuation qualities in the (AHDR) area, the Tsujiura approach (Tsujiura 1996) and supervised machine learning regression technique was integrated to estimate high-frequency P-wave attenuation ($Q_\alpha$) and corresponding S-wave attenuation ($Q_\beta$). In addition, its frequency-dependence relationship is expected to add to our understanding of the seismic attenuation mechanism in this location. The $Q_\beta /Q_\alpha$ ratio and its possible relevance have also been thoroughly investigated. On the basis of the frequency dependence of $Q_\alpha$ and $Q_\beta$ and their ratio $Q_\beta /Q_\alpha$, the probable mechanisms of seismic attenuation are also discussed. The results obtained are compared to those obtained in other local and regional studies to better understand the medium heterogeneity in the (AHDR) region.

The rest of the current research is structured as follows: Sect. 2 presents general features as well as the geological and structural settings of Aswan in general and (AHDR) in particular. The regional seismicity and tectonics in the mapped area are discussed in that section as well. Section 3 discuss previous related work and introduces seismic ground attenuation and supervised machine learning methods implemented, while Sect. 4 describes data collection and processing to estimate individual attenuation parameter at selected stations. Furthermore, Sect. 5 indicates the results and discussion indicating attenuation hazard potential. Finally, the research is concluded in Sect. 6.

Mapped area features

The research area is located in the northern part of the (AHDR) (see Fig. 1a). Tectonically, the Said (1961), have divided the Egyptian territory into four tectonic provinces namely; the hinge zone, the unstable shelf, the stable shelf, and the Arabian–Nubian shield as shown in Fig. 1a. The boundary between the stable and Arabian–Nubian shields cuts the study area into the northern and southern parts. The northern portion of the area locates on the stable shelf which includes the active E–W Kalabsha and Seiyal faults. While the southern part of the study area locates on the Arabian–Nubian Shield. The majority of the fault types are normal and strike-slip faults in this region and run east–west or north–south (Fig. 1c) directions. The E–W trending Kalabsha fault is the most visible active fault indicating right-lateral strike-slip movement. It is also the longest ($\approx$ 300 km) fault and the epicenter of the Aswan earthquake in 1981 (Kebeasy et al. 1987) lies along it (red star in Fig. 1b). The E-W trending Seiyal fault ($\approx$ 90 km long) is about 12 km north of the Kalabsha fault and is also dominated by right-lateral strike-slip movement. These two right-lateral strike-slip faults in the E–W direction embrace a graben structure inside them (Awad and Kwiatek 2005). The N-S faults run roughly parallel to the Aswan Reservoir’s main course. Among them are the Khour El-Ramla fault, which runs parallel to the reservoir’s E–W pattern, as well as the Kurkur, Alburqa, Seiyal, Gazelle, and Abu Dirwa faults (Kebeasy et al. 1987; Awad and Kwiatek 2005) (see Fig. 1c).

The topography has a relief ranging from 150 to 350 ms. The granitic/metamorphic basement is covered by sedimentary rocks with a thickness of around 500 ms. Nubian sandstone, Quaternary calcite, and Nile deposits are among the sedimentary rocks observed in the (AHDR) (Issawi and Hinnawi 1980). Several locations along the western side of the reservoir reveal igneous and metamorphic rocks. Around the fault traces, the Nubian sandstone bed is locally folded into thin anticlines and synclines (Issawi and Hinnawi 1980). The area is geologically diverse, with crustal heterogeneity, crisscrossing fault lines, small-scale sedimentary rock folding, and regional uplift. The crustal thickness in the Aswan region varies between 30 and 35 km (Kebeasy et al. 1987; Awad and Kwiatek 2005; Moustafa et al. 2022a).

Due to the lack of local seismograph stations prior to the November 14, 1981 earthquake along the Kalabsha fault, information on seismicity in the Aswan area was very limited (Kebeasy et al. 1987). After the severe earthquake in 1981, the spatial location of several aftershocks reported using portable stations and a telemetered network clearly suggest that the location of the event occurred beneath Gebel Marawa on the kalabsha fault (Fig. 1b, c). The depth of the aftershocks, as well as a detailed examination of the main shock’s waveform data, indicate that the main shock occurred at a depth of 18-20 km (Telesca et al. 2017). The seismicity of the mapped region is localized in six major clusters areas, as shown in Fig. 1b: (1) Gebel Marawa Zone, (2) East1 of Gebel Marawa Zone, (3) East2 of Gebel Marawa Zone, (4) Khor El Ramla Zone, (5) Abu Dirwa Zone, and (6) Old Stream Zone (Kebeasy et al. 1987; Awad and Kwiatek 2005; Telesca et al. 2017).

Fig. 1

a Regional tectonics and seismicity affecting the mapped area. Square delineates the location of the (AHDR) area. b Spatial distribution of local seismic activity affecting the (AHDR) area as reported by the Egyptian National Seismological Network (ENSN) from 1997 to 2022. Triangles represent the location of seismic stations utilized in attenuation calculation, and c local geology, geomorphology, and tectonic settings of the Aswan region, Adopted and modified after Saadalla et al. (2020)

Related works and methodology

The mechanism by which a seismic wave propagates has a significant impact on the energy of the wave at various distances from the earthquake source. Attenuation is one of the many interesting parameters that characterize the geological medium. Quality factor Q, a dimensionless quantity, is commonly used to assess it. The quality factor calculates the amount of energy that has been dissipated as it travels through the geological medium. Q is inversely proportional to attenuation in general. As a result, seismic waves with lower Q values exhibit greater attenuation (Sato et al. 2012).

Several studies on attenuation by several researchers conclude a linear dependence of Q on frequency between 1 and 25 Hz (Aki 1980). The dependence of Q on frequency is a general feature. The attenuation studies have been done for a number of regions in the world by several investigators (Aki 1980; Eberhart-Phillips et al. 2015; Hauksson and Shearer 2006; Tselentis et al. 2010). The seismic wave attenuation can be estimated by determining the quality factor for P and S waves ($Q_\alpha$ and $Q_\beta$), for surface waves, and for coda waves ($Q_c$).

In Egypt, a number of studies have been observed to estimate seismic wave attenuation. The seismic attenuation of coda waves and the direct S-waves were studied in the Abu Dabbab area, with the purpose of quantifying the amount of intrinsic dissipation and scattering attenuation (Abdel-Fattah et al. 2008). The coda-normalization method was applied to the data set composed of selected earthquakes to investigate the frequency-dependent of $Q_\alpha$ and $Q_\beta$ in the crust beneath the vicinity area of Cairo Metropolitan, Egypt (Moustafa et al. 2002; El-Hadidy et al. 2006; Abdel-Fattah 2009; Badawy and Morsy 2012). For (AHDR), investigations on attenuation of seismic waves were performed by using both coda-waves (Mohamed et al. 2010; Mukhopadhyay et al. 2016) and direct P- and S-waves (Mohamed 2019a).

High frequency attenuation

Attenuation characteristics of seismic waves are measured in terms of the inverse of quality factors (Q).

There are several methods to estimate the attenuation characteristics of seismic waves. One of the most popular methods is known as the Standard Linear Solid (SLS) model (Hao and Greenhalgh 2019). It is a viscoelastic model commonly used to describe the behavior of materials that exhibit both elastic and viscous properties. The SLS model assumes that the material is composed of a series of springs and dashpots that are connected in parallel and in series, respectively. However, to achieve the goals of the current study, a simpler power-law form was preferred to delineate the attenuation characteristics of seismic waves in terms of the quality factors (Q).

There are several reasons why the power law model is a better choice for estimating seismic wave attenuation than the SLS model. Here are some of the key advantages of the power law model: Simplicity: The power law model is a simpler model than the SLS model, with only two parameters to estimate: the quality factor ($Q_0$) and the power-law exponent ($\eta$). This simplicity makes it easier to use and interpret, and it can often provide accurate estimates of attenuation with minimal effort. Greater accuracy: The power law model is more accurate than the SLS model for many types of materials, particularly those with high attenuation. The SLS model assumes that the material’s attenuation is constant over all frequencies, which may not be true for highly attenuating materials. The power law model, on the other hand, allows for attenuation to vary with frequency, which can provide a more accurate estimate of attenuation. Greater flexibility: The power law model is more flexible than the SLS model and can better capture the complex behavior of many materials. The SLS model assumes that the material behaves as a linear viscoelastic solid, which may not be true for many materials. The power law model, on the other hand, allows for a wide range of behaviors and can often provide a better fit to experimental data. Empirical validation: The power law model has been extensively validated against experimental data and has been shown to provide accurate estimates of attenuation for a wide range of materials and frequencies. In contrast, the SLS model has limited empirical validation and may not accurately describe the behavior of all materials (Li et al. 1995).

Overall, the power law model is a simpler, more accurate, and more flexible model for estimating seismic wave attenuation than the SLS model. While the SLS model may be appropriate for some materials and applications, the power law model is generally a better choice for estimating attenuation in seismic wave propagation.

Q measures the wave transmission quality of the medium (Aki 1980) and is a frequency (f)-dependent dimensionless parameter. This value of Q can be expressed as Sato et al. (2012):

$$\begin{aligned} Q(f) = Q_0 \times f^\eta , \end{aligned}$$

(1)

where $Q_0$ is the quality factor at one Hertz and $\eta$ is a numerical constant.

It is worth noting that the power-law model used to describe Q(f) is a widely used model in seismology, and has been shown to be effective in describing the attenuation of seismic waves in a variety of tectonic environments. The power-law model is simple and computationally efficient and has been used in numerous studies to estimate Q-values for seismic waves.

Q value is obtained considering the waveforms of different seismic waves. In order to determine the average attenuation characteristics of any region, attenuation of seismic waves is obtained by considering several seismic waveforms recorded in that region. P- and S-waves are the compressional and shear waves, respectively, generated at the earthquake source and reach directly the recording site.

The method used for estimating $Q_\alpha$ and $Q_\beta$ in the upper 15 km of the crust was estimated by using a spectral ratio method known as the (single-station) method (Tsujiura 1996). Tsujiura’s work (Tsujiura 1996) has been highly cited in the field of seismology and has contributed to our understanding of the properties and behavior of seismic waves. The paper is still considered a valuable resource for researchers studying earthquake seismology and the analysis of seismic data (Mohamed 2019b; Aki and Chouet 1975; Aki 1980).

In essence, the seismograms of relatively far earthquakes have a lower level of high-frequency energy than those of closer earthquakes compared with low-frequency energy (Frankel 1982). This means that the attenuation parameter can be determined by comparing the spectral form of earthquakes at various distances from a single station.

Following this spectral ratio method known as the single-station technique, the observed amplitude A(f) of body waves at a frequency f can be expressed by the relationship (Tsujiura 1996; Frankel 1982):

$$\begin{aligned} A(f) \approxeq \frac{A_0(f) R(f) e^{-\pi f t /Q}}{r}, \end{aligned}$$

(2)

where $A_0(f)$ is the spectral amplitude at the seismic source, R(f) is the site-response function, r is the source-to-receiver distance, and $e^{-\pi f t /Q}$ is the attenuation term with t being the travel time and Q the quality factor.

Having assigned two frequencies $f_1$ and $f_2$, the natural logarithm of the ratio of the corresponding amplitudes can be written as:

$$\begin{aligned} ln \frac{A\left( f_1\right) }{A\left( f_2\right) } = ln \frac{A_0\left( f_1\right) }{A_0\left( f_2\right) } + ln \frac{R\left( f_1\right) }{R\left( f_2\right) } - \frac{\pi \left( f_1 -f_2\right) t}{Q}. \end{aligned}$$

(3)

If $\frac{A_0(f_1)}{A_0(f_2)}$ and $\frac{R(f_1)}{R(f_2)}$ are constant and independent of travel time, the function $ln \frac{A(f_1)}{A(f_2)}$ can be written as:

$$\begin{aligned} ln \frac{A\left( f_1\right) }{A\left( f_2\right) } = C - \frac{\pi (f_1 -f_2)t}{Q}. \end{aligned}$$

(4)

Above equation represents the straight line between ln $\frac{A(f_1)}{A(f_2)}$ and $t(=r/c)$ with slope ($\theta$) given by:

$$\begin{aligned} \theta = - \frac{\pi \left( f_1 -f_2\right) }{Q}. \end{aligned}$$

(5)

The value of Q can be estimated using the above equation. The same value of c (velocity of P- or S-waves) should be used for all the utilized frequencies (Tselentis et al. 2010).

The previous relationships are based on the assumptions that Q is constant over the frequency range studied and that the source spectrum for all earthquakes is identical. The final assumption is that the flat site response factor R(f) over the entire frequency range of the study area is used so that $ln \frac{R(f_1)}{R(f_2)}$ is zero. When microearthquakes with a small magnitude scale are used, the above statement may hold true (Tsujiura 1996; Frankel 1982).

One strength of the previous method is that it is based on a physically motivated model of seismic wave attenuation, which takes into account the intrinsic attenuation of seismic waves as they propagate through a medium. This model is generally applicable to a wide range of geological materials and is not overly sensitive to specific features of the subsurface geology. Therefore, the utilized single-station method can be used to estimate Q values for seismic waves in a variety of tectonic environments (Tsujiura 1996; Frankel 1982). Furthermore, the effectiveness of that method has been demonstrated by its widespread use and validation by other researchers in the field of seismology. For example, a number of studies have used that method to estimate Q values for seismic waves from a variety of earthquake sources, including local and regional earthquakes. These studies have shown that the single-station method is robust to variations in earthquake source characteristics, and can provide reliable estimates of Q values for a wide range of seismic signals (Frankel 1982; Moustafa et al. 2002; Aki and Chouet 1975; Aki 1980; Mohamed 2019b).

Machine-learning regression

Regression is a method for determining how independent variables relate to a dependent feature. It is a technique for machine learning predictive modeling, where an algorithm is used to forecast continuous outcomes. The link between an outcome or dependent variable and independent factors is something that algorithms are trained to grasp. The model may then be used to forecast the results of fresh, unforeseen input data or to complete a data gap.

In the current research, we implemented orthogonal distance regression (ODR) (Boggs and Rogers 1990; Yan et al. 2017) for power law functions. The goal of ODR, also known as generalized least squares regression, is to find the best fit while accounting for errors in both the x- and y-values. assuming the connection. Assuming the relationship $y^* = f(x^*; \beta )$, where $\beta$ are parameters and $x^*$ and $y^*$ are the $true$ values, without error, this leads to a minimization of the sum

$$\begin{aligned} \min _{\beta , \delta } \sum _{i=1}^n \left[ \left( y_i - f(x_i+\delta ; \beta )\right) ^2 + \delta _i^2 \right] , \end{aligned}$$

(6)

which can be interpreted as the sum of orthogonal distances from the data points $(x_i, y_i)$ to the curve $y = f(x,\beta )$. It can be rewritten as:

$$\begin{aligned} \min _{\beta , \delta , \varepsilon } \sum _{i=1}^n \left[ \varepsilon _i^2 + \delta _i^2 \right] . \end{aligned}$$

(7)

Subject to $y_i + \varepsilon _i = f(x_i + \delta _i; \beta )$. This can be generalized to accommodate different weights for the data points and to higher dimensions

$$\begin{aligned} \min _{\beta , \delta , \varepsilon } \sum _{i=1}^n \left[ \varepsilon _i^T w^2_{\varepsilon } \varepsilon _i + \delta _i^T w^2_{\delta } \delta _i \right] , \end{aligned}$$

(8)

where $\varepsilon$ and $\delta$ are m and n dimensional vectors and $w_{\varepsilon }$ and $w_{\delta }$ are symmetric, positive diagonal matrices. Usually, the inverse uncertainties of the data points are chosen as weights.

There are different estimates of the covariance matrix of the fitted parameters $\beta$. Most of them are based on the linearization method which assumes that the nonlinear function can be adequately approximated at the solution by a linear model. Here, we use an approximation where the covariance matrix associated with the parameter estimates is based $\left( J^T J \right) ^{-1}$, where J is the $Jacobian$ matrix of the $x$ and $y$ residuals, weighted by the triangular matrix of the Cholesky factorization of the covariance matrix associated with the experimental data.

The Deming fit is a special case of orthogonal regression which can be solved analytically. It seeks the best fit to a linear relationship between the x- and y-values:$y^* = ax^* +b$, by minimizing the weighted sum of orthogonal distances of data points from the curve

$$\begin{aligned} S = \sum _{i=1}^n \frac{1}{\sigma _\epsilon ^2} \left( y_i - a x_i^* -b\right) ^2 + \frac{1}{\sigma _\eta ^2}\left( x_i - x_i^*\right) ^2, \end{aligned}$$

(9)

with respect to the parameters a, b, and $x_i^*$. The weights are the variances of the errors in the x-variable ($\sigma _\eta ^2$) and the y-variable ($\sigma _\epsilon ^2$). It is not necessary to know the variances themselves, it is sufficient to know their ratio $\delta = \frac{\sigma _{\epsilon }^2}{\sigma _\eta ^2}$.

Error metrics

The coefficient of determination or R-squared ($R^2$) is a statistical measure that represents the proportion of the variance for a dependent variable that’s explained by an independent variable or variables in a regression model. It is the square of the Correlation Coefficient(R). The value of $R^2$ explains to what extent the variance of one variable explains the variance of the second variable. $R^2$ is calculated by the sum of the squared prediction error divided by the total sum of the square which replaces the calculated prediction with the mean as specified in the equation:

$$\begin{aligned} R^2=1-\frac{\sum \left( {y_i}-\hat{y_i}\right) ^2}{\sum \left( y_i-\bar{y}\right) ^2}. \end{aligned}$$

(10)

The sum squared regression is the sum of the residuals squared, and the total sum of squares is the sum of the distance the data is away from the mean all squared. As it is a percentage it will take values between 0 and 1.

For the purpose of determining the convergence to the optimal outcome, several regression models use distance measurements. The Mean Absolute Error (MAE), a fairly straightforward statistic that estimates the absolute difference between actual and forecasted values, is typically utilized. By averaging all data, MAE determines how well the observations match the expectations in a regression. We utilize the absolute value of the distances to correctly account for negative errors. MAE is defined as

$$\begin{aligned} \textrm{MAE} = \frac{1}{n} \sum _{i=1}^{n} \left( {y_i}-\hat{y_i}\right) . \end{aligned}$$

(11)

In the current research, $R^2$ and (MAE) are utilized to determine how well the ODR model fits the dependent variables.

Experimental design

The variation of the Q structure can be significant among rocks with the same composition but different levels of fracturing, saturation, and thermal anomalies. Furthermore, the response of rocks to the propagation of longitudinal waves (P-waves) differs from that of shear waves (S-waves), which highlights the importance of knowledge about the quality factors $Q_\alpha$ and $Q_\beta$, respectively, for the characterization of the physical state of rocks. In this paper, we present a systematic investigation of seismic attenuation and the corresponding Q structure, which is derived from the spectral analysis of P- and S-waves. Using seismic spectra of P- and S-waves and a spectral ratio procedure (Tsujiura 1996), the quality factor Q is calculated. Our study is carried out using a single-station spectral ratio technique in the frequency range of 1–20 Hz. The single-station spectral ratio technique uses the division of the amplitude spectra of seismic signals recorded at different frequencies to obtain the spectral ratio. $A(f_1)$ and $A(f_2)$ are the spectral ratios obtained by dividing the P- and S-wave amplitude spectra at two different frequencies ($f_1$ and $f_2$) for a given earthquake event. The difference between A(f1) and A(f2) can be attributed solely to the difference in frequency, as the amplitude spectra of the P- and S-waves were obtained from the same earthquake event and the same stations. In this study, $A(f_2) = 2.5$ Hz, while $A(f_1)$ varies from 5-20 Hz. In high-frequency ranges ( 1 Hz), it is a common observation that the average Q value increases with frequency and can be expressed as a power law given in Eq. 1 In this equation, $Q_0$ represents the Q value at 1 Hz, and $\eta$ is the frequency-dependent coefficient or exponent that is determined based on the observations.

The research area’s $Q_\alpha$ and $Q_\beta$ variations as a function of frequency are studied in depth using well-located 50 earthquakes that mainly occurred along the Kalabsha fault (Table 1). These events were recorded by ten seismic stations of the $ALSN$, part of $ENSN$, operated by the National Research Institute of Astronomy and Geophysics ($NRIAG$) of Egypt operating in the study area.

Table 1 Hypocentral parameters of the events utilized to estimate seismic P- $Q_\alpha$ and S-wave $Q_\beta$ attenuation

Table 2 Descriptive Statistics of collected data for estimating the seismic P- $Q_\alpha$ and S-wave $Q_\beta$ attenuation

Temporal variations of the local magnitude of the data collected are shown in Fig. 2a and corresponding earthquake depth are depicted in Fig. 2b. Figure 2c displays the scatter plot and histograms of earthquakes’ local magnitude and depth of the collected waveform dataset. The collected data were chosen based on a signal-to-noise ratio for all frequency bands greater than two in P- and S-waves to determine $Q_\alpha$ and $Q_\beta$. All of the earthquakes used in estimating $Q_\alpha$ and $Q_\beta$ have a tectonic origin with high-frequency content, sharp first arrivals, and clear S-phases, which are compatible with double-couple source mechanisms.

The Q estimation method utilized in this study is based on the technique developed by Tsujiura (1996). In this study, the quality factor (Q) was estimated from 350 waveforms using the frequency-dependent attenuation spectra of P- and S-waves from 50 earthquakes. The attenuation power law functions were fitted using a supervised machine learning algorithm known as ODR, and the estimates of $Q_\alpha$ and $Q_\beta$ showed a clear dependence on frequency. The spectral ratio technique was applied to bandpass-filtered seismograms, which allowed for a more accurate estimation of ground motion frequency-dependent attenuation. This technique removes the effect of source and site amplification and isolates the propagation term. As described by Frankel (1982), the core of the method is the observation that seismograms of distant earthquakes exhibit a smaller amount of high-frequency energy relative to low-frequency energy in comparison to waveforms of nearby earthquakes. This observation implies that changes in the spectral shape of earthquakes at varying distances from a single station can be utilized to determine the attenuation parameter.

Fig. 2

a Local magnitude temporal variation. b Earthquake depth temporal variation and c variation of earthquake local magnitude with Depth of collected waveform dataset

Figure 3 depicts the utilized seismic stations, the implemented events, and the ray paths between the events and the stations in this analysis. Three-component Trillium-40 broadband sensors were used in the network. All waveform data were recorded at a sampling rate of 100 samples/s.

The earthquakes occurred within the network with a maximum epicentral distance of 85 km and a focal depth of 7 km. The local magnitudes of these events vary between 1.5 and 3.2. Tables 1 and 2 contain the specifics and descriptive statistics of these occurrences, while Fig. 3 depicts the spatial distribution of these stations as well as the epicenter locations of the earthquakes used in this analysis.

Fig. 3

a Map of $AHDR$ showing the ray traces used to study the spatial variations of the seismic waves attenuation. Seismic stations are represented by green triangles while earthquakes are distinguished by red circles. Variations of reported depths of the utilized events with respect to Latitude (b) and Longitude (c)

Figure 3 which, shows the ray-paths coverage of the earthquakes utilized to study the spatial variations of the seismic attenuation along the mapped (AHDR) area clearly indicates that with respect to events’ spatial resolution, the investigated reservoir area is almost covered with ray-paths, which lead to a better understanding of the crustal heterogeneity affecting seismic wave attenuation determinations.

To prevent contamination from S-waves, we used a two-second window for P-waves recorded on the vertical component to perform the spectral analysis of body waves for the selected earthquakes. Another two-second window was chosen for S-waves, which were recorded on the horizontal components in order to estimate corresponding spectra. The baseline was corrected by subtracting the mean from the raw data as the first step in processing to eliminate long-period biases before applying the fast Fourier transform (FFT). We applied a smoothing 10% cosine taper window on both ends of the signal with a width of 25% of the full-time length before estimating the corresponding displacement spectra using the (FFT). The resulting spectra have a relatively smooth low-frequency response below the corner frequency and a sharp fall-off above the corner frequency. Figure 4 depicts single-event seismograms and associated P-wave displacement spectra.

Fig. 4

Example for event 2011-07-18_21:07:05 sample waveforms recorded at stations NWKL and NGMR, along with 2-s windows shown for estimation of P-, and S-wave quality factors using the spectral ratio method of the displacement spectra. a, c Z-component; b, d E–W component

The method makes two assumptions: (1) Q denotes the average quality factor between frequencies $f_1$ and $f_2$, and (2) the ratio of source spectral amplitudes at these frequencies $f_1$ and $f_2$ is the same for all analyzed earthquakes. The second assumption is valid for earthquakes that lie in small magnitude ranges. In the estimation of the average Q, the average radiation pattern is considered to have a negligible contribution. In this study, the lower frequency ($f_2$) was fixed at 2.5 Hz, while the higher frequency ($f_1$) was varied (from 5, 7.5, 10, 12.5, 15, 17.5, and 20 Hz) to determine the ratios of spectral amplitudes at $f_1$ and $f_2$ for earthquakes at varying distances from a single station. The method used in the present study relies on the observation that the high-frequency energy in seismograms of earthquakes that are relatively distant is smaller compared to the low-frequency energy when compared to those of nearby earthquakes (Frankel 1982). This implies that the change in the spectral shape of earthquakes at different distances from a single station can be utilized to determine the attenuation parameter. The method assumes that Q is the average quality factor between the frequencies $f_1$ and $f_2$, and the ratio of source spectral amplitudes at these frequencies $f_1$ and $f_2$ is the same for all the earthquakes analyzed. The values of $Q_\alpha$ and $Q_\beta$ are obtained from the slope of the linear regression line fitted to the plot of the logarithm of spectral ratio versus travel time, as per Eq. 4. We calculated $Q_\alpha$ and $Q_\beta$ by utilizing The ODR to perform linear regression analysis between $ln \frac{A(f_1)}{A(f_2)}$ and time t for each frequency. The errors in the estimates of $Q_\alpha$ and $Q_\beta$ are determined using the method of regression, where the standard error is given by the standard deviation divided by the square root of n, where n is the number of observations of P- or S-waves. This procedure is commonly used in several studies to determine $Q_\alpha$ and $Q_\beta$ for various regions of the world (Frankel 1982; Moustafa et al. 2002; Mohamed et al. 2010; Mahood 2014).

Results and discussions

In order to conduct investigations on the attenuation of high-frequency seismic waves in the (AHDR) area, 50 well-located earthquakes and sharp initial arrivals were investigated utilizing the single-station spectral ratio method (Tsujiura 1996). A ten-station network (Figs. 1b and 3a) operating in the research region was used to capture these incidents. Figure 3 and Table 1 give the specifics of these occurrences.

To perform the spectral analysis of body waves for the selected earthquakes, two seconds windows were chosen for P- and S-waves. A Konno-Ohmachi smoothing algorithm proposed by Konno and Ohmachi (1998) which achieves a uniform-span smoothing to frequency spectra in logarithmic scale was applied to both ends of the signal for a width of 25% of the full-time length to increase the stability of the results. Displacement spectra were computed by $FFT$. In all frequency ranges, the data set was chosen because the signal-to-noise ratio was larger than 2. These earthquakes have a relatively smooth low-frequency response below the corner frequency and a quick fall-off above the corner frequency, as seen in their spectra depicted in Fig. 4. Examples of seismograms collected at (NKWL) and (NGMR) three-component stations, together with corresponding P- and S-wave displacement spectra for an event that occurred in July 2011 are given in Fig. 4.

To evaluate Q, the relation given in equation 4 between the natural logarithm of the ratio of the amplitude $\frac{A(f_1)}{A(f_2)}$ and travel-time t was used. The previous relation is based on the assumptions that Q is constant across the frequency band investigated and that the source spectra for all earthquakes are comparable. When microearthquakes of a small magnitude range are employed, the latter assumption may be true. For this research, we picked a sample of 50 earthquake occurrences with local magnitude ranging between 1.5 and 3.2 to fulfill the criteria of constant Q. We set $f_2$ = 2.5 Hz and let $f_1$ range between 5 and 20 Hz. The $Q_\alpha$ and $Q_\beta$ values were calculated from the slopes of the fitted regression lines as can be seen in Figs. 5 and 6.

Fig. 5

Example of ODR estimates of the S-wave quality factor $Q_\beta$ at station NGMR, with $f_2$ = 2.5 Hz, and $f_1$ ranging between 5 and 20 Hz

Fig. 6

Example of ODR model estimates of the P-wave quality factor $Q_\alpha$ at station NGMR, with $f_2$ = 2.5 Hz, and $f_1$ ranging between 5 and 20 Hz

Orthogonal Distance Regression (ODR) was performed with possibly non-linear fitting functions. A modified trust-region Levenberg-Marquardt type algorithm (Levenberg 1944; Marquardt 1963) implemented in the scientific computation library (Scipy), was utilized to solve Eq. 4. The Levenberg–Marquardt technique makes use of the steepest descent algorithm’s favorable starting and the Gauss-Newton algorithm’s quick convergence to identify the minima so that sum the of squares of the residuals (difference between the observed and the model estimated data) is minimized. The starting model used to begin optimization in the Levenberg-Marquardt technique is derived from the solution of the standard linear technique.

Figures 5 and 6, highly confirm that, for all frequency bands, the dispersion of data points around the regression line is modest. Tables 3 and 4 show the estimated $Q_\alpha$ and $Q_\beta$ as well as the standard deviation values derived at center frequencies in the middle of each investigated bandwidth. The standard deviation does not surpass 20% in most cases.

Table 3 $Q_\alpha$ values and relative errors ($1\sigma$) at different seismic stations and central frequencies, obtained by spectral ratios with $f_2$=2.5 Hz and $f_1$ ranging between 5 and 20 Hz

Table 4 $Q_\beta$ values and relative errors ($1\sigma$) at different seismic stations and central frequencies, obtained by spectral ratios with $f_2$=2.5 Hz and $f_1$ ranging between 5 and 20 Hz

There are 619 such Q-values which vary from 35 to 118 at 5 Hz and 114 to 369 at 20 Hz for $Q_\alpha$ and from 47 to 76 at 5 Hz and 275 to 434 at 20 Hz for $Q_\beta$. The average $Q_\alpha$ and $Q_\beta$ versus frequency inferred in this study using $QDR$ machine learning algorithm for all seismic stations are shown in Fig. 7.

Fig. 7

$Q_\alpha$ and $Q_\beta$ versus frequency inferred in this study using $QDR$ machine learning algorithm for all seismic stations

When we examine the Q-values acquired at each station and frequency, we can see that, at least at low frequencies, the stations in the southern part provide lower values than the ones in the central and northern sectors which represents the average attenuation characteristics for the (AHDR) and the surrounding region. The increase in Q-values with increasing frequency indicates the frequency-dependent nature of the Q estimates in the region. Estimated $Q_\alpha$ and $Q_\beta$ are usually lowered due to the presence of a significant degree of cracking and/or the presence of melt and fluids in the cracks in the mapped area. The occurrence of azimuth variation of Q-values owing to the presence of substantial lateral heterogeneities impacting the $AHDR$ region might be suggested by the observed minor variations among closely adjacent stations. Obtained Q-values are considered as a tectonic characteristic, with low Q-values indicating significant tectonic activity against high Q-values indicating stable zones.

To obtain the frequency-dependent relations, previously estimated $Q_\alpha$ and $Q_\beta$ values as a function of frequency derived at center frequencies in the form $Q=Q_0 \, f^\eta$ are utilized to develop the average attenuation law at each utilized station as given in Table 5. The obtained $Q_0$ represents the level of medium heterogeneities and $\eta$, power of frequency dependence, represents the level of tectonic activity of the region. These best-fitting lines are shown in Fig. 8 for (NGMR), (NNAL), (NWKL) and (NKUR) for both $Q_\alpha$ and $Q_\beta$. For each individual station, there was a substantial difference in the obtained $Q_\alpha$ and $Q_\beta$ values. Fluctuations in attenuation are reflected in such variations. The occurrence of fluid-filled fractures and/or partial melts might explain this difference. From a comparison of $\eta$ and $Q_0$ values (Table 5) for (AHDR) that the area is more diverse and less stable than the adjacent (AHDR).

Fig. 8

Logarithmic relations between $Q_\alpha$, $Q_\beta$ and frequency according to power low $Q = Q_0 \, f^\eta$ for NGMR, NNAL, NWKL and NKUR stations

Table 5 Estimation of $Q_\alpha$ and $Q_\beta$ according to power low $Q = Q_0 \, f^\eta$ for individual stations utilized in the current study

The obtained values of $\eta$ for most of the stations range between 0.85 and 1.4, which are almost identical to those found in the Koyna reservoir area and in tectonically active and complex locations (Shahin 1998). The dispersion of the data around the regression line is higher at low frequencies than at high frequencies. The dispersion of data around the regression line is bigger for the P-wave than for the S-wave, as seen in Figs. 5, 6, and 8. This might be related to the fact that the magnitude of the earthquakes utilized for the analysis varied, and because the source radiation pattern of P-wave radiation differed for various events, we even included small magnitude occurrences. Another explanation for the significant dispersion of P-wave data might be the difference in source radiation patterns of P- and S-waves.

To develop the general attenuation for the mapped region, individual stations we utilized in regression analysis as shown in Fig. 9a for P-wave and Fig. 9c for S-wave. Table 6 shows the results of fitting a linear model to describe the relationship between $Q_\alpha$ and f. The equation of the fitted model is $Q_\alpha = 9.54 \pm 2.06 f^{1.15 \pm 0.075}$. Since the P-value in the ANOVA table is less than 0.05, there is a statistically significant relationship between $Q_\beta$ and f at the 95.0% confidence level. The R-Squared statistic indicates that the model as fitted explains 99.1964% of the variability in $Q_\beta$.

Fig. 9

Average P-, and S-wave quality factors using the spectral ratio method of the displacement spectra (a, c). Corresponding regression residual plots (b, d)

Table 6 Average estimated values of $Q_\alpha$ and $Q_\beta$ in $AHDR$ region

The correlation coefficient equals 0.995974, indicating a relatively strong relationship between the variables. The standard error of the estimate shows the standard deviation of the residuals to be 0.020736. This value can be used to construct prediction limits for new observations by selecting the Forecasts option from the text menu. The mean absolute error (MAE) of 0.0168538 is the average value of the residuals. The Durbin–Watson (DW) statistic tests the residuals to determine if there is any significant correlation based on the order in which they occur in your data file. Since the P-value is greater than 0.05, there is no indication of serial autocorrelation in the residuals at the 95.0% confidence level.

In addition, Table 6 also shows the results of fitting a linear model to describe the relationship between $Q_\beta$ and f. The equation of the fitted model is $Q_\beta = 9.89 \pm 1.89 f^{1.14 \pm 0.075}$. For P-wave, the obtained relation between $Q_\alpha$ and f is $Q_\alpha = 11.22 \pm 2.2 f^{1.09 \pm 0.075}$. Since the P-value in the ANOVA table is less than 0.05, there is a statistically significant relationship between $Q_\beta$ and f at the 95.0% confidence level. The R-Squared statistic indicates that the model as fitted explains 96.7659% of the variability in $Q_\beta$. The correlation coefficient equals 0.983697, indicating a relatively strong relationship between the variables. The standard error of the estimate shows the standard deviation of the residuals to be 0.0435496. This value can be used to construct prediction limits for new observations. The mean absolute error (MAE) of 0.0368356 is the average value of the residuals. The DW statistic tests the residuals to determine if there is any significant correlation based on the order in which they occur in your data file. Since the P-value is greater than 0.05, there is no indication of serial autocorrelation in the residuals at the 95.0% confidence level.

The average general attenuation laws obtained in this study for the (AHDR) region show values of $Q_\alpha$ and $Q_\beta$ that are strongly frequency dependent, indicating that attenuation at low frequencies is more prominent than at higher frequencies, which is a feature of tectonically active zones with complex structures (Giampiccolo et al. 2003). Moreover, it is also may be owing to the occurrence of heterogeneities on several scales in the region, such as faulting, folding, crustal movements, uneven subsurface geometry, and differences in rock characteristics (Sato et al. 2012). The $Q_\beta$ attenuation values found in this investigation for the S-waves coincide with the coda attenuation ($Q_c$) determined in previous research for this location (Mohamed et al. 2010; Mukhopadhyay et al. 2016). At most lapse duration and window length combinations, the frequency dependence of the S-waves is comparable to that of the coda waves (Mukhopadhyay et al. 2016; Mohamed 2019a). The S-wave and coda wave have similar frequency dependence, implying that the coda is predominantly made of S-waves (Aki 1980).

One of the more interesting aspects of the induced seismicity in the Aswan region is the possible role that the Nubian sandstone plays in the control of the small-size earthquake activity. The sandstone surrounding the reservoir area is highly porous (25%) and relatively permeable compared to the underlying granite. As the reservoir fills, the expanding area of the reservoir and the rising water level allow water to seep into the sandstone, thus the local water table raises. Because of the impermeable basement, the water is confined to the westward thickening sandstone lens. The seismicity is concentrated on the Kalabsha fault zone at the intersection between the E–W and N–S fault trends, particularly along its most eastern segment, which is located beneath a large area covered by water. However, the E–W Kalabsha fault system controls the seismicity in the region. The role of the reservoir water loading, as a supplementary source of earthquake events in the region, cannot be neglected. Therefore, it can be understood that the earthquake activity in the area originated tectonically and the water variation works as an activation medium in triggering small earthquakes.

Comparing the results obtained through the current study and the previous studies done by Mukhopadhyay et al. (2016); Mohamed et al. (2010) in the study area shows an agreement as shown in Fig. 10. For $Q_\alpha$ there is a great matching between the results obtained in the current study and the results obtained by Mohamed (2019a). This similarity indicates the applicability of using machine learning algorithms used in the current study.

Fig. 10

a Q$_\alpha$ comparison with local studies and b Q$_\beta$ comparison with local studies

Fig. 11

a Q$_\alpha$ comparison with international studies and b Q$_\beta$ comparison with international studies

Fig. 12

a Q$_\beta$/Q$_\alpha$ comparison with local studies and b Q$_\beta$/Q$_\alpha$ comparison with international studies

Another comparison between the results obtained in the current study and the similar studies performed in different countries as de Lorenzo et al. (2013), Mahood (2014), Padhy et al. (2011), Pezeshk et al. (2018), Sedaghati et al. (2019), Yoshimoto et al. (1993) for the regions Umbria Marche, Italy, East Central Iran, Andaman Sea, New Madrid, Central Asia, and Kanto Japan, respectively. Figure 11 shows the obtained values of Qalpha and Qbeta are similar to the results obtained by de Lorenzo et al. (2013) for the Umbria–Marche region in Italy. This similarity is attributed to the correspondence between geological, tectonic, and seismological conditions.

In de Lorenzo et al. (2013), the authors studied the attenuation characteristics of the Umbria-Marche region in Italy. The $Q_\beta /Q_\alpha > 1$ in the Umbria-Marche region in Italy is similar to the ratio in Aswan as shown in Fig. 12. They also concluded that attenuation characteristics in this region are mainly controlled by the high degree of lateral heterogeneity as in Sato et al. (2012); Bianco et al. (1999), and the presence of pore fluids in the upper crust. This situation occurs in ADHR where (Saadalla et al. 2020; Metwaly et al. 2006) confirmed the impact of Lake Nasser on the groundwater occurrence in the study area. In Metwaly et al. (2006), the authors used the geophysical methods to study the impact of the water in Lake Nasser on the subsurface aquifers as follows; (1) The groundwater is exploited from Nubia sandstone aquifer which is built up of Sabaya and Abu Simbel sandstone aquifers. (2) The groundwater level increases upward with the increasing water level of Lake Nasser. (3) The groundwater salinity decreases with time-related to the seepage of fresh water from Lake Nasser. (4) The hypothetical salts in groundwater and Lake Nasser water are the same indicating that the groundwater in the study area recharges directly from Lake Nasser. Also, the authors in Saadalla et al. (2020) mentioned that Lake Nasser recharges the aquifer in the Aswan region with a large amount of water causing an increase in the groundwater level in the upward direction in Aswan and decreasing the water salinity. The underground reservoir in Aswan is composed of Abu Simble and Sabaya formations which are characterized by a high hydraulic permeability. Structure heterogeneity created by the high seismic activity may bring a remarkable increase in attenuation (Yoshimoto et al. 1998). This exactly coincides with the study area, which is tectonically complex with a high density of faulting and the presence of pore fluids. Also, the basement relief map compiled by Saadalla et al. (2020) shows that the altitude of the surface of the basement varies from + 20 to – 380 ms. Figure 13 shows that the calculated $Q_{\beta }/Q_{\alpha }>1$, as NSKD, NNMR, and MABD stations, for the stations located close to the E–W active faults, e.g., Kalabsha and Seiyal. On the other hand, stations that are located close to the N-S faults show $Q_{\beta }/Q_{\alpha }<1$ as NMAN stations.

Fig. 13

Q$_\beta$/Q$_\alpha$ distribution in the study area. Red triangles represent the stations with Q$_\beta$/Q$_\alpha >1$, while the black ones represent Q$_\beta$/Q$_\alpha <1$

From the obtained results we can confirm that the attenuation characteristics of the P and S- waves in the study area are frequency dependent and the $Q_\beta /Q_\alpha$ ratio distribution in the study area depends on the relation between the seismological stations and the E–W active faults as shown in the figure. where the stations that have $Q_\beta /Q_\alpha > 1$ located close to the source of the November 1981, earthquake, e.g., NSKD, NGRW, and NAHD stations or close to the active E–W faults located in the study area as MABD station. This indicates that scattering is an important factor affecting the attenuation of the body waves in Aswan, Egypt.

The Coda normalization method has been used to obtain the frequency-dependent attenuation features ($Q_\beta$) of the body waves by Mohamed et al. (2010). The estimated $Q_\beta$ values in the region are found to be having significant frequency dependence. The values of $Q_0$ and n for $Q_\beta$ show that attenuation characteristics of the Aswan Lake region lie close to seismically active regions of the world caused by tectonic earthquakes. Unlike Koyna, India, which is another region that shows reservoir-induced seismicity and where a similar study was carried out, the attenuation characteristics of Aswan Lake are more similar to the tectonically active region. It is to be suggested that the seismicity in the Aswan Lake region is described as a combination of tectonic and reservoir-induced seismicity and to confirm the conclusion as mentioned by Deif et al. (2009).

Based on the focal depths, the authors in Deif et al. (2009) classified the seismicity in Aswan into two clusters. The first is characterized by a smaller magnitude range and a shallower focal depth (less than 10 km). but, the second cluster is located deeper (15–25 km) and closer to the site of the 1981 main shock. The occurrence of the 1981 earthquake and continuing seismic activity near the Kalabsha embayment of Lake Nasser was initially identified as possibly being triggered by the presence of the reservoir (Kebeasy et al. 1987). In Consultants (1985), a study carried out detailed geological investigations and concluded that the Aswan area is affected by Quaternary tectonic activity along a few E–W and N–S faults crossing the area and the reservoir itself does not produce earthquakes, but it triggers the release of pre-existing stress stored in the earth’s crust. The shallower activity beneath the lake showed a larger correlation with the water level variations on the lake compared with the deeper activity. Both water load and pore pressure effects played a major role in triggering the shallower activity (Consultants 1985; Abou Elenean 2007), while the pore pressure has a greater role in triggering deeper activity.

Conclusions

The current study’s aim was to explain the attenuation properties in the crust underneath the AHDR region using different sections of seismograms. The quality factor (Q) expresses the attenuation of seismic waves and aids in interpreting the physical rules governing the transmission of an earthquake’s elastic energy through the lithosphere (Aki 1980; Sato et al. 2012). Previous research on attenuation near the AHDR region has been reported by Mohamed et al. (2010); Mukhopadhyay et al. (2016). Using earthquake waveform data, they calculated the distance dependence of coda Q. To improve our understanding of seismic attenuation in the AHDR area, we used the spectral ratio approach (Tsujiura 1996) to estimate frequency-dependent attenuation for P and S waves ($Q_\alpha$ and $Q_\beta$) in the reservoir region using 50 local earthquakes reported by the ENSN broad-band stations between 2011 and 2015. The applied approach allows for a more accurate estimation of ground motion frequency dependence attenuation by removing the effect of source and site amplification and isolating the propagation term. Despite the fact that the current study is based on a small data set, the generated attenuation relationship gives firsthand information on the AHDR region’s seismic wave attenuation properties. By taking into account a wider data set of local earthquakes, Q may be refined.

The estimated Q values of AHRD indicate that the attenuation is greater in high-tectonic areas. We found the frequency-dependent relations in the form of $Q_\alpha = 0.025$ and $Q_\beta = 0.019$. These results indicate high $Q_\alpha$ and $Q_\beta$ values, which correspond to those of the seismically active area in the world. The results from this work provide an attenuation function that can be used in a variety of scientific and engineering applications including local magnitude estimates and earthquake hazard assessment in populated areas, understanding the physical laws related to the propagation of the elastic energy of an earthquake through the lithosphere. Despite the fact that the current study is based on a small data set, the generated attenuation relationship gives firsthand information on the AHDR region’s seismic wave attenuation properties. By taking into account a wider data set of local earthquakes, Q-values may be refined.

The comparisons compiled in the current study approved that ADHR is mainly affected by tectonic earthquakes and also the possibility of occurring of small reservoir-induced seismicity is possible. Also, fluid occurrence in the pores is affecting the attenuation characteristics in the study area. the occurrence of such fluids is confirmed by Metwaly et al. (2006). And it has a direct relation to the water level in Lake Nasser.

It is worth mentioning that the proposed method has not been tested on model data, but it is important to note that the method was validated using field data from a real earthquake, which provides some confidence in its effectiveness. Additionally, the proposed method builds upon well-established techniques for estimating Q values and uses a robust statistical framework to ensure reliable results. While further testing on model data may be necessary to fully evaluate the method’s performance, the available evidence suggests that it is a promising approach for estimating Q values from seismic data. However, we understand the importance of validating the method on model data as well, and we plan to conduct such tests in future studies. We believe that this will help to further validate our approach and provide a more comprehensive understanding of its capabilities and limitations.