Shear-wave attenuation (Qβ) in Northwestern Baja California from spectral ratios and inversion analysis
Atenuación de ondas transversales (Qβ) en el noroeste de Baja California a partir de tasas espectrales y análisis de inversión
Luis Munguía1,*, Rogelio Arce1
1 División de Ciencias de la Tierra, Centro de Investigación Científica y de Educación Superior de Ensenada (CICESE). Carretera Ensenada-Tijuana 3918, Zona Playitas, 22860. Ensenada, Baja California, México.
* Corresponding author: (L. Munguía) This email address is being protected from spambots. You need JavaScript enabled to view it.
How to cite this article:
Munguía, L., & Arce, R., (2026). Shear-wave attenuation (Qβ) in Northwestern Baja California from spectral ratios and inversion analysis: Boletín de la Sociedad Geológica Mexicana, 78(2), A121125. https://doi.org/10.18268/BSGM2026v78n2A121125
Manuscript received: July 29, 2025. Corrected manuscript received: October 18, 2025. Manuscript accepted: October 28, 2025.
ABSTRACT
This study presents new estimates of the frequency-dependent shear-wave quality factor (Qβ) for the Peninsular Ranges of Baja California (PRBC), a key segment of the Pacific–North America plate boundary characterized by complex crustal structures and active deformation. Accurate characterization of seismic attenuation is essential, as its proper correction is required to obtain unbiased earthquake source parameters, tomographic images, and ground-motion predictions. The analysis is based on broadband velocity recordings from 16 earthquakes (Mw 4.0–5.2, focal depths 5–15 km) at source-to-site distances of 40–191 km, providing high-quality waveforms with good azimuthal coverage. Two independent methods were applied: (i) joint inversion of multiple-event velocity spectra and (ii) a single-station spectral ratio method using a reference frequency, both based on the geometric mean of the horizontal displacement spectra. The two methods yielded consistent results, with the joint inversion demonstrating greater robustness due to the simultaneous incorporation of multiple events and propagation paths. The joint inversion produced a power-law relationship Qβ = 41.2 (± 0.20) f 0.84(± 0.08) over 2–31 Hz, while the reference-frequency method yielded a nearly identical model, Qβ = 41.3 (± 0.20) f 0.84 (± 0.08), within the 8–20 Hz range where a clear linear trend was observed. The resulting attenuation parameters are consistent with previous models for the region, confirming their reliability and internal consistency. These findings establish robust and regionally representative attenuation constraints for the PRBC, improving understanding of crustal heterogeneity and energy dissipation mechanisms. The results provide quantitative evidence of moderate to high crustal attenuation (Qβ ≈ 250–350 at 10 Hz) and extend the frequency coverage and stability of Qβ estimates. Overall, the proposed model offers reliable attenuation parameters for use in regional seismological and earthquake-engineering applications.
Keywords: Frequency-dependent Qβ, seismic attenuation, spectral ratio method, inversion analysis, northwestern Baja California.
RESUMEN
Este estudio presenta nuevas estimaciones del factor de calidad de ondas S dependiente de la frecuencia (Qβ) para las Sierras Peninsulares de Baja California (PRBC), un segmento clave del límite de placas Pacífico–Norteamérica caracterizado por estructuras corticales complejas y deformación activa. La caracterización precisa de la atenuación sísmica es fundamental, ya que su corrección adecuada permite obtener parámetros de fuente, imágenes tomográficas y predicciones de movimiento del terreno libres de sesgos. El análisis se basa en registros de velocidad de banda ancha correspondientes a 16 sismos (Mw 4.0–5.2, profundidades focales de 5–15 km) con distancias fuente–sitio entre 40 y 191 km, que proporcionan formas de onda de alta calidad y buena cobertura azimutal. Se aplicaron dos métodos independientes: (i) la inversión conjunta de espectros de velocidad de múltiples eventos y (ii) el método de razón espectral de una sola estación con frecuencia de referencia, ambos basados en el promedio geométrico de los espectros de desplazamiento horizontal. Ambos métodos produjeron resultados consistentes, siendo la inversión conjunta más robusta por incorporar simultáneamente múltiples eventos y trayectorias de propagación. Esta inversión produjo una relación tipo ley de potencia Qβ= 41.2 (± 0.20) f 0.84(± 0.08) en el intervalo 2–31 Hz, mientras que el método de frecuencia de referencia generó un modelo prácticamente idéntico, Qβ = 41.3 (± 0.20) f 0.84 (± 0.08) en el rango 8–20 Hz, donde se observó una clara tendencia lineal. Los parámetros de atenuación obtenidos concuerdan con modelos previos, confirmando su confiabilidad y consistencia interna. Estos resultados establecen restricciones de atenuación robustas y representativas para la PRBC, aportando evidencia cuantitativa de una atenuación cortical moderada a alta (Qβ ≈ 250–350 a 10 Hz). El modelo propuesto mejora la comprensión de la heterogeneidad cortical regional y proporciona parámetros confiables para aplicaciones sismológicas e ingenieriles.
Palabras clave: Qβ dependiente de la frecuencia, atenuación sísmica, método de tasa espectral, análisis por inversión, noroeste de Baja California.
1. Introduction
This study focuses on estimating the shear-wave quality factor Qβ in the Peninsular Ranges of Baja California (PRBC ), located in the western sector of northern Baja California. Due to the region’s persistent seismic activity, a detailed characterization of subsurface properties—including the attenuation of seismic waves—is essential for improving our understanding of wave propagation and associated seismic hazards.
The seismic quality factor Qβ quantifies the attenuation of shear (S) waves as they propagate through the Earth’s crust, capturing the combined effects of intrinsic absorption and scattering. Higher Qβ values correspond to lower attenuation and more efficient wave propagation, making this parameter essential for characterizing lithospheric properties and modeling seismic wave behavior. Two prior studies have investigated seismic wave attenuation in the PRBC. Rebollar et al. (1985) analyzed direct S-waves and coda waves from local earthquakes (M 3–4) recorded at short epicentral distances (≤ 30 km). From coda waves, they obtained a frequency-dependent attenuation relationship of the form Q ( f) = 37 f 0.87 in the 3–24 Hz range. For direct S-waves, they reported Q = 13 f 1.03 for short lapse times (shallow paths) and Qβ = 70 f 0.74 for longer lapse times (sampling deeper crustal layers). These findings indicate that seismic quality factor Qβ tends to increase with both depth and frequency in the shallow crust. In contrast, Castro et al. (1997) estimated Qβ from the spectral amplitudes of 34 local earthquakes (M 2.2–4.0) recorded at distances of 20–190 km, finding Qβ = 28.3 f 1.0 in the 0.3–12.6 Hz frequency range. Their results point to scattering as a significant contributor to the observed attenuation in the PRBC.
The goal of the present study is to derive frequency-dependent Qβ values to improve our understanding of seismic wave attenuation in this tectonically active region. The analysis uses high-quality broadband recordings from the Northwest Mexico Seismic Network (RESNOM), operated by the Centro de Investigación Científica y de Educación Superior de Ensenada, Baja California (CICESE). We first apply a joint inversion technique to estimate Qβ from the spectral amplitudes of velocity seismograms recorded during earthquakes in the study area. To complement this, Qβ is also estimated using the reference frequency method, which effectively removes common source and site effects by assuming they remain approximately constant over narrow frequency bands (e.g., Tsujiura, 1966; Patanè et al., 1994). In this alternative approach, a reference frequency fref is selected from the smooth displacement spectrum—typically at low frequencies (~2-3 Hz) where attenuation is minimal or better constrained. The displacement amplitude at frequency f is then normalized by that at fref, forming the ratio A( f,R)/A( fref ,R), where R is the source-to-receiver distance. Qβ is subsequently estimated from the slopes of the linear trends in the plots of the natural logarithm of the amplitude ratio versus distance at selected frequencies.
This study provides the first well-constrained, frequency-dependent Qβ model specifically for the Peninsular Ranges of Baja California, defining the S-wave attenuation characteristics in a region previously described only by constant-Q or limited local estimates based on lower-magnitude events, short distances, or narrow frequency ranges. The results demonstrate that, when high-quality data are available, both the joint inversion of multiple-event velocity spectra and the single-station reference-frequency method yield highly consistent estimates of Qβ across the analyzed frequency range. Moreover, these findings provide a foundation for future investigations into the spatial variability of Qβ across the region. A more comprehensive understanding of this key parameter will, in turn, facilitate the development of improved regional ground-motion attenuation models, which are critical for evaluating seismic hazards at different distances from earthquake sources.
2. Seismotectonic setting and data
The northern Baja California region encompasses a crucial segment of the transform boundary between the Pacific and North American tectonic plates. Major fault systems, such as the Imperial, Cerro Prieto, Laguna Salada, Indiviso, and San Miguel–Vallecitos faults, accommodate a significant portion of the relative plate motion (Frez and González, 1991; Hauksson et al., 2010; Munguía and Vidal, 1991). These active faults are the source of frequent moderate to large earthquakes (M > 5.0), making the region highly relevant for seismic hazard assessment. Notable historic regional earthquakes are indicated with numbered circles in Figure 1. Circle 1 corresponds to the April 4, 2010 El Mayor–Cucapah earthquake (Mw 7.2), which ruptured the El Mayor–Cucapah fault system (Hauksson et al., 2010; Munguía et al., 2010). Circles 2 and 3 denote the 1979 Imperial Valley (Mw 6.5) and 1980 Victoria (Mw 6.3) earthquakes, located along the Imperial and Cerro Prieto faults, respectively (Anderson et al., 1986; Archuleta, 1984).
In this study, we focus on estimating the shear-wave quality factor Qβ in the Peninsular Ranges of Baja California, located in the western portion of northern Baja California. The seismic history of the region includes the 1954 earthquakes (M 6.0 and 6.3; circles 5 and 4 in Figure 1; Leeds, 1979) and the 1956 San Miguel sequence (M 6.8, 6.1, 6.3, and 6.4; circles 6–9; Doser, 1992; Shor and Roberts, 1958), which together highlight the area’s high tectonic activity. Additionally, in 1975, 1985, and 1988, four moderate earthquakes (5.0 ≤ M ≤ 5.4) occurred in the central PRBC, in the so-called Pino Solo area, situated between the San Miguel and Sierra Juárez faults (González, 1987; Vidal and Munguía, 1991; Vidal et al., 2010).
Figure 1 shows the epicentral locations of the earthquakes analyzed in this study (blue circles), as reported in the RESNOM catalog for the period 2015–2024. During this interval, in addition to the occurrence of the Mw 4.0–5.2 earthquakes analyzed here, the RESNOM network underwent a substantial expansion through the installation of additional stations equipped with broadband, high-resolution instrumentation (Vidal-Villegas et al., 2018). As a result, the selected earthquakes cover a broader magnitude range and were recorded with higher-quality instruments than those used in previous investigations. The lower magnitude limit was defined considering that earthquakes with Mw < 4 are typically recorded by a smaller number of stations and exhibit lower signal amplitudes. Although slightly reducing this threshold could increase the number of events available for analysis, it is unlikely that a larger dataset would significantly alter the results obtained.
The broadband seismic stations that recorded the analyzed events are shown as white squares in Figure 1. These stations are equipped with Guralp CMG-3ESPC or Trillium Compact broadband velocity sensors paired with 24-bit Reftek 130-01 digitizers (Table 1). All velocity sensors have a natural frequency of 0.0083 Hz (corresponding to a 120-s natural period) and a damping ratio of 0.71, providing a broadband response suitable for seismic analysis. The stations record ground velocity at a sampling rate of 100 Hz. Additional information on instrumentation and network operations is provided in Vidal-Villegas et al. (2018).
3. Methodology and data processing
3.1. JOINT INVERSION OF SPECTRAL DATA FROM MULTIPLE EARTHQUAKES
Earthquakes with moment magnitudes ranging from 4.0 to 5.2 and recorded at source-to-receiver distances between 23 and 191 km were selected for the analysis. To ensure spectral consistency, only data from broadband stations with a flat instrumental response across the frequency range of interest were considered.
As an initial processing step, the instrument response was removed from each recorded seismogram to obtain ground velocity in physical units (cm/s). For spectral analysis, 20-s time windows beginning at the S-wave arrival were extracted from the instrument-corrected recordings to isolate stable S-wave energy while minimizing contamination from P-waves, coda, and surface waves. A 5% cosine taper was applied at both ends of each window to reduce spectral leakage. The data were subsequently filtered using a fourth-order Butterworth filter with corner frequencies of 0.2 and 40 Hz. Fourier amplitude spectra were then computed and smoothed using one-third-octave band averaging to suppress high-frequency fluctuations.
Assuming that the instrument-corrected amplitude spectrum is affected by both geometrical spreading and anelastic attenuation, the observed spectral velocity, V(f, R), at frequency f and hypocentral distance R, for an earthquake with seismic moment M₀, can be modeled as: (e.g., Boore, 1983; Hough et al., 1988; Singh et al., 1982):
where
In these expressions, C is a constant that incorporates several physical and geometrical factors, including the radiation pattern Rθϕ, the free-surface amplification FS, the density ρ, and the shear-wave velocityβ. The term S(f) represents the velocity source spectrum, modeled according to the ω² formulation proposed by Brune (1970); G(R) is the geometrical spreading function; Qβ is the frequency-dependent shear-wave quality factor; and κ₀ is the near-surface, distance-independent attenuation parameter that accounts for high-frequency decay in the shallow crust. A value of κ₀ = 0.02 s was adopted in this study, consistent with values reported for comparable geological conditions and supported by results from Munguía (2026).
The geometrical spreading function, G(R), used in this study follows the two-part model proposed by Singh and Ordaz (1994), which distinguishes between body-wave and surface-wave propagation regimes:
This formulation reflects the physical transition from geometrical spreading of body waves at shorter distances to a surface-wave-dominated regime at larger distances, as observed in the region. A transition distance R0 = 80 km is adopted here, consistent with previous studies in the region (e.g., Castro et al., 2009).
Taking the natural logarithm of both sides of Equation (1) and rearranging terms, one obtains (e.g., Joshi et al., 2010):
Using this equation, the velocity spectra of one or more earthquakes can be inverted to estimate the two primary unknowns: the frequency-dependent shear-wave quality factor Qβ and the source corner frequency f0, evaluated over a set of specified frequencies. However, if the corner frequencies are independently determined beforehand—as was done in this study—the inversion problem is significantly simplified, reducing it to the estimation of Qβ alone. The residual term E in equation (2) accounts for all unmodeled effects, random error, or discrepancies between observed and predicted spectral amplitudes.
3.2 THE SINGLE-STATION REFERENCE-FREQUENCY METHOD APPLIED TO MULTIPLE EVENTS
Tsujiura (1966) introduced the single-station reference-frequency spectral analysis, which assumes that path attenuation is the dominant factor governing the observed S-wave spectra, whereas source radiation and site effects are either negligible or effectively minimized through normalization by spectral amplitude ratios (see also Joshi et al., 2010). Consequently, by normalizing the direct S-wave spectral amplitudes to a carefully selected reference frequency, the effects of source radiation and other non-attenuation factors are minimized, allowing the attenuation to be reliably inferred. The rate of decay of the natural logarithm of the normalized spectral amplitude ratios as a function of source-to-receiver distance provides the basis for estimating the frequency-dependent shear-wave quality factor (Qβ). The following provides a detailed description of the complete calculation method.
The spectral amplitude A(f) at frequency f of the S-waves is related to the source-to-station distance, R, the site response, Sr(f), and the quality factor Qβ through the following expression (e.g., Patanè et al., 1994),
where A0(f) is a parameter dependent on the source characteristics. Thus, if two frequencies fc and fref are specified, the natural logarithm of the ratio between the spectral amplitudes at those frequencies is:
Since the first two terms in Equation (4) are independent of distance, the plot of ln[A(fc)/A(fref)] as a function of distance R exhibits a linear trend with a slope given by m = – π (fc – fref )/(Qββ). The slope is determined by applying a linear least-squares fit to the data, from which the corresponding shear-wave quality factor (Qβ) is estimated for each analyzed frequency fc. This procedure is systematically repeated over the range of selected frequencies and for all propagation paths considered, thereby yielding a comprehensive set of frequency-dependent shear-wave quality factor values (Qβ). To ensure an effective characterization of frequency-dependent attenuation, the selection of fc and fref generally encompasses a frequency range representative of the seismic waves analyzed. The criteria and procedure for selecting these frequencies are described in detail in the Results section presenting the Qβ estimates.
4. Qβ Results
4.1. FREQUENCY-DEPENDENT QΒ ESTIMATES FROM JOINT INVERSION OF MULTIPLE EVENTS
This section estimates the shear-wave quality factor (Qβ) as a frequency-dependent parameter using joint inversion of spectral amplitudes from multiple earthquakes. For this purpose, data from 16 earthquakes with moment magnitudes ranging from 4.0 to 5.2, each recorded by 2 to 8 broadband stations, were used (see Table 2). The dataset encompassed a well-distributed collection of spectral observations across a broad range of source–receiver paths (see Figure 1), which contributed to improving the robustness and stability of the inversion procedure employed to estimate Qβ.
Using Equation (2) as the analytical framework, joint inversions were performed on 73 horizontal velocity spectra derived from the selected earthquakes, including both north-south and east-west components. In this procedure, Qβ was estimated independently for each horizontal component and for their geometric mean spectra to assess consistency across polarization directions. Each of the three joint inversions was carried out using 11 logarithmically spaced frequencies spanning the 2–31 Hz range, thereby ensuring adequate spectral resolution across the analyzed bandwidth. Results for Qβ obtained from these joint inversions are shown in Figure 2. In this figure, panels (a) and (b) present the frequency-dependent estimates derived from the north-south and east–west velocity spectra, respectively, while panel (c) shows the Qβ values obtained from the averaged horizontal velocity spectra.
Each plot in Figure 2 includes a regression line with error bars that illustrate the relatively low uncertainty associated with the Qβ estimates. The application of a robust regression method minimizes the influence of outliers, resulting in a more stable and representative fit to the data. The obtained results exhibit a well-defined frequency-dependent behavior of shear-wave attenuation and demonstrate strong consistency between the two horizontal components. This close correspondence suggests that polarization effects are negligible within the analyzed frequency range and confirms the reliability of the estimates derived from the geometric mean of the horizontal spectra.
On this basis, the frequency-dependent quality factor Qβ (f) was parameterized using a power-law relationship of the form Qβ = Q₀ fn , enabling the characterization of the crustal attenuation properties in the study region. In this formulation, Q₀ and n denote the frequency-independent and frequency-dependent terms, respectively, which together describe the overall attenuation behavior of shear waves within the analyzed frequency range. The resulting parameter values, Q₀ and n, from all three inversions are summarized in Table 3.
4.2 ESTIMATION OF QΒ USING THE SINGLE-STATION REFERENCE-FREQUENCY METHOD
To estimate the shear-wave quality factor (Qβ) using the single-station reference-frequency method, broadband velocity recordings from the 16 earthquakes listed in Table 1 were analyzed.
The corresponding Fourier displacement spectra were computed from these recordings following the procedure described in Section 3.1. The analyzed events occurred at focal depths between 5 and 15 km and were recorded at epicentral distances ranging from 40 to 191 km. Most earthquakes (12) were shallow, with focal depths of 5–9 km, whereas the remaining four occurred at depths of 11–15 km.
As in the joint inversion process described above, to ensure a robust and directionally unbiased representation of ground motion, the geometric mean of the N-S and E-W horizontal displacement spectra were computed prior to calculating the spectral ratios A(fc)/A(fref). This procedure minimizes azimuthal effects and provides a representative measure of the overall horizontal shaking. The reference and comparison spectral frequencies, fref and fc, correspond to the central frequencies of narrow bands defined as fref ± Δ f and fc ± Δ f respectively.
To select appropriate fref and fc frequency values, a series of tests was carried out. In these tests, fref values of 1, 2, 3, and 4 Hz were examined, with bandwidths (Δ f ) ranging from 0.2 to 0.5 Hz. Likewise, fc values were selected from higher spectral bands fc ± Δ f, using the same bandwidths. The results indicated that adopting fref = 2 Hz, Δ f = 0.2 Hz and fc values of [6, 8, 10, …, 24] Hz yielded stable, linear trends in the plots of ln[A(fc)/A(fref)] versus distance, providing reliable Qβ estimates for each analyzed frequency. This selection of fref and fc values encompasses the frequency range most relevant to the analyzed seismic waves, thereby enabling a robust characterization of frequency-dependent attenuation.
Tests performed with fref values lower or higher than 2 Hz yielded less stable and less linear ln[A(fc)/A(fref)] versus distance relationships. Conversely, variations of Δf between 0.2 and 0.5 Hz produced only minor differences in the resulting Qβ estimates, indicating that the method is relatively insensitive to small changes in the bandwidth parameter and effectively captures the spectral amplitudes without introducing appreciable noise or bias.
Figure 3 illustrates the plots of ln[A(fc)/A(fref)] as a function of source-to-site distance (R) for each analyzed frequency ( fc). In all cases, the logarithmic amplitude ratios exhibit a consistent decrease with distance, confirming the reliability of the derived Qβ values. Figure 4 shows the logarithmic variation of Qβ, obtained from the results in Figure 3, as a function of the corresponding central frequencies (fc). A robust linear regression was applied to these data to determine the empirical relationship between these parameters. Although Qβ values were obtained over the 6–24 Hz frequency range, a well-defined linear trend is observed only between 8 and 20 Hz. Outside this interval, the estimates become less stable, primarily due to source-size effects at lower frequencies and increased scattering at higher frequencies. The solid line in Figure 4 represents the best-fit regression to the data within this stable interval, whereas the error bars denote the uncertainties associated with the individual Qβ estimates. This analysis yields the following frequency-dependent relationship: Q = 41.3 (± 0.20) f 0.84 (± 0.08).
The derived parameters (Q₀ and n) reveal a moderate-to-high degree of crustal attenuation (Qβ ≈ 250–350 at 10 Hz), consistent with the presence of a heterogeneous and highly fractured crustal structure in the study area. This behavior reflects the combined influence of intrinsic absorption and scattering effects associated with complex lithological and tectonic features of the Peninsular Ranges. Although conceptually simple, the single-station reference-frequency method turns out to be an effective tool for isolating path attenuation by normalizing spectral amplitudes to a reference frequency, thus providing reliable results even in regions with sparse seismic station coverage. However, the assumption of a strictly linear relationship between ln[A(fc)/A(fref)] and distance likely represents an idealization of the actual attenuation processes, which are influenced by lateral variations in crustal properties and the presence of multiple scattering along heterogeneous propagation paths.
5. Discussion and conclusions
The main objective of this study was to estimate the frequency-dependent shear-wave quality factor (Qβ) for the Peninsular Ranges in the northwestern region of Baja California. To achieve this, a high-quality database of broadband seismic recordings was compiled, consisting of earthquakes with moment magnitudes between 4.0 and 5.2 and hypocentral distances ranging from 40 to 191 km. To calculate Qβ, the Fourier amplitude spectra of 73 horizontal ground velocity recordings from 16 earthquakes were jointly inverted following the approach of Joshi et al. (2010). The spectra of the north-south and east–west velocity components were inverted independently, as was their horizontal geometric mean. As shown in Figure 2, the shear-wave quality factors calculated in all three cases are highly consistent. The exponential model Qβ = 41.2 f 0.84 was adopted as larger dataset that includes more deep-focus the representative relationship, as it was derived from the joint inversion of the averaged north-south and east–west velocity spectra.
To complement the results from the multiple-event joint inversion, Qβ was also estimated using the single-station reference-frequency method. For consistency, the same broadband velocity recordings from the earthquakes used in the joint inversion were employed. Using this alternative approach, Qβ values were estimated over the 6–24 Hz frequency range; however, a clear linear trend in the logarithmic plot of Qβ versus frequency was observed only between 8 and 20 Hz. Within this frequency interval, the complementary analysis yielded a frequency-dependent relation of Qβ = 41.3 (± 0.20) f 0.84 (± 0.08). Notably, this relationship closely resembles the one obtained through the multiple-event joint inversion, highlighting the robustness of the methods despite their methodological differences. The obtained Qβ relationships are based on data from 16 events with focal depths ranging from 5 to 15 km, with the majority (twelve events) concentrated between 5 and 9 km. An attempt was made to assess potential variations in Qβ with focal depth. Although some evidence suggested that the parameters Q₀ and n may vary with depth, the limited number of recordings from events deeper than 15 km prevented any well-substantiated conclusions. To address this limitation, future studies should incorporate a earthquakes, particularly those deeper than 15 km. This would enable a more comprehensive analysis of depth-dependent attenuation, helping to clarify whether Qβ increases with depth, as expected due to reduced fracturing, lower porosity, and more homogeneous rock conditions in the lower crust.
For comparison, Table 4 and Figure 5 present the attenuation results (Qβ) obtained in this study alongside those from two previous investigations in the PRBC region ( Castro et al., 1997; Rebollar et al., 1985) and one conducted in the neighboring region of northeastern Sonora, Mexico (Castro et al., 2008). It should be emphasized that the relationships shown in rows 4 and 5 of Table 4 represent Qc values determined from coda-wave analyses, which can exhibit different magnitudes and frequency dependencies compared to the direct shear-wave Qβ estimates. As illustrated in Figure 5, the attenuation results obtained in this study are in close agreement with the power-law model Qβ = 37.0 f 0.87 reported by Rebollar et al. (1985) and with the exponential as expected due to reduced fracturing, lower models Qβ = 28.3 f 1.0 and Q= 31.6 f 0.9 proposed by Castro et al. (1997) and Castro et al. (2008), respectively. The lower Q(f) values reported by Castro et al. (2008) relative to those obtained for the PRBC (Table 4 and Figure 5) can be attributed to the distinct tectonic framework of northeastern Sonora. This region lies within the Gulf Extensional Province, which forms part of the northern Mexican Basin and Range, characterized by pronounced crustal thinning and high heat flow that favor enhanced seismic attenuation. Furthermore, the consistency between the multiple-event joint inversion and single-station reference-frequency spectral ratio results and those obtained from other independent methods provides robust evidence supporting the reliability of the attenuation estimates derived in this study.
In summary, the strong agreement between the frequency-dependent shear-wave quality factor obtained in this study and those reported in previous regional investigations attests to the robustness of the applied methodologies and provides new insight into the attenuation properties of the crust in the Peninsular Ranges of Baja California.
At a reference frequency near 10 Hz, the estimated Qβ values, ranging between roughly 250 and 350, are indicative of moderate to high crustal attenuation within the study region. These values are consistent with a heterogeneous and fractured lithosphere, where both scattering and intrinsic absorption contribute significantly to energy dissipation.
A final note regarding the advantages and limitations of the applied techniques is warranted. The combined use of joint inversion of multiple-event velocity spectra and the single-station reference-frequency method proved effective for characterizing frequency-dependent attenuation. Although the joint inversion covered the 2–31 Hz frequency range, the attenuation trends are best defined between 8 and 20 Hz, where both techniques yield consistent, low-uncertainty results and the ln[A(fc)/A(fref)]–distance relationships exhibit linear behavior. Outside this interval, the estimates are less stable due to source-size effects at lower frequencies and increased scattering at higher frequencies. Moreover, the obtained Qβ values represent an effective attenuation parameter that combines both intrinsic and scattering contributions without explicit separation.
Despite these limitations, the proposed Qβ model provides a physically consistent, region-specific characterization of shear-wave attenuation, thereby improving the reliability of strong-motion simulations, source-parameter corrections, and regional seismic hazard evaluations in northern Baja California.
Contributions of authors
(1) Conceptualization: LM; (2) Data analysis or acquisition: LM, RAV; (3) Methodological or technical development: LM, RAV; (4) Drafting of the original manuscript: LM; (5) Drafting of the revised and edited manuscript: LM, RAV; (7) Fieldwork: LM; (8) Interpretation: LM.
Funding
This work was carried out with the financial support of the Center for Scientific Research and Higher Education of Ensenada, Baja California (CICESE).
Acknowledgments
The authors gratefully acknowledge the long-term financial support provided by the Center for Scientific Research and Higher Education of Ensenada, Baja California (CICESE). We also extend our sincere thanks to all the personnel responsible for the continued operation of the RESNOM seismic network. Their dedication and sustained efforts have been essential to this work, and we are deeply appreciative of their contributions. The authors express their gratitude to the anonymous reviewers for their insightful comments and constructive suggestions, which contributed significantly to improving the clarity and overall quality of the manuscript.
Conflicts of interest
The authors declare that they have no conflicts of interest related to this study.
Handling editor
Raúl Ramón Castro Escamilla.
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