Group velocity in western Colombia from seismic noise and small earthquakes

Velocidad de grupo en el occidente de Colombia a partir del ruido sísmico y de pequeños sismos

Francisco J. Chávez-García1,*, Hugo Monsalve Jaramillo2,(†), Jose J. Vila Ortega1,2 

1 Universidad Nacional Autónoma de México, Instituto de Ingeniería, Coordinación de Ingeniería Sismológica. Circuito Escolar S/N, Ciudad Universitaria, Coyoacán, 04510, Ciudad de México.

2  Grupo Quimbaya, Universidad del Quindío. Carrera 15 #12N, Armenia, Quindío, Colombia.

*Autor para correspondencia: (F. J. Chávez-García) This email address is being protected from spambots. You need JavaScript enabled to view it.

† Lamentablemente, nuestro amigo y colega Hugo Monsalve falleció en abril pasado. Este será el último trabajo publicado por una persona muy entusiasta que ponía la investigación por arriba de todo. Descanse en paz.

How to cite this article: Chávez-García, F. J., Monsalve Jaramillo, H., & Vila Ortega, J. J. (2026). Group velocity in western Colombia from seismic noise and small earthquakes. Boletín de la Sociedad Geológica Mexicana, 78(2), A301025. https://doi.org/10.18268/BSGM2026v78n2A301025

Manuscrito recibido: August 8, 2025. Manuscrito corregido: October 10, 2025. Manuscrito aceptado: October 24, 2025.

ABSTRACT

Seismic noise and earthquake records were used to determine group velocity distribution in the region. The analysis was restricted to vertical components to avoid ambiguity in identifying Rayleigh waves. 47 small earthquake records were processed using the multiple filter technique. We also used six months of continuous records of seismic noise in 12 broad band stations from Servicio Geológico Colombiano to estimate Green’s functions from seismic interferometry (long-term average of cross-correlation between station pairs). In this analysis we have shown that a non-linear stack of individual cross-correlation windows allows improving signal-to-noise ratios in those Green’s functions. These results were also processed with the multiple filter technique to estimate group velocities. In total, 111 group velocity dispersion curves were computed, which is not enough to compute a seismic tomography in the region of study, especially considering its size and the complexity of its geology. In addition, the period range for which results were obtained using small earthquakes is significantly different from that using seismic noise. However, we are able to estimate a reliable average group velocity of the region and show the variability of group velocities due to its complex geology.

Keywords: multiple-filer technique, small earthquakes, seismic noise, group velocity, Rayleigh waves, seismic interferometry.

RESUMEN

Se utilizó ruido sísmico y registros de terremotos para determinar la distribución de la velocidad de grupo en la región. El análisis se limitó a las componentes verticales para evitar ambigüedades en la identificación de las ondas Rayleigh. Se procesaron 47 registros de pequeños terremotos mediante la técnica de filtrado múltiple. También utilizamos seis meses de registro continuo de ruido sísmico en 12 estaciones de banda ancha del Servicio Geológico Colombiano para estimar las funciones de Green a partir de la interferometría sísmica (promedio a largo plazo de la correlación cruzada entre pares de estaciones). Se demostró que un apilamiento no lineal de ventanas individuales de correlación cruzada permite mejorar la relación señal-ruido en dichas funciones de Green. Estos resultados también se procesaron con la técnica de filtrado múltiple para estimar las velocidades de grupo. Calculamos un total de 111 curvas de dispersión de velocidad de grupo, lo cual no es suficiente para calcular una tomografía sísmica en la región de estudio, especialmente teniendo en cuenta su tamaño y la complejidad de su geología. Además, el intervalo de periodos para el que se obtuvieron resultados utilizando pequeños terremotos es significativamente diferente del que se obtiene utilizando ruido sísmico. Sin embargo, se pudo estimar una velocidad de grupo media fiable de la región y mostrar la variabilidad de las velocidades de grupo y la complejidad de la geología.

Palabras clave: técnica de filtrado múltiple, pequeños terremotos, ruido sísmico, velocidad de grupo, ondas Rayleigh, interferometría sísmica.

1. Introduction

Colombia occupies the northernmost part of South America, where three different plates interact: Nazca, Caribbean and South American. Along its Pacific coast it is subject to subduction of the Nazca plate and has high tectonic activity (Taboada et al., 2000). The result is a highly complex geology (three mountain ranges divide the country along a north-south direction) and an active seismicity. The Cauca-Patía basin is an elongated inter-mountain depression 390 km long that divides two of those mountain ranges, the central and western ranges of the Colombian Andes, along the direction N24E. The geology of this region includes rocks from a wide range of ages, from Cambric to Mesozoic to Cenozoic (Figure 1). The seismicity of the region is moderate (Dimate et al., 2005) and is the result of late Miocene strike-slip and reverse regional faults. There have been significant earthquakes that have affected the region which are the 1882 El Tambo earthquake (Mw 6.5); the 1906 Tumaco earthquake (Mw 8.9), which caused a tsunami; the 1974 event (Mw 6.6) that affected El Darien; and the 1984 earthquake (Mw 5.5), which caused significant damage in Popayán. The shallow velocity structure in western Colombia is largely unknown in spite of its hosting major Colombian cities like Popayán, Cali, Pereira, and Armenia. High-quality seismic networks have only been installed recently. For example, (Monsalve et al., 2013) analyzed data from only two stations to tackle the crustal structure beneath the western Andes. More recently, station coverage in the region has improved thanks to the efforts by Servicio Geológico Colombiano. Seismic data has been useful to study the seismotectonics of the region. (e.g., Warren, 2014; Salazar and Vargas, 2015; Monsalve-Jaramillo et al., 2018). In addition, by incorporating data from several neighboring countries, (Poveda et al. 2018, 2023) were able to study the crustal structure in the region from surface wave dispersion analyses. Regional shear wave velocity distribution and shear wave anisotropy were determined in northwestern South America. Those results are important to understand the complex interaction among the different plates in the region. However, the local subsoil structure is still required to be able to model observed ground motion and to better understand the influence of the geological structure on expected ground motion for future destructive events in the region. In this paper we have used seismic noise and small earthquake records to determine group velocity distribution in the region. Our first objective was to compute a seismic tomography of the region in terms of group velocity. However, the paucity of the data made this impossible. Our results are restricted to a rough evaluation of regional variation of group velocities in the period range from 2 to 10 s. In addition, we show that different data, seismic noise and small earthquakes, provide estimates of group velocity in a different period range. However, both results show good agreement in the period range where they overlap.

2.Data

At the beginning of this project, we centered on earthquake data recorded by the stations of Observatorio Sismológico del Suroeste Colombiano (OSSO), some of them jointly operated with Servicio Geológico Colombiano (SGC). OSSO operates 9 stations in the region (Figure 1). From its catalog, we selected 47 vertical component records from 25 small events (M < 4.7) with epicenters in the region of interest and with records of acceptable quality (Table 1). This is quite a small number of records in spite of analyzing the period 2010 to 2017 and is totally inadequate for our initial objective of computing a tomography of Rayleigh group velocity for the region. For this reason, we turned our attention to seismic noise. SGC acquires and stores continuous signals from the 12 broad band stations it operates in the region (Figure 1). Therefore, we can analyze continuous seismic noise from those stations using seismic interferometry. It has been shown (e.g., Campillo, 2006; Chávez-García and Rodríguez, 2007) that the long-term average of the cross-correlation of seismic noise records of two stations converges to the Green’s function between the two sites. This relation has been observed in ultrasonics (Lobkis and Weaver, 2001), acoustics (Sabra et al. 2005), and ambient seismic noise (Shapiro et al., 2005). The Green’s function includes all possible propagation modes between the two stations. However, it is usually observed that only the fundamental mode of Rayleigh waves may be recovered when we analyze the vertical component. In our case, this partial result is acceptable to complement earthquake data. We recovered continuous seismic noise records for the first six months of 2019 from the 12 broad band stations operated by SGC shown in Figure 1. The distance between station pairs is between 45.4 and 410.7 km. For 12 stations, the possible number of trajectories is 66. We selected hour-long record windows, which allowed for easier processing. If due to transmission or registry problems, the seismic traces were interrupted, it is easy to delete the files that do not have the correct size.

Figure 1. The insert shows the location of the area shown in the main figure. The main figure shows the geological map of western Colombia. The triangles indicate the location of SGC and OSSO stations, whose data are analyzed in this paper. Solid circles indicate the epicenters of the 25 earthquakes detailed in Table 1.

Tabla 1. Data of the small earthquakes recorded by OSSO stations

3. Analyses

We chose to analyze group velocity either from earthquake or seismic noise data. Estimating a group velocity dispersion curve from an earthquake record is straightforward. We use the proven multiple filter technique (Dziewonski et al., 1969; Herrmann, 1985). Each record is filtered with a battery of bandpass filters and the envelope of the filtered trace is computed. When we plot those amplitudes as a function of frequency of the filter, we obtain a map of the energy distribution as a function of frequency and group velocity (time along the trace may be directly translated to group velocity for a fixed epicentral distance). An example of the results is given in Figure 2. This figure shows the energy map just described for event 36 recorded at station GAR (the epicentral distance is 112 km). We observe that the maximum amplitudes of the energy of the record propagated with a to a group velocity about 2 km/s in the period range between 2 and 4 s. The coordinates of the maxima describe the group velocity dispersion curve which we ascribe to the fundamental mode of Rayleigh waves. The analysis of seismic noise is slightly more involved. As stated above, we estimated Green’s functions between station pairs from average cross-correlation functions. In spite of some station malfunctions, the large amount of seismic noise records allowed us to analyze over 2000 one-hour windows of seismic noise records for each station pair. We explored two possible ways to compute an average cross-correlation. The first was the simple linear superposition of the normalized cross-correlations. The second was a non-linear stack of normalized cross-correlations where a weight is applied as a function of phase coherency (Schimmel et al., 2011). The weight function depends on lag time and frequency, this allows to downweight the incoherent portions of the stack in the time-frequency domain. Figure 3 shows an example of the results from the two averaging procedures for station pair BBA-GUY, separated by a distance of 410.4 km. A Rayleigh wave pulse is observed at about 150 s lag time in the positive part of the traces. Even though the pulse is observed in both traces, it is noted that the non-linear average permits defining it more precisely, while the result of the linear stacking shows greater ambiguity. Due to this, we only analyzed the non-linear stacking results. Theoretically the average cross-correlation should be symmetrical regarding zero lag time if the distribution of the sources of seismic noise is homogeneous in space. Figure 3 indicates that this does not occur for this station pair. Given the amount of data, we computed average cross- correlations for each of the six months of records available and then an average trace for all the data.

Figure 2. Result of the multiple filter technique for the record of event 36 (M 3.1) at station GAR (112 km epicentral distance). This figure shows the energy distribution of the record in the period- group velocity plane. Red color indicates the largest amplitudes, while blue color shows the smallest amplitudes. The different symbols point to the location of local maxima for each period value (squares indicate the largest amplitude for each period value)

For each station pair we compared all those averages and selected the trace for which the Rayleigh wave pulse was more prominent. In most cases, the selected average corresponded to a single one-month data. Moreover, we observed significant differences between average cross-correlation functions computed for the different months, as was also observed by Mulumulu et al. (2023). This suggests significant variation in seismic noise sources as a function of time along the semester of data, in agreement with the expected contribution of ocean-related seismic noise sources for the periods where the Rayleigh wave pulse is recovered. Figure 4 shows the seismic section built with non-linear averaged cross-correlation functions for all station pairs. For each station pair, the average cross-correlation function is plotted at the corresponding distance between stations. We can observe the Rayleigh pulses mainly in the positive part (causal) with arrival time around 150 s at 400 km of distance, indicating a group velocity around 2.6 km/s, as expected for the pulse’s low dominant frequencies. The acausal part of the traces (negative lag times) also shows this pulse but with a larger scatter. An additional pulse is observed about zero lag time for distances up to 300 km. However, this is an artifact (group velocity would be larger than 10 km/s) that does not perturb our results as it is separated from the Rayleigh wave pulse.

Figure 3. Example of linear (top) and non-linear (bottom) averages for the cross-correlation of seismic noise recorded at stations BBA and GUY (distance between stations is 410.4 km). A total of 3156 one-hour windows was averaged.

Figure 4. Seismic section showing the average cross-correlation of seismic noise for all 66 station pairs analyzed. The non-linear average for each station pair is plotted at the corresponding distance between stations.

Final average cross-correlation traces were processed using the same procedure used for the earthquake data; the multiple filter technique. The only difference was the need to select the positive or negative part of the trace for processing. Figure 5 shows an example of the energy map plotted as a function of group velocity and period for station pair BBA-GAR, separated by a distance of 410.7 km. The maximum values on this map define a Rayleigh wave group dispersion curve in the period range from 5 to 14 s, with velocities between 2.5 and 3 km/s

Figure 5. Result of the multiple filter technique analysis of the average cross-correlation between stations BBA and GAR, separated a distance of 195.9 km. Red color indicates the largest amplitudes, while blue color shows the smallest amplitudes. The different symbols point to the location of local maxima for each period value (squares indicate the largest amplitude for each period value).

4. Results

Our first intention was to compute a tomography of group velocity using the dispersion curves determined from our data. This was not possible. The number of paths for which a dispersion curve could be estimated was too small: 47 curves from earthquakes recorded at OSSO stations and 64 curves from interferometry of seismic noise recorded at SGC stations. An additional problem was posed by the period range for which those curves could be determined. All the analyzed earthquakes have small magnitudes. The signal- to-noise ratio of our records was acceptable only in a very short period range and mostly between 0.25 and 1.4 Hz (0.7 to 4 s period). In contrast, seismic noise yielded dispersion curves mostly in the frequency range from 0.08 to 0.3 Hz (3 to 12 s period). Therefore, our two datasets do not complement each other. A group velocity tomography of the region is not possible with our data. However, some results may still be gleaned. Figure 6 shows the group velocity dispersion curves estimated from seismic noise recorded at two station pairs: PAL- PRA (distance between stations is 203.4 km) and PAL-URM (distance between stations is 280.2 km). The paths for those two pairs of stations are similar (Figure 1) even if the distance between stations shows some difference. The dispersion curves are quite similar suggesting that the subsoil structure between the two station pairs does not have large variations. The shape of the curves suggests that dispersion is controlled by a thick layer (thicker than 10 km) over half space with a very small impedance contrast. Figure 6 also indicates the reliability of group velocity estimates and hints to small uncertainties in the group velocity estimates. 

Figure 6. Comparison of the group velocity dispersion curves obtained for two station pairs from seismic noise: PAL-PRA (203.5 km distance) and PAL-URM (279.9 km distance). The path between the two station pairs is similar and so are the obtained dispersion curves.

Consider now the comparison between the results obtained from earthquake data and seismic noise. It proved difficult to compare group velocity dispersion between both datasets. As stated above, the narrow period range of the results for earthquake data and its difference with the range for which results were obtained using seismic noise limit possible comparisons between similar paths. An exception is shown in Figure 7, where we compare group velocities estimated from a small earthquake (epicentral distance of 87 km) with that from seismic noise (102.2 km distance between stations). The differences between the two curves are not large and both show very little dispersion. This suggests that the shear-wave velocity of the Cretaceous formations is between 2.1 and 2.2 km/s. The shape of the curve for event s24 suggests the presence of a slightly higher velocity medium underlying the Cretaceous at about 6 to 9 km depth.

Figure 8 shows all our estimated dispersion curves together. As noted before, the frequency range of both sets of curves has only a small overlap. In addition, with a few exceptions, most of the curves derived from earthquake data are extremely short. As a result, the number of group velocity estimates for each frequency is small; the largest number is 12 estimates for two frequencies about 1.2 s period. The number of group velocity estimates from seismic noise for a single period value is larger (a maximum of 57 values but only for three period values about 7 s) but still too few to compute a reliable tomography, especially considering the size of the area where the stations are deployed. Figure 9 compares the average value of group velocity for each of our two datasets. Both curves together describe a reasonable estimate of Rayleigh wave group velocity dispersion between 1 and 13 s period. The discrepancies between the two curves observed between 3 and 5 s can be eadily explained by the number of values used to compute these average values: less than 10 for earthquake data and more than 40 for seismic noise. We believe that the joint dispersion curve may be considered a representative average dispersion curve for the region. This conclusion is supported by the good agreement we observe with the results presented in Figure 11 in Poveda et al. (2018), even if the period overlap with their study is very small.

Figure 7. Comparison of group velocity dispersion curves obtained from earthquake and seismic noise data. The black line with open circles was obtained for the average cross-correlation between stations PAL and YOT, separated 102.3 km. The red line with open squares is the result for the record of event s24 at station PAL (86.9 km epicentral distance)

Figure 8. All dispersion curves determined from our data. Blue lines show the group velocity dispersion curves obtained from 47 records of the 25 small earthquakes described in Table 1. The green lines show the 64 dispersion curves obtained from the cross-correlation of seismic noise recorded in the 12 stations of SGC.

Figure 9. Average group velocity dispersion curves computed from the data shown in Figure 8: from earthquakes records (OSSO) and from the cross-correlation of seismic noise (SGC). The different period range for which each dataset provides useful results is evident.

5. Conclusions

We have presented the results of the analysis of small earthquakes recorded by the stations of OSSO and six months of continuous seismic noise recorded by broad band stations operated by SGC. We estimated group velocity dispersion curves from both datasets. Given that we restricted our analysis to vertical components, those curves may be identified with Rayleigh wave dispersion. The paucity of made it impossible to compute a seismic tomography of group velocity as was our first objective. Only 47 records on 9 stations from small events were useful in the catalogue of OSSO to estimate group velocity in the region. Most of these records provided group velocities in very short period ranges for periods smaller than 4 s and at most 12 records provided estimates for the same period value. Group velocities from earthquake data show a large scatter between 2 and 3.5 km/s. In contrast, interferometry of seismic noise recorded in the broad band stations of SGC provided better results. From the 66 possible station pairs for 12 stations, 64 yielded useful group velocity dispersion curves. They span a longer period range and for some periods we have 57 group velocity estimates. Group velocities show an expected increase with increasing period and show a smaller scatter than the results of earthquake data. However, the number of paths was still too small considering the size of the region and its complex geology. In spite of recent efforts, station coverage is still too sparse in Latin America. We observed small uncertainty in our group velocities as estimated from similar paths for two pairs of broad stations, or between seismic noise interferometry and earthquake records. Two station pairs (FLO-GAR and FLO-URM) allowed estimating the shear wave velocity of the Precambrian rocks in the region at 3 km/s. The average of all dispersion curves gives a plausible estimate of group velocity for the region.

Contributions of authors

HMJ recovered the original data. FJCG, HMJ, and JJVO analyzed the data. JJVO prepared the maps and processed the statistics of the data. FJCG wrote the first draft and prepared the figures. All three authors revised the manuscript and made final corrections.

Funding

This work was funded by the vice-rectory of research at Universidad del Quindío, internal call code 1105. The authors also thank the support from Programa de Intercambio Académico de la Coordinación de la Investigación Científica at Universidad Nacional Autónoma de México for exchange activities conducted within the framework of this project between UNAM and Universidad del Quindío.

Acknowledgments

This project would not have been conducted without the seismic data analyzed. The authors thank the Colombian Geological Service (SGC) for providing seismological and accelerographic data of the networks it operates. Gratitude is also due to Dr. Elkin Salcedo, director of the Seismological Observatory of the Colombian Southwest (OSSO), for providing access to data registered by the OSSO’s Seismic Network in Cali. Dr. Lina Ospina Ostios and Cesar Augusto Cardona transmitted the requested traces. The comments by Dr. Esteban Poveda and an anonymous reviewer were helpful to improve the manuscript.

Conflicts of interest

The authors declare that they have no conflicts of interest.

Handling editor

Carlos Alberto Vargas Jiménez.

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