Examining the Interior of the Llaima Volcano, Chile: Evidence from Receiver Functions

Jordan Bishop

Honor’s Thesis The University of North Carolina, Chapel Hill Department of Geological Sciences

Advisor: Dr. Jonathan M. Lees

April 27, 2016

1 1 Abstract

2 The Llaima volcano is the second most active volcano in the southern Andes. However,

3 despite its frequent eruptions and close proximity to the towns of Melipueco and Vilc´un,not

4 much is known about the interior of the volcano. In 2012, a petrologic study was conducted on

5 the volcano, producing the ﬁrst images of what its magmatic system is like. However, seismic

6 imaging of the interior of the volcano had yet to be conducted. In this paper, we apply receiver

7 functions to produce the ﬁrst seismic study of the interior of the Llaima volcano. An iterative

8 deconvolution technique was applied to both deep local events and teleseismic earthquakes

9 recorded by seismometers near the Llaima. Once receiver functions were calculated, H-κ

10 stacking was applied to probe the Earth structure under the volcano and search for areas of

11 partial melting. From this survey, it was found that the Mohorovii discontinuity (Moho) was

12 located at approximately sixty kilometers beneath the volcano, and that a pocket of partial

13 melting was found at approximately twenty kilometers depth. This study provides the ﬁrst

14 look at the deep magmatic system structure underneath Llaima.

15 Keywords — Llaima Volcano, Receiver Functions, H-κ Stacking, Crustal Structure

1 16 1 Introduction

17 The Llaima volcano in Chile is one of the most active volcanoes in the world, with more than

18 50 observed eruptions since 1640 ([Naranjo and Moreno, 2005]). While many of these eruptions are

19 small, the eruption mechanics causing such frequent eruptions are unknown, and more information

20 about the crustal structure beneath Llaima is needed.

21 While many investigations have been done on the petrology and eruption history of this highly

22 active volcano, the interior of the volcano has not yet been examined using seismic imaging and

23 remains virtually unknown. In this study, we apply an iterative deconvolution technique to compute

24 receiver functions from a dense array around the Llaima volcano. By applying stacking techniques to

25 the receiver functions we attempt to provide the ﬁrst seismic evidence of Llaima’s internal geometry.

26 2 Previous Work

27 2.1 Geologic Background

28 Llaima is a basaltic to basaltic-andesitic (51.0-55.7% SiO2) stratovolcano located in the Chilean

29 Southern Andes Volcanic Zone (SAVZ). Active since the late Pleistocene, the present complex, one

3 30 of the largest in the region (volume = 400 km ), was formed through strombolian, hawaiian, and

31 minor subplinean eruptions [Naranjo and Moreno, 1991, 2005].

32 By examining olivine-hosted melt inclusions from four diﬀerent eruptions, Maisonneuve et al.

33 [2012] concluded that magma is stored at shallow depths (≤ 4 km) beneath Llaima where it un-

34 dergoes intense degassing and crystallization before eruption. A dike complex beneath Llaima was

35 then proposed to feed this shallow region.

2 Figure 1: A proposed dike complex beneath Llaima [Maisonneuve et al., 2012]

36 2.2 A summary of InSAR Modeling applied to Llaima

37 One of the motivations behind this thesis is a series of papers published on Llaima from 2010

38 to 2015. Fournier et al. [2010] used a combination of L band (23.6 cm) and C band (5.6 cm) radar

39 satellites in an attempt to detect deformation in volcanoes. Focusing primarily on Latin America,

40 they found deformation on the Llaima, Lonquimay, Laguna del Maule, and Cait´envolcanoes. They

41 detected an 11 cm subsidence on the eastern ﬂank of Llaima during December 2007. Due to

42 the close proximity to the January-February 2008 eruption, it was suggested that the eruption is

43 associated with an eruption process. The authors concluded it was the result of sector collapse and

44 creep movement. It should be noted that no associated deformation was detected with the 2003

45 and 2007 eruptions at Llaima; potentially due to poor temporal or spatial modeling as a result of

46 interferogram decorrelation.

47 Bathke et al. [2011] applied a model-assisted phase unwrapping and modeling approach to noisy

48 interferograms in an attempt to characterize deformation sources. They applied this technique to a

49 similar data set at Fournier and discovered two deformation periods on Llaima: subsidence between

50 11/2003 and 05/2007 and uplift from 05/2007 to 11/2008. For both periods, they used inverse

51 modeling to determine that a magma body was located approximately 1 km to the southeast of

52 the summit crater of Llaima. Furthermore, they constrained the depth of the subsidence source

3 6 53 to 6-12 km and the depth of the uplift source to 4-9 km, with volume changes of 4.5 − 10 × 10

3 6 3 54 m and 6 − 20 × 10 m , respectively. They then noted that the uplift and deﬂation sources are

55 possibly at to the same source due to sources of error such as 1) uncertainty with depth calculation

56 from inverse modeling (see Dawson and Tregoning [2007]) the use of a simple point source model in

57 the forward modeling, 3) upward migration of the magma during magma inﬂow, and 4) combined

58 magmatic and hydrothermal activity (see Battaglia et al. [2006]).

59 Three main forms of error arise when using InSAR to measure deformation on stratovolcanoes.

60 Temporal decorrelation can occur in signals due to dense vegetation, snow and ice cover, and rapid

61 gullying of sediments [Lu and Dzurisin, 2014]. Geometric distortions (foreshortening-layover) can

62 also occur due to the steep slopes of the volcano. Tropospheric chemical and physical properties

63 can also cause a changing phase delay between successive SAR images, resulting in a bias from both

64 short-wavelength and long-wavelength interferogram artifacts [Fournier et al., 2010]. In addition

65 to discussing the errors above Remy et al. [2015] noted how reliable solutions to the tropospheric

66 bias problem do not yet exist; see their paper for more details. Particularly, Remy et al. [2015]

67 analyzed the magnitude and variation of water vapor over Llaima using estimates from Medium-

68 Resolution Imaging Spectrometer (MERIS) and Moderate Resolution Imaging Spectroradiometer

69 (MODIS) data, which is known to be a large source of error in InSAR imaging [Li, 2011]. As part of

70 their analysis, they used a Mogi point source model in a homogeneous elastic half-space to calculate

71 displacement vectors. The point source was placed at 7km depth to correspond with the deformation

72 source proposed by Bathke et al. [2011]. The displacement vectors were then converted to phase

73 values and compared to the interferograms. From their analysis, they cautioned the interpretation of

74 ground displacement less than ± 7 cm when using a single interferogram to view the entire volcanic

75 ediﬁce. They then concluded that there was no clear evidence of ground surface displacement in the

76 2003-2011 InSAR data, and that the observed fringes are due to tropospheric eﬀects rather than

77 ground displacements. Finally, Remy et al. [2015] postulated that the lack of coeruptive ground

78 displacement at Llaima may have been due to a number of factors: displacement below the accuracy

4 79 of the sensors, displacement related to a deep source, displacement related to a very shallow source,

80 displacement conﬁned to the incoherent peak area of the volcano, or that preeruptive inﬂation and

81 posteruptive deﬂation were observed in a single orbital cycle [Lu and Dzurisin, 2014].

82 2.3 Receiver Function Theory

83 2.3.1 A Deconvolution Problem

84 Teleseismic receiver functions are time series derived by deconvolving the source time func-

85 tion from raw seismic records on three-component seismograms [Langston, 1979]. The theoretical

86 displacement for a P-wave in the time domain is given by:

DV (t) = I(t) ∗ S(t) ∗ EV (t)

DR(t) = I(t) ∗ S(t) ∗ ER(t) (2.1)

DT (t) = I(t) ∗ S(t) ∗ ET (t)

87 where I(t) is the instrument impulse response, S(t) is the eﬀective source time function for the

88 earthquake, and EV (t), ER(t), and ET (t) are the impulse responses of the vertical, radial, and

89 transverse components, respectively.

90 In practice, the source time function S(t) of the earthquake can be approximated by the vertical

91 component of the seismogram [Langston, 1977b], therefore I(t)∗S(t) ≈ Dv(t). With the assumption

92 that instrument responses are matched to components, ER(t) and ET (t) can then be approximated

93 by deconvolving the instrument response and source time function from the the components DR(t)

94 and DT (t). From the convolution theorem, this process is accomplished by division in the frequency

95 domain:

D (ω) D (ω) E (ω) = R ≈ R R I(ω)S(ω) D (ω) V (2.2) DT (ω) DT (ω) ET (ω) = ≈ I(ω)S(ω) DV (ω)

5 96

97 As noted in Langston [1979], the deconvolution in (2) may be numerically unstable due to

98 random noise and the limited bandwidth of the signal. Numerous deconvolution algorithms have

99 since been developed [Clayton and Wiggins, 1976; Oldenburg, 1981; Ligorra and Ammon, 1999;

100 Park and Levin, 2000] with both frequency-domain and time-domain approaches. In this study, we

101 calculated radial receiver functions using an iterative deconvolution technique [Ligorra and Ammon,

102 1999]. First illustrated by Kikuchi and Kanamori [1982], this technique has the advantages of

103 both constraining the spectral shape at long periods and intuitively stripping information from

104 the original signal in order of decreasing importance. Least squares minimization is applied to the

105 diﬀerence between the horizontal seismic trace and the iteratively updated convolution of a spike

106 train (i.e. the estimated receiver function) with the vertical component of the seismogram. The

107 convolution of the estimated receiver function with the vertical seismic trace is subtracted from

108 the radial component of the seismogram with each iteration, and then the process is repeated for

109 diﬀerent spike amplitudes and lags. The residual between the convolution of the vertical component

110 and receiver function and the radial component of the seismogram is reduced with each additional

111 spike, and the iterations stop once the misﬁt reaches some tolerance.

112 2.3.2H- κ Stacking

Figure 2: Ray paths for Ps, PpPs, PpSs, and PsPs phases (from Zhu and Kanamori [2000])

113 One of the most common receiver function processing techniques is the Zhu and Kanamori

114 [2000] H-κ stacking algorithm. Sharp velocity discontinuities, such as the Moho, often lead to

115 seismic wave polarization (see Figure 1). In a radial receiver function, the signal corresponding to

116 the P-to-S conversion (Ps) is usually the largest spike after the direct P arrival. The time separating

6 117 the P and Ps arrivals can be used to estimate crustal thickness:

t s H = P (2.3) q 1 2 q 1 2 2 − p − 2 − p Vs Vp

118 where Vp and Vs are the average crustal velocities of the P and S waves, respectively, and p is

119 the ray parameter of the incoming wave. Depth estimation from this method is advantageous due

120 to its robustness to lateral velocity variations, however, there is a trade-oﬀ between the estimated

121 thickness H and the Vp/Vs ratio κ. To better constrain this interchange, later phase arrivals are

122 also used to estimate crustal thickness:

t H = P pP s (2.4) q 1 2 q 1 2 2 − p + 2 − p Vs Vp

123 t H = P sSs+P sP s (2.5) q 1 2 2 2 − p Vs

124 which can also be used to estimate H and κ.

125 Stacking is an important technique to increase the signal-to-noise ratio of a time series. This method

126 utilizes a stacking scheme in the H-κ domain:

s(H, k) = w1r(t1) + w2r(t2) − w3r(t3) (2.6)

127 where r(t) is the radial receiver function, tj=1,2,3 are the predicted arrival times for the Ps, PpPs,

128 and PpSs + PsPs phases at crustal thickness H and Vp/Vs ratio κ, found by equations 3, 4, and 5; P3 129 and wj=1,2,3 are weighting factors ( j=1 wj = 1). The sum s(H, κ) is the largest when all three

130 phases are coherently stacked at the correct H and κ.

7 131 2.3.3 Jackknife and Bootstrap Estimations of Error

132 The Quenouille-Tukey jackknife technique is a nonparametric tool for estimating the bias and

133 variance of a statistic of interest [Efron, 1979; Efron and Tibshirani, 1986; Miller, 1974]. The

134 jackknife is deﬁned in terms of the quantitiesρ ˆ(i) =ρ ˆ(x1, ..., xi − 1, xi, ..., xn):

1 " n # 2 n n − 1 X X σ (ˆρ) = {ρˆ − ρˆ }2 , ρˆ = ρˆ /n (2.7) J n (i) (.) (.) (i) i=1 i

135 According to Efron and Tibshirani [1986], the jackknife method can be interpreted as a linear

136 approximation to the statistic of interest R. This approximation matches a linear function p to

137 the sample statistic at the n points corresponding to the deletion of a single xi form the observed

138 data set x1, x2, ..., xn. This means that the jackknife can only be applied to statistics where a

139 linear approximation is applicable, so it has trouble approximating statistics as the median of a

140 data set. The bootstrap estimation of a sample statistic is another nonparametric technique

141 that is simple in practice and has a number of attractive statistical qualities [Efron and Tibshirani,

142 1986]. Particularly, analysis using the bootstrap technique is used to calculate standard errors and

143 conﬁdence intervals on statistics with unknown distributions. We will ﬁrst describe the method

144 before going on to elaborate on its properties. In the following analysis, we assert that observed

∗ 145 data x1, x2, ..., xn consists of independent and identically distributed observations. Furthermore, F

146 represents an unknown probability distribution [Efron and Tibshirani, 1986].

147 In executing the bootstrap method:

148 1. After Efron and Tibshirani [1986], we construct an empirical sample probability distribution

∗ 149 F , where each element x1, x2, ..., xn is weighted equally.

∗ ∗ 150 2. With the distribution F ﬁxed, select a random sample of size n from F ,

∗ ∗ xi = xi , i = 1, 2, ..., n (2.8)

8 ∗ ∗ 151 This sample is called the bootstrap sample of the distribution F . Because F is an empirical

152 distribution of the data, the bootstrap sample is the same as a random sample of size n drawn

153 with replacement form the actual sample x1, x2, ..., xn.

∗ ∗ 154 3. The sampling distribution of a statistic of interest, R(x ,F ), is approximated by the bootstrap

155 distribution, i.e. the distribution induced by step (1), of:

R∗ = R(x∗,F ∗) (2.9)

∗ 156 with F held ﬁxed at its observed value.

∗ 157 4. The standard deviation of the R values are then calculated and then used as the standard

158 error on the calculated statistic.

159 Fisher consistency is a property of estimators that asserts that the estimator will return the true

160 value of the statistical parameter if estimate was calculated using the entire population rather than

161 a sample of the population. By applying the Fisher consistency to our particular statistic estimation

∗ 162 problem, we see that the bootstrap estimation of a statistic R will be exactly right for F = F . It

163 turns out that the bootstrap estimate is also the nonparametric maximum likelihood estimate of

164 the true standard error.

165 In the bootstrap procedure, calculating the bootstrap distribution is the most diﬃcult part,

166 and there are three methods to do this:

167 1. By direct theoretical calculation.

168 2. By making a Monte Carlo approximation to the bootstrap distribution. In this method,

∗j 169 repeated calculations of x , j = 1, 2, 3, ..., N are found by taking random samples of size n

∗ 170 from F . The histogram of the corresponding statistics is then taken as an approximation to

171 the bootstrap distribution.

9 172 3. By Taylor series expansion methods (i.e. delta methods, which are similar to the inﬁnitesimal

173 jackknife (see [Jaeckel, 1972])).

174 In this paper, we will approximate the bootstrap distribution using the Monte Carlo method.

175 As mentioned above, the bootstrap method is related to the jackknife method through the

176 Taylor series expansion, now used to approximate the bootstrap distribution. In fact, the jackknife

177 can be viewed as a bootstrap estimate applied to a linear approximation [Efron and Tibshirani,

178 1986]. By adding a linear approximation to the data, the jackknife requires n resamples, while

179 the bootstrap requires 50 to 200 resamples for accurate estimation. However, the bootstrap is free

180 from being a linear approximation and thus is applicable to a wider variety of statistics than the

181 jackknife, such as ﬁnding the median of an unknown data set.

182 2.4 Applications of Receiver Functions

183 Receiver functions have been widely applied to look at crustal structure[Lombardi et al., 2008;

184 Julia and Mejia, 2004; Chevrot, 2000; Owens and Zandt, 1997]. In these studies, obtaining the

185 Moho depth and average crustal Vp/Vs ratio was the primary objective.

186 This technique has also been applied to volcanic regions to search for low velocity zones (LVZ),

187 which have usually been interpreted as regions of partial melt. Volcanism, such as that at Mt.

188 Vesuvius [Agostinetti and Chiarabba, 2008], Mt. Iwate [Nakamichi et al., 2001], and the hot spot

189 beneath Iceland [Darbyshire et al., 2000] has been explored this way.

190 An interesting application of teleseismic receiver functions is their use in calculating the Poisson

191 ratio of the region beneath them [Chevrot, 2000]. The Zhu and Kanamori H-κ stacking technique

Vp 192 can be used to extract the ratio κ underneath a station. This ratio is related to the Poisson ratio Vs

193 µ through the following equation: 1 1 µ = (1 − ) (2.10) 2 κ2 − 1

10 Vp 194 Watanabe [1993] demonstrated the positive correlation between partial melting and ratio. Owens Vs

195 and Zandt [1997] concluded that a Poisson ratio greater than 0.30 was strong evidence for extensive

196 crustal melting.

197 3 Data and Analysis

198 In this study, 25 broadband, 3-component stations (Guralp 40T and Nanometrics Trillium

199 120T) were deployed around and on the Llaima volcano from January 2015 to March 2015. From

200 this deployment, 35 teleseismic earthquakes were used to generate 423 receiver functions. From

201 the 25 stations, the stations near the peak of the volcano (denoted by the red box) were primarily

202 focused on. Furthermore, station BAD was not considered due to a suspected error with the seis-

203 mometer to earth coupling.

204 In calculating the receiver functions, the iasp91 earth model was used. In the iterative decon-

205 volution procedure, a Gaussian width of 5 was also used. Standard errors on the H-κ results were

206 determined using 200 bootstrap resamples.

11 Figure 3: Seismic station deployment around the Llaima Volcano in Chile.The stations focused on in this study are denoted by the red box.

Figure 4: The global distribution of earthquakes

12 Earthquake Latitude Longitude Depth (km) Magnitude

1 13.93 120.69 149.83 5.3 2 30.48 142.16 10 5.3 3 73.22 6.46 10 5.4 4 4.61 119.76 11 5.5 5 -23.35 -70.88 20.56 5.2 6 5.75 125.38 78.36 5.2 7 -19.89 -69.145 97.5 4.0 8 -23.99 -66.89 211 4.1 9 -14.52 -75.78 42 4.3 10 -20.59 172.60 10 5.0 11 -21.38 170.23 10 5.0 12 -14.34 -76.74 11.49 4.6 13 28.57 142.49 20.75 5.0 14 51.92 179.58 102 5.5 15 73.21 6.37 10 5.0 16 14.97 147.05 45.74 5.0 17 5.87 127.05 103.9 5.0 18 -5.38 102.46 36.51 5.0 19 -5.65 146.3279 49 5.7 20 -32.06 -70.17 111 4.2 21 -24.28 -67.01 163.68 4.2 22 -17.03 168.52 219.96 6.8 23 -29.46 60.75 15.08 5.0 24 -56.37 -26.69 48.94 5.1 25 -14.06 -74.56 95 4.5 26 -21.19 -68.75 122.7 4.4 27 27.46 56.19 9 5 28 9.61 122.38 56.84 5.1 29 -18.79 -174.79 82.5 5.2 30 -37.91 -75.33 10 4.8 31 34.46 25.09 37 5.1 32 56.64 -169.12 5.5 5.4 33 -20.82 169.72 10 5.1 34 -49.32 -8.12 10 5.6 35 -1.54 145.21 14 5.9

Table 1: Earthquake data used in this study.

13 Station Latitude Longitude Number of Traces

BAD -38.6441 -71.7829 15 BVL -38.7561 -71.7925 23 CHM -38.7560 -71.5855 13 CIN -38.6844 -71.7029 17 CTF -38.7637 -71.7217 8 DTH -38.7457 -71.7227 11 GEO -38.7029 -71.6982 12 HFH -38.7510 -71.7603 18 HRD -38.6955 -71.7303 7 HRS -38.7259 -71.7800 18 LAG -38.6935 -71.5980 24 LAH -38.6364 -71.7253 23 LST -38.7292 -71.6837 15 MAG -38.8551 -71.8941 12 MDV -38.8996 -71.8741 16 MIC -38.6565 -71.7123 2 PAX -38.8203 -71.7430 18 POW -38.8094 -71.7993 2 RAB -38.8949 -71.7367 8 RLW -38.7059 -71.7639 11 ROD -38.9348 -71.8244 3 SCT -38.6729 -71.7235 17 SMM -38.6908 -71.7914 27 STM -38.6879 -71.7651 21 TRL -38.7545 -71.6456 11

Table 2: The data for the 25 deployed seismic stations

207 4 Results and Discussion

208 Before this study, the internal plumbing system of Llaima was largely unknown. [Bathke et al.,

209 2011] applied inverse modeling to InSAR data and proposed structures at both 4-9 km and 6-12

210 km, however these results are contested. Maisonneuve et al. [2012], using evidence from petrologic

211 data, proposed a magmatic body ≤ 4 km beneath the volcano with an accompanying dike complex.

212 However, these conjectured structures have not previously been conﬁrmed using seismic data.

213 After applying the H-κ technique of Zhu and Kanamori [2000], it was noticed that the discon-

14 214 tinuity (H) converged to shallow values for some stations (e.g. station BVL).

Figure 5: The initial H-κ plot of station Figure 6: The red box (Figure 3) inset BVL. of the Llaima stations.

215 As the Moho in the southern Andes is between 30 and 40 km [Tassara et al., 2006], this

216 data suggests that there are other discontinuities under Llaima that could cause P-wave to S-wave

217 conversions. To search for possible converters, slices of depth structure were examined using the

218 H-κ stacking method.

Figure 7: Possible discontinuities revealed by slices of earth structure.

15 Figure 8: Possible discontinuities revealed by slices of earth structure.

Figure 9: Possible discontinuities revealed by slices of earth structure.

219 This method of searching in depth intervals could also be interpreted as bandpass ﬁltering

220 the H-κ algorithm results, where the maximum overlap was returned in a depth band. From the

221 resulting search, two main discontinuities are evident, one at approximately 20 km and another at

222 approximately 60 km. While this value is deeper than expected for the region [Tassara et al., 2006],

223 the 60 km discontinuity is interpreted as the Moho depth for the area.

16 224 The 20 km discontinuity is interpreted as an area of partial melting beneath Llaima. It is

225 visible on all 9 stations focused on in this study with the exception of station SMM (Figures 7, 8,

226 and 9).

227 From the collection of stations CTF, DTH, and HFH (Figure 7), a possible converter around

228 40 km depth is possible, but more analysis is necessary. In particular, this converter is not visible

229 on the nearby station CTF, so the ray paths to stations DTH and HFH need to be examined.

230 Other possible discontinuities are possible within the region, and one interpretation of the

231 complex converter pattern seen in Figure 8 and Figure 9 is that there is a system of complex

232 melting geometries beneath the volcano. However, it needs to be stressed as well that some of

233 these possible discontinuities may be numerical artifacts stemming from the division of depth into

234 intervals that include neither the 20 km discontinuity or the 60 km discontinuity.

235 5 Conclusions

236 This study presents a ﬁrst look at the deep magmatic system structure underneath the Llaima

237 volcano in Chile. By applying receiver functions taken from a dense array around the volcano, it was

238 determined that a magmatic body is present at approximately 20 km depth beneath the volcano.

239 This partial melt body could be feeding the shallow region proposed by [Maisonneuve et al., 2012]

240 via the dike system.

241 In future work, forward modeling using synthetic receiver functions [Ammon et al., 1990] can

242 be used to examine these discontinuities further. For an example of this technique, see Chmeilowski

243 et al. [1999]. Furthermore, more analysis can be completed on the Vp/Vs ratios obtained from

244 the H-κ stacks for the region, which provides more information on the percentage of partial melt

245 [Chevrot, 2000].

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