SEARCH

SEARCH BY CITATION

Abstract

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Green's Function Retrieval
  5. 3. Scattered Waves in the Green's Function
  6. 4. Passive Image Interferometry at Mount Merapi
  7. 5. Depth Dependence of the Velocity Changes and Hydrological Modeling
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[1] We propose passive image interferometry as a technique for seismology that allows to continuously monitor small temporal changes of seismic velocities in the subsurface. The technique is independent of sources in the classical sense and requires just one or two permanent seismic stations. We retrieve the Green's functions that we use for interferometry from ambient seismic noise. Applying passive image interferometry to data from Merapi volcano we show that velocity variations can be measured with an accuracy of 0.1% with a temporal resolution of a single day. At Mt. Merapi the velocity variations show a strong seasonal influence and we present a depth dependent hydrological model that describes our observations solely based on precipitation.

1. Introduction

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Green's Function Retrieval
  5. 3. Scattered Waves in the Green's Function
  6. 4. Passive Image Interferometry at Mount Merapi
  7. 5. Depth Dependence of the Velocity Changes and Hydrological Modeling
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[2] Imaging techniques with elastic waves such as seismic tomography, reflection seismic or ultrasonic imaging proved their great abilities for the determination of spatial structure. Numerous applications range from medicine to hydrocarbon exploration. However, in some fields of geophysics and nondestructive testing, monitoring temporal changes is of greater interest than details of the spatial structure. Especially for monitoring of volcanoes, fault zones, dams, and hydro-carbon or geothermal reservoirs, it is valuable to observe changes of elastic properties like seismic velocity even if the precise spatial structure is unknown. A technique named coda wave interferometry (CWI) has been proposed [Snieder et al., 2002; Snieder, 2006] for measuring weak changes of seismic velocities using multiple scattered waves. CWI has been applied to measure velocity changes associated with heat, pressure, and water saturation in a rock sample [Grêt et al., 2006], with temperature changes in a building [Larose et al., 2006] and with earthquakes [Nishimura et al., 2000; Peng and Ben-Zion, 2006]. Velocity changes were also reported to precede eruptions of Merapi volcano [Ratdomopurbo and Poupinet, 1995; Wegler et al., 2006]. The major handicap of CWI, which hinders continuous monitoring in the field, is the requirement of repeatable sources. This results in temporally irregular measurements when repeating earthquakes (multiplets) are used [Ratdomopurbo and Poupinet, 1995; Peng and Ben-Zion, 2006] or necessitates repeatable active sources that are expensive on shore [Wegler et al., 2006; Nishimura et al., 2000].

[3] We suggest to use a technique called passive imaging to obtain the signals for CWI. This technique requires only one or two permanent stations and works without active sources. The basic principle of passive imaging is that the Green's function (GF, or impulse response) between two points A and B can be retrieved by cross-correlation of a random isotropic wave field sensed at A and B [Derode et al., 2003; Sánchez-Sesma and Campillo, 2006; Wapenaar, 2004; Snieder, 2004]. Applications of passive imaging were reported from helioseismology [Duvall et al., 1993] and from acoustics [Lobkis and Weaver, 2001]. In seismology GFs were retrieved from seismic noise and from coda waves of earthquakes [Campillo and Paul, 2003; Paul et al., 2005; Roux et al., 2005; Shapiro et al., 2005]. So far the practical recovery of the GF with passive imaging has only been demonstrated for ballistic surface waves and P-waves [Roux et al., 2005]. Evidence for the emergence of scattered waves from the GFs in seismology has been missing so far. In this study we show that scattered waves can be retrieved by correlation of seismic noise.

[4] We study GFs at Mt. Merapi (Figure 1) which is one of the most active strato volcanoes on earth. Its activity is characterized by dome growth and partial dome collapse threatening the surroundings with pyroclastic flows. Most recent activity started in middle of April 2006 and caused evacuations of several thousand inhabitants in May and June. Since 1997 three seismic arrays have been operated on Mt. Merapi [Wassermann and Ohrnberger, 2001]. We focus on data from stations GRW0 and GRW1 (Figure 1) because these sensors were connected to a common digitizer which provides precise relative timing. Data are almost continuous between August 1997 and June 1999.

image

Figure 1. Location of seismic stations on Mt. Merapi. Triangles denote seismometers and stars indicate sources of active CWI measurements [Wegler et al., 2006].

Download figure to PowerPoint

2. Green's Function Retrieval

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Green's Function Retrieval
  5. 3. Scattered Waves in the Green's Function
  6. 4. Passive Image Interferometry at Mount Merapi
  7. 5. Depth Dependence of the Velocity Changes and Hydrological Modeling
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[5] Green's functions are retrieved by cross-correlating different one-day seismic records that are high-pass-filtered at 0.5 Hz. To down-weight the contribution of coherent phases such as teleseismic body waves in the correlation we clip the records at one standard deviation of the recorded seismic noise. Additionally, we average the causal and acausal parts of the cross-correlation functions. Since we use three-component receivers we can reconstruct the full Green's tensor (GT [Paul et al., 2005]) consisting of nine GFs, by correlating all combinations of the components.

3. Scattered Waves in the Green's Function

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Green's Function Retrieval
  5. 3. Scattered Waves in the Green's Function
  6. 4. Passive Image Interferometry at Mount Merapi
  7. 5. Depth Dependence of the Velocity Changes and Hydrological Modeling
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[6] In order to apply CWI on the GFs retrieved with passive imaging we first establish that multiply scattered or reflected waves are contained in the GF. We present two arguments. Firstly, GFs retrieved from noise at different days show coherent phases at late lapse times denoted τ (Figure 2a). Given a distance of about 170 m between stations GRW0 and GRW1 the late arrivals (e.g., the one marked by the arrow in Figure 2a) clearly correspond to indirect wave paths, i.e., reflected or scattered waves. Coherent phases can also be observed in the auto-correlation function (see auxiliary material Figure S1), that is an approximation of the zero offset GF. Secondly, we study the envelopes of the GT in rotated coordinates where L is oriented along the connecting line of the stations, Q is perpendicular to the free surface and T is perpendicular to L and Q. Figure 3 shows envelopes of the Green's tensor components in which the off-diagonal components are averaged and the traces have been normalized in the time window between 10 s ≤ τ ≤ 12 s. Two different regimes can be observed. The early part (τ < 2 s) contains surface waves that travel in a low velocity layer at a group velocity of about 200 m/s. After two seconds lapse time all GT components exhibit a common decay. This shape is reminiscent of the typical decay of coda wave envelopes from active sources. We can fit the decay with a diffusion model [e.g., Wegler and Lühr 2001] expressed by: W(τ) ∝ τ−3/2 exp[−]. Here W is the seismogram envelope, τ denotes lapse time, and b is the absorption parameter. Our estimates of parameter b using GFs reconstructed from seismic noise agree well with measurements on Mt. Merapi performed with active sources [Wegler and Lühr, 2001]. This supports the hypothesis that the late part of the GFs consists of scattered coda waves.

image

Figure 2. Coherent phases in the Green's function coda. (a) Cross-correlation between Z-components from stations GRW0 and GRW1 for several days. Note the coherent phase marked by the arrow. (b) Closeup around the phase marked by the arrow in Figure 2a. This phase which is seen in all GFs arrives earlier in late May 1999 than in early May. This change in the delay time corresponds exactly to the apparent velocity change of 0.015% per day as seen in Figure 4.

Download figure to PowerPoint

image

Figure 3. Envelopes of the GT components between stations GRW0 and GRW1 in rotated coordinates (see text for orientation of coordinates). Nondiagonal components of the GT are averaged with their counterparts. Thin gray lines show LL, QQ, TT and LQ components of the GT which can be excited by ballistic waves. Thin black lines show the LT and QT components which can not be excited by ballistic waves. The best fitting diffusion model is shown by a bold line.

Download figure to PowerPoint

4. Passive Image Interferometry at Mount Merapi

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Green's Function Retrieval
  5. 3. Scattered Waves in the Green's Function
  6. 4. Passive Image Interferometry at Mount Merapi
  7. 5. Depth Dependence of the Velocity Changes and Hydrological Modeling
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[7] We have presented evidence for the fact that the GFs obtained from cross-correlations of seismic noise do not only contain the ballistic wave part of the GF as previously shown in the seismological literature [Campillo and Paul, 2003; Shapiro et al., 2005; Paul et al., 2005; Roux et al., 2005] but also reflected and scattered waves. This opens the possibility to apply interferometric methods to the late part of the passively retrieved Green's functions (images). We call this technique passive image interferometry (PII). It allows to precisely infer changes in the medium by comparing the GFs retrieved from the noise records at different time periods.

[8] Standard CWI [Snieder et al., 2002] measures the delay times (δτi) in various time windows i centered around lapse times τi as the time shifts that result in the best correlation of the segments in these windows. The relative delay time (δτ/τ) is then the mean of all δτi/τi values. In contrast we determine the relative delay time as the factor by which the time axis of one trace has to be stretched or compressed to obtain the best correlation with the other trace. This has two advantages. Firstly δτ/τ need not to be small. And secondly δτ itself need not to be small compared to the dominant wavelength. So we can use much longer and later time windows which makes our estimates more stable. If the time delay is caused by a spatially homogeneous relative velocity change δv/v the relative delay time is independent of the lapse time at which it is measured and δv/v = −δτ/τ. In this case error estimates are obtained by choosing consecutive non-overlapping time windows in which the correlations are calculated separately. This gives independent estimates of the relative delay time and we can calculate mean and standard deviation.

[9] Passive image interferometry is applied to almost two years of nearly continuous seismic records from Merapi volcano, Indonesia. We estimate velocity changes for each one-day GF (between station GRW0 and GRW1) with respect to a reference trace assuming that δv/v is spatially homogeneous. As reference trace we use a stack of all one-day GFs in January 1998. Figure 4a shows the daily relative velocity variation obtained from the LL component of the GT between 2 and 8 s lapse time. We do not use lapse times smaller than 2 s because the surface waves contained in the GFs prior to 2 s have a different spatial sensitivity to velocity variations. Gray shading in Figure 4a marks the standard deviation of independent measurements in three consecutive 2 s time windows starting at 2, 4, and 6 seconds lapse time. Seismic velocity shows temporal variations of a few percent with a clear seasonal trend. Except for a constant offset, the curve only marginally depends on the period used to generate the reference trace. Results obtained from the TT component of the GT are virtually identical (see auxiliary material Figure S2a). We obtain similar results with passive image interferometry using auto-correlation functions of a single station, i.e. zero offset GFs (see auxiliary material Figure S2b).

image

Figure 4. Measured and modeled velocity variations at Merapi volcano. (a) Red dots mark the measurements in the 2–8 s time window. Individual measurements in the 2–4 s, 4–6 s, and 6–8 s seconds lapse time windows and their standard deviation are indicated by light gray dots and gray shading respectively. Results of the active CWI experiment [Wegler et al., 2006] are indicated by green and blue lines. Inset shows a close up around these active measurements. The blue line corresponds to the measurements at the GRW station (used here). Green line shows measurements from station KEN on the southern flank of Mt. Merapi. (b) (bottom) Daily precipitation rate (blue) and modeled ground water level (black). (top) Measured (light red dots) and modeled (dark red line) velocity variations in the 2–4 s time window. Same for the 6–8 s time window in blue.

Download figure to PowerPoint

[10] The blue curve in Figure 4a shows the results of CWI measurements [Wegler et al., 2006] made at the same stations (GRW) but with an active source (BAT in Figure 1). Results from the southern flank of Merapi volcano (station KEN, source BEB) are shown by the green curve. Considering the daily variability of our measurements and the source receiver distance of more than 3 km used for the active measurement, we conclude that our measurements are in agreement with the results of the active experiment. The advantage of our new method is that we can continuously monitor changes without an expensive active source.

[11] Actually the velocity changes can directly be seen in the GFs. Figure 2b shows a close-up around the phase marked by the arrow in Figure 2a. The coherent phase tends to arrive earlier in late May than in early May 1999. This corresponds to the almost linear velocity increase of about 0.015% per day in May 1999 that can be observed in Figure 4.

5. Depth Dependence of the Velocity Changes and Hydrological Modeling

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Green's Function Retrieval
  5. 3. Scattered Waves in the Green's Function
  6. 4. Passive Image Interferometry at Mount Merapi
  7. 5. Depth Dependence of the Velocity Changes and Hydrological Modeling
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[12] The periodicity of the velocity fluctuations of approximately one year in this tropical environment suggests a climatic influence most likely by precipitation. Another observation also supports a connection with precipitation: The amplitudes of the estimated velocity variations depend on the lapse time at which they are measured in the GFs. This has never been reported for CWI measurements before and indicates that the velocity perturbations are spatially inhomogeneous. We can explain this observation together with details of the temporal variation with a hydrological model of the ground water level (GWL).

[13] We assume that drainage of ground water occurs through a stationary aquifer that can approximately be described by Darcy's law. Then the drainage is proportional to the height of the ground water table which results in an exponential decrease of the water level after rain events. A convolution of the precipitation rates with this exponential function thus gives the ground water level GWL (below surface) at time ti:

  • equation image

Here ϕ is porosity, a is the parameter describing the decay, GWL0 is the asymptotic water level, and p(tn) denotes the daily precipitation. Good agreement of such a model was found with water level measurements in a well [Akasaka and Nakanishi, 2000]. Daily precipitation data were provided by the NASA/Goddard Space Flight Center's Laboratory for Atmospheres [Huffman et al., 2001].

[14] To relate the ground water level with delay times we define the depth (z) and time dependent relative slowness perturbation S(ti,z) and a reference water level GWLref that we choose equal to the mean level of January 1998. Then S(ti, z) = δs for GWL(ti) < z < GWLref, S(ti, z) = −δs for GWLref < z < GWL(ti) and S(ti, z) = 0 elsewhere. δs is the relative slowness difference between the states saturated and dry. The delay time δτ at time ti measured at lapse time τ is then

  • equation image

where K(z, τ) is the sensitivity kernel [Pacheco and Snieder, 2005]. We use the kernel in the approximation of coincident source and receiver with a diffusivity constant D = 0.05 km/s2 as estimated at Mt. Merapi [Wegler and Lühr, 2001]. The kernel decays with distance r from the station as r−1 exp(−r2/).

[15] With a genetic algorithm we found the best model with the following parameters: GWL0 = 51 m, ϕ = 0.03, a = 0.008 d−1, and δs = 0.17. ϕ and δs are only constrained by the nonlinearity of K(z, τ) in the depth range occupied by GWL(ti). Other combinations of ϕ and δs with a similar δs/ϕ may also fit the data reasonably. Figure 4b shows the daily rainfall, the inferred GWL and the modeled apparent homogeneous velocity variation for the 2–4 s and 6–8 s time windows together with the measured values. Considering that the precipitation data are averages over an area of approximately 100 by 100 km and the simplicity of our hydrological model we can explain the velocity variations in remarkable detail. The model also explains the difference between the blue and the red curves in Figure 4b that represent the measurements at different lapse times. We are thus confident that the observed velocity variations are related to precipitation via changes in the ground water level. The successful explanation of the lapse time dependence of the relative delay times by depth dependent velocity perturbations indicates that the coda is made up of scattered body waves rather than surface waves.

[16] For spatially inhomogeneous velocity perturbations we can characterize the accuracy of our method by the scatter of measurements around a common trend. In rain-free periods like the first three month in the study period we obtain a standard deviation of 0.1%.

[17] Assuming that the annual rainfall is similar each year we can compare our observation with measurements from 1991 [Ratdomopurbo and Poupinet, 1995]. Indeed a velocity increase of a little more than 1% was observed during the period from April until September 1991. During April to October 1998 and April to June 1999 we observe a similar increase. According to our interpretation these periods of increasing velocities are caused by a falling ground water level in the dry season. We conclude that the effect of stress changes inside the volcano on velocity changes [Ratdomopurbo and Poupinet, 1995; Wegler et al., 2006] is secondary.

6. Conclusions

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Green's Function Retrieval
  5. 3. Scattered Waves in the Green's Function
  6. 4. Passive Image Interferometry at Mount Merapi
  7. 5. Depth Dependence of the Velocity Changes and Hydrological Modeling
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[18] Our observation shows that the hydrological conditions can change the seismic velocities by more than 10% in a depth range of several tens of meters. This effect should be taken into account in studies of the local velocity structure. With the hydrological model we provide an independent check for PII. It proves that deterministic information about the propagation medium is contained in the GFs at large lapse times, i.e. one can retrieve scattered and reflected waves by correlation of seismic noise. This provides the basis for passive seismic imaging with non-ballistic waves. We anticipate this observation to stimulate a variety of studies in reflection seismology using correlations of seismic noise.

[19] The temporal velocity variations detected at Mt. Merapi in this study are dominated by shallow perturbations and demonstrate the potential of PII. If the scattering is weaker or the changes close to the stations are smaller the sensitivity kernel allows the detection of more distant changes. Monitoring of the exploitation process of geothermal or hydrocarbon reservoirs with PII seems possible as well as the monitoring of nuclear waste disposal sites. We think that PII can be used for routine monitoring in various engineering, geotechnical, and geophysical applications. In a separate study we report on a drop of seismic velocity associated with the Mid-Niigata earthquake in Japan that we detected with PII (U. Wegler and C. Sens-Schönfelder, Fault zone monitoring with passive image interferometry, submitted to Geophysical Journal International, 2006). Crucial for the results presented here is the precise relative timing of the two sensors. But we show that similar results can be obtained from just a single station. This means that PII can be applied to data from any existing permanent seismograph station and we expect other interesting discoveries from the application of PII in different environment.

Acknowledgments

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Green's Function Retrieval
  5. 3. Scattered Waves in the Green's Function
  6. 4. Passive Image Interferometry at Mount Merapi
  7. 5. Depth Dependence of the Velocity Changes and Hydrological Modeling
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

[20] We would like to thank GFZ Potsdam for the kind permission to use this great seismological data set. The data were collected in frame of the interdisciplinary joint project “Decade Volcano MERAPI, Indonesia” (subproject: Sche280/9, Zs 4/16, Zs 4/19) running from 1997 until 2002, which was funded by the German Research Foundation (DFG) and GFZ Potsdam.

References

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Green's Function Retrieval
  5. 3. Scattered Waves in the Green's Function
  6. 4. Passive Image Interferometry at Mount Merapi
  7. 5. Depth Dependence of the Velocity Changes and Hydrological Modeling
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

Supporting Information

  1. Top of page
  2. Abstract
  3. 1. Introduction
  4. 2. Green's Function Retrieval
  5. 3. Scattered Waves in the Green's Function
  6. 4. Passive Image Interferometry at Mount Merapi
  7. 5. Depth Dependence of the Velocity Changes and Hydrological Modeling
  8. 6. Conclusions
  9. Acknowledgments
  10. References
  11. Supporting Information

Auxiliary material for this article contains two composite figures.

Auxiliary material files may require downloading to a local drive depending on platform, browser, configuration, and size. To open auxiliary materials in a browser, click on the label. To download, Right-click and select “Save Target As…” (PC) or CTRL-click and select “Download Link to Disk” (Mac).

See Plugins for a list of applications and supported file formats.

Additional file information is provided in the readme.txt.

FilenameFormatSizeDescription
grl22294-sup-0001-readme.txtplain text document1Kreadme.txt
grl22294-sup-0002-fs01.epsPS document364KFigure S1. Figure 2 with auto-correlation of the Z-component from station GRW1.
grl22294-sup-0003-fs02.epsPS document36KFigure S2. Similar to Figure 4A but obtained from the TT component of the GT between the stations GRW0 and GRW1 (A) and obtained from the auto-correlation of the east component of station GRW1 (B).

Please note: Wiley Blackwell is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.