See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/271701233
Improve Micro-Earthquake Hypocenter using Simulated Annealing and Travel Time Tomography Inversion in Geothermal Exploration
Conference Paper · March 2014
DOI: 10.13140/2.1.3678.7529
CITATION
1
READS
637 2 authors:
Rexha Verdhora Ry
Bandung Institute of Technology 33PUBLICATIONS 72CITATIONS
SEE PROFILE
Andri Dian Nugraha
Bandung Institute of Technology 274PUBLICATIONS 1,599CITATIONS
SEE PROFILE
All content following this page was uploaded by Rexha Verdhora Ry on 02 February 2015.
The user has requested enhancement of the downloaded file.
PROCEEDINGS, 3rd International ITB Geothermal Workshop 2014 Institut Teknologi Bandung, Bandung, Indonesia, March 3-7 , 2014
Improve Micro-Earthquake Hypocenter using Simulated Annealing and Travel Time Tomography Inversion in Geothermal Exploration
Rexha Verdhora Ry1and Andri Dian Nugraha2
1Geophysical Engineering, Faculty of Mining and Petroleum Engineering, Institut Teknologi Bandung, Jalan Ganesha No.10, Bandung 40132, Indonesia
Email: [email protected]
2Global Geophysical Group, Faculty of Mining and Petroleum Engineering, Institut Teknologi Bandung, Jalan Ganesha No.10, Bandung 40132, Indonesia
Email: [email protected]
ABSTRACT
Observation of micro-earthquake activity in the geothermal exploration is used to detect the fracture and permeability zone. It is necessary for determining the location of precise hypocenter which the process involves finding a hypocenter location that has minimum error between the observed and the calculated travel times. When solving this nonlinear inverse problem, a local optimization technique can easily produce a solution for which minimizes error function, but its function itself depends on initial model and does not necessarily take its global minimum. Other methods such as simulated annealing can be applied to such global optimization problems. Unlike local methods, the convergence of the simulated annealing method is independent of the initial model. Previously, hypocenter location at “RR” Geothermal Field has been determined by Geiger’s method. However, in this study, simulated annealing method was applied on same data and 1-D velocity model to relocate hypocenter and minimize error function. The travel times were calculated using ray tracing shooting method. Our results show hypocenter location has smaller RMS error compared to the previous study that can be statistically associated with better solution. Furthermore, the new hypocenter location data will be used as input to produce 3-D seismic velocity structure for Vp, Vs, and the ratio Vp/Vs by seismic tomography. The travel times on the 3-D velocity model were calculated using ray tracing pseudo-bending method. Inversion method which used for tomography modeling is iterative damped least square. Our tomography inversion results indicate the presence of low Vp/Vs at depths of about 1 – 3 km below MSL. We interpreted this feature may be associated with a steam-saturated rock in the reservoir area of “RR” geothermal field.
Another possibility is that the reservoir’s phase system may has changed from water-saturated to steam-saturated.
Keywords: micro-earthquakes, seismic tomography, geophysical inversion, ray tracing.
INTRODUCTION
Micro-earthquakes (MEQ), also known as micro- seismic, may be utilized in the exploration, production, and monitoring phases of the development of a geothermal field. This technique maps active fault failure on shear zones, as well as fluid compression. It is necessary for determining the location of precise hypocenter. Hypocenter determination involves finding a hypocenter location that has minimum error between the measured and the theoretical travel times. Other methods such as simulated annealing can be applied to such global optimization problems. Unlike local methods, the convergence of the simulated annealing method is independent of the initial model. Hypocenter location which has smaller RMS will be statistically associated with better solution.
The data used occurred during one year in the geothermal field "RR" from the period of January to December 2007. The data are composed of 573 events with 3099 P wave phases and 2499 S wave phases. Delay time seismic tomography is used for imaging the three-dimensional velocity structure of the subsurface for the P wave (Vp), S wave (Vs), and ratio of Vp/Vs. The presence of a fluid phase or partial melting in the study area can be indicated by the observation of velocity anomalous and ratio of Vp/Vs (Wang et al., 1990 and Takei, 2002). Initial velocity model used is the 1-D velocity model of the P wave phase (Vp) and S wave phase (Vs).
Parameterization model block used had dimension 1.5 x 1 x 0.5 km3, so we had 10 x 10 x 16 blocks.
.
METHODOLOGY Simulated Annealing
Simulated annealing (SA) method (Grandis, 2009) is based on the thermodynamic processes of crystal formation in a substance. The simulated annealing algorithms used were developed by White (1984) and Weber (2000), and then modified to solve hypocenter location in this case.
The initial value of T0 should be as small as possible but in such a way that virtually all simulation steps are accepted. To estimate the optimal value of T0 we used a procedure based on trial error. Then, we got the values of the cost function for a predefined number of system configurations randomly chosen around the initial configuration. T0 was chosen to be greater than or equal to the standard deviation of the previously calculated cost values.
The decrement should be chosen such that a few number of simulation steps suffice to reestablish at each temperature Tk. We used simple decrement rule such as Tk+1 = 0.99Tk.
In our implementation Lk is determined such that for each values of Tk a minimum number of simulation steps, Amax is accepted, where Amax is a predefined fix number. However, as Tk approaches 0, acceptance probability decreases and eventually the value of Lk reach infinity. Consequently, Lk is not allowed to exceed some constant Lmax to avoid extremely large number of simulation steps at low values of Tk . Let U denote the number of the consecutive temperatures for which the number of the accepted simulation steps is zero. If U exceeds a predefined number, Umax, the annealing procedure stops. In other words, the procedure stops if the system configuration is not altered for Umax number of consecutive temperatures, or if the configuration remains unchanged for Umax x Lmax number of consecutive simulation steps.
The parameters of hypocenter position (x, y, and z coordinates) will be updated during iteration of inversion process. Updating parameter formulated as follow (Vakil-Baghmishes & Navarbaf, 2008):
𝑑𝑘= 𝑠𝑖𝑔𝑛 (𝑟𝑎𝑛𝑑[0,1] − 0.5) 𝑇𝑘 [(1 +𝑇1
𝑘)|2 (𝑟𝑎𝑛𝑑[0,1]−1|
− 1] (1) So the produced dk by Eq. 1 belongs to [-1,1] and the rate of change in k-th iteration will be:
∆𝑥𝑘= 𝑑𝑘 (𝑥 max − 𝑥 min ) (2) In Eq. 2, the interval [xmax , xmin] represents permissive range of change in the k-th iteration.
Xmax and Xmin values will be depended on possible range from first iteration.
The shooting method was used in this hypocenter determination study as ray tracing method to determine possible ray path in 1-D velocity model and calculate synthetic travel time from hypocenter to receiver. Inversion and ray tracing algorithm were developed in MATLAB.
Delay Time Tomography
The pseudo-bending method was used in this seismic tomography study as ray tracing method to determine possible ray path in 3-D velocity model and calculate synthetic travel time from hypocenter
to receiver. Pseudo-bending (Um & Thurber, 1987) is an approach in minimization of travel time based on Fermat’s Principle by giving small perturbations gradually on ray paths. Ray tracing algorithm was developed by Syahputra et al. (2012).
For resolve tomography inversion, iterative damped least square is implemented. We also added norm and gradient damping to constrain blocks without ray and to produce smooth solution model, respectively (Widiyantoro et al., 2000). Inversion algorithm was developed in MATLAB.
Figure 1. Workflow of delay time tomography.
RESULT
Hypocenter Determination
Annealing parameters took the following values:
Amax = 10, Lmax = 15 , and Umax= 20. Figure 2 shows the results of the inversion process in this study. The range of hypocenters depth were between elevation of 0.55 to -8.67 km where the deep micro- earthquakes occurred at depths of 6 ─ 8.67 km below mean sea level (or elevation -6 to -8,67 km) and shallow micro-earthquakes occurred at depths of 0 ─ 0.55 km above mean sea level (or elevation 0 to 0.55 km).
Figure 2. The map of the distributions of the relocated micro-earthquake events using simulated annealing method in this study (green dots) and stations (black reverse triangles).
The results, which are relocated hypocenters location that determined by simulated annealing,
have smaller RMS compared to the results from previous study (shown in Figure 3). It can be concluded that simulated annealing method statistically produced better solution.
Figure 3. The histograms of RMS residual of micro- seismic location determination from previous study (left) and simulated annealing method in this study (right).
Model Resolution
Checkerboard Resolution Test (CRT) is a forward modeling method that aims to test the reliability of the inversion technique used in tomographic inversion and to see the resolution throughout the model space. The resolution test will be performed on the same data configuration of the hypocenter and station. Model anomalies obtained by multiplying the +10% and -10% of the initial velocity model (1-D velocity model).
Figure 4. Tomogram of horizontal cross-section of CRT from iterative damped least square. Only area with good resolution are plotted. Positive anomalies are shown by blue color and negative anomalies are shown by red color.
3-D Velocity Structure
Figure 5 shows the result of delay time tomography inversion in vertical cross section. The zones of low Vp/Vs ratio (around 1.45 - 1.65) can be interpreted to be associated with steam-saturated rock. These zones can be identified as the reservoir of “RR”
geothermal field. The reservoir zones are located at 12 - 18 km WE, 8 - 12 km NS, and depth of 1 - 3 km below MSL. The existences of the reservoir area are supported by the data of well-trajectory, where the zones of high Vp/Vs are around the injection wells and the zones of low Vp/Vs are around the production wells (shown in Figure 6).
Figure 5. Tomogram of vertical cross-section (North- South) from: (a) Vp, (b) Vs, and (c) Vp/Vs ratio at N-S 9, 10, 11, and 12 km, and well-trajectory (production: black lines, injection: red lines).
Only area with good resolution are plotted.
Positive anomalies are shown by blue color and negative anomalies are shown by red color.
Figure 6. (a) Volume forms of low Vp/Vs zones and well-trajectory of production wells (black lines) and (b) Volume forms of high Vp/Vs zones and well-trajectory of injection wells (red lines).
0 0.1 0.2 0.3 0.4 0.5 0.6 0
20 40 60 80 100 120
RMS (s)
Occurence
Geiger`s Method
0 0.1 0.2 0.3 0.4 0.5 0.6 0
20 40 60 80 100 120
RMS (s)
Occurence
Simulated Annealing Method
a) )
b) )
c) )
c c’ c c’ c c’
d d’ d d’ d d’
e e’ e e’ e e’
f f’ f f’ f f’
Previous studies stated that the reservoir in the “RR”
geothermal field is the dominance of the water reservoir (Stimac et al., 2008). It becomes interesting when tomographic imaging identify the zones in reservoir area to be associated with steam- saturated rock. Gunasekara et al. (2003) mention that the exploitation and production of the geothermal field can cause changes in the reservoir phase system. The progressive depletion of pore fluid causes the replacement of pore fluid with vapor. In addition, the pressure drop in the reservoir causes a decrease in the boiling point, resulting in boiling and vapor phase is formed. However, whether changes occur in the phase system of “RR”
geothermal field reservoir, it could not be concluded yet.
CONCLUSION
It can be concluded that the proposed simulated annealing approach to hypocenter determination is a very robust and useful method. It is shown that the results from simulated annealing method have smaller RMS than Geiger’s method. We assumed that the solution from Geiger’s method trapped at local minima due of poor initial model. Unlike this local method, the convergence of the simulated annealing method is independent of the initial model.
The inversion results indicate the presence of low Vp/Vs at around 1.45 – 1.65 in the reservoir area at elevation of -1 to -3 km (MSL = 0 km), interpreted as steam-saturated rock in the reservoir area of
“RR” geothermal field. The existences of the reservoir area are supported by the data of well- trajectory, where the zones of high Vp/Vs are around the injection wells and the zones of low Vp/Vs are around the production wells.
When compared with other studies in this field, it is possible that the reservoir’s phase system has changed from water-saturated to steam-saturated.
However, this interpretation still need to compare with other geophysical and geological studies in the study area
REFERENCES
Grandis, H., 2009. Pengantar Permodelan Inversi Geofisika. Penerbit Himpunan Ahli Geofisika Indonesia, pp. 93-100.
Gunasekara, R.C., Foulger, G.R., and Julian, B.R., 2003. Reservoir depletion at The Geysers geothermal area, California, shown by four- dimensional seismic tomography, J. Geophys.
Res., Vol. 109, No. B3, 2134.
Stimac, J., Nordquist, G., Suminar, A., and Azwar, L.S., 2008. An Overview of The Awibengkok Geothermal System, Indonesia, Geothermics 37, Elsevier.
Syahputra, A., Nugraha, A.D., and Fathkhan, 2012.
Development of 3D Seismic Tomography Software: Application to Synthetic Data for Geothermal Exploration. 1st ITB Geothermal Workshop 2012.
Takei, Y., 2002. Effect of pore geometry on VP/VS:
From equilibrium geometry to crack, J.
Geophys. Res. Vol. 107, No. B2, 2043.
Um, J. and Thurber, C., 1987. A fast algorithm for two-point seismic ray tracing, Bull. siesm. Soc.
Am., 77, pp. 972-986.
Vakil-Baghmishes, M. and Navarbaf, A., 2008.
Modified very fast simulated annealing algorithm. 2008 International Symposium on Telecommunications.
Wang, Z., M. L. Batze, and A. M. Nur., 1990. Effect of different pore fluids on seismic velocities in rock, Can. J. Explor. Geophys., Vol. 26 NOS. 1
& 2, pp. 104-112.
Weber, Z., 2000. Seismic travel time tomography: a simulated annealing approach, Elsevier. Physics of Earth and Planetary Interiors, 199, pp. 149- 159.
White, S.R., 1984. Concepts of scale in simulated annealing, Proc. IEEE Int. Conference on Computer Design, Port Chester, pp. 646–651.
Widiyantoro, S., Gorbatoc, A., Kernnett, B.L.N., and Fukao, Y., 2000. Improving Global Shear Wave Traveltime Tomography Using Three Dimensional Ray Tracing and Iterative Inversion. Geophys.J.Int., 141, pp 747-758.
View publication stats
