Temperature field simulation in 3-D of a magma - C.I.E.

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Temperature field simulation in 3-D from cooling of a magma chamber in the La
Primavera caldera, Jalisco, Mexico
Surendra P. Verma1,*, Usy C. Arredondo-Parra1, Jorge Andaverde2, Efraín Gómez-Arias3
1
Departamento de Sistemas Energéticos, Centro de Investigación en Energía, Universidad
Nacional Autónoma de México, Priv. Xochicalco s/no., Col. Centro, Temixco, Mor. 62580,
Mexico.
2
Facultad de Ciencias Químicas, Universidad Veracruzana, Av. Universidad km 7.5, Col. Santa
Isabel, Coatzacoalcos, Ver. 96538, Mexico.
3
Posgrado en Ingeniería, Centro de Investigación en Energía, Universidad Nacional Autónoma
de México, Priv. Xochicalco s/no., Col. Centro, Temixco, Mor. 62580, Mexico.
*
Corresponding author: spv@cie.unam.mx
Manuscript submitted to: International Journal of Energy Research, special issue,
September 15, 2010.
Summary
The La Primavera caldera is situated in the western part of the Mexican Volcanic Belt (MVB),
close to the triple junction of Tepic-Zacoalco, Colima, and Chapala Rifts. It is a promising
geothermal field with several deep wells already drilled. Thermal modeling is an important
geophysical tool as documented in the study of this and other geothermal areas of Mexico. Using
computer program TCHEMSYS, we report new simulation results of three-dimensional (3-D)
thermal modeling of magma chamber underlying this caldera through its entire eruptive history.
Equations (quadratic fit) describing the simulated temperatures as a function of the age, volume
and depth of the magma chamber are first presented, which indicate that both the depth and age
of the magma chamber are more important parameters than its volume. The best model was the
one that has the emplacement age of the magma chamber of 0.15 Ma, the top of the chamber at a
depth of 4 km, and the chamber volume of 600 km3. Recharge events of fresh magma at the
middle part of the magma chamber were also considered at 0.095 Ma, 0.075 Ma and 0.040 Ma.
The simulation results were evaluated in the light of the actually measured temperatures in five
geothermal wells. Future work should involve smaller mesh size of 0.050 km on each side
(instead of the current 0.250 km) and take into account petrogenetic processes of fractional
crystallization, assimilation, and magma mixing as well as heat generation from natural
radioactive elements. It would also be of much use to make TCHEMSYS work in an automatic
way, which could efficiently provide the best model(s) for each application.
Keywords: heat budget; temperature field; modeling; geothermal field; magma chamber
2
1. INTRODUCTION
Temperature field simulation from a magma chamber constitutes an important area of research to
understand the origin and evolution of calderas and assess their geothermal potential [1-7]. In
Mexico, such work has been carried out mainly in the Los Humeros caldera of the eastern part of
the Mexican Volcanic Belt [8-13] (MVB; see Figure 1, [14]).
The La Primavera caldera is situated in the western part of the MVB near the triple
junction of three rifts or graben systems, viz., Tepic-Zacolaco rift, Colima rift, and Chapala rift
(MVB, Figure 1). Exploratory well-drilling work to 2,986 km subsurface depth indicated high
temperatures [15-19]. The only available temperature field simulation study in this caldera [20]
was carried out in two-dimensions (2-D), assuming the top of the magma chamber at 5 to 7 km
depth and horizontal dimensions of 10 to 12 km width. The resulting isotherms were qualitatively
compared with the actually measured formation temperatures.
In this work our aim was to carry out thermal simulation in three dimensions (3-D) of
several different models of a magma chamber assumed to underlie this caldera as the primary
heat source. The entire eruption history of the caldera was simulated for different models of the
magma chamber (volume and depth), its emplacement age, as well as for different physical
properties of the region. These results enabled us to propose two equations that were used to
understand the sensitivity of these parameters to the simulated temperature field.
2. GEOLOGICAL SYNTHESIS
The geology of the La Primavera caldera (about 12 km diameter) has been summarized by
several researchers [15-29]. Different eruptive events were dated by Mahood and Drake [25]
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using K-Ar method. These dates vary from about 0.145 to 0.025 Ma. Figure 2 presents a
simplified geologic map of the area as well as the locations of drill wells.
The nature of regional basement in the La Primavera area is not clearly known because of
an extensive, thick cover of younger volcanic rocks. Drilling (Figure 3) has revealed that the
oldest units consist of granitic and granodioritic rocks below about 3000 m subsurface depth.
This deeper layer is overlain by dominantly andesitic rocks about 800 m thick. The third
lithologic unit about 70 m thick consists of rhyolites. The upper unit is a sequence of lithic tuffs
and minor andesites of an average thickness of about 1500 m.
The La Primavera caldera is a very young (Late Pleistocene) volcanic complex, in which
the oldest pre-caldera lavas are about 65 m thick peralkaline rhyolites at about 400 m depth. The
earliest eruptions of pre-caldera lavas took place between about 0.145 and 0.100 Ma. The
eruption of caldera-forming event (40 km3 of Tala tuff) occurred at about 0.095 Ma. Tala tuff and
caldera-lake sediments overlie these peralkaline rocks. Soon afterwards, central domes and older
ring domes (about 5 km3) were emplaced. Eruption of younger ring domes (about 3 km3) took
place at about 75 ka, which was followed by uplift and final eruption of southern arc lavas (about
7 km3) at about 0.060-0.025 Ma (Figure 3).
Thermal manifestations (hot springs with actually measured temperatures around 65ºC
associated with geological faults and fumaroles related to caldera collapse and to later magma
insurgence) were also studied by Mahood et al. [16] for estimating subsurface temperatures from
solute geothermometers. Solute geothermometers for spring water indicated moderately high
subsurface temperatures at La Primavera (148ºC to 172ºC from Na/K geothermometer [30, 31]
and 155ºC to 175ºC from Na-K-Ca geothermometer [32, 33]). The 18O (SO4-H2O)
4
geothermometer [34] provided slightly higher temperature estimates of 184ºC to 192ºC. The
actually measured bottom hole temperatures were between 170ºC and 350ºC [16, 17, 19].
3. CONCEPTUAL MODEL
Figure 4 presents a simplified conceptual model for simulating temperature field distribution in
the La Primavera caldera. The diameter of the magma chamber was assumed to be 12 km, similar
to the caldera diameter. It was supposed to be surrounded by granitic and granodioritic rocks
actually encountered at deeper levels during drilling operations. For simulation purposes, the drill
well geology (Figure 3) was simplified as three distinct layers, the deepest one consisting of
granitic-granodioritic rocks. The geothermal reservoir was assumed to be at 2 to 3 km subsurface
depth. The shallowest layer was assumed to be dominantly rhyolite.
4. THERMAL MODELING
We used the computer program TCHEMSYS (Thermal and CHEmical Modeling of a VolcanicGeothermal SYStem) by Verma and Andaverde [12], which was written in Fortran, and consists
of 8 modules that can simulate thermal and chemical evolution of a magma chamber in a
maximum domain of 30 km in horizontal directions and 20 km in the vertical direction, i.e., in a
space of 30x30x20 (18,000) km3. The 3-D heat flow and chemical mass-balance equations are
solved in the control volume mode, with the volume size of 0.250 km in each direction, i.e.,
0.250x0.250x0.250 (0.015625) km3 amounting of 1,152,000 control volumes for the entire
simulated region.
5
Verma and Andaverde [12] used this program to simulate the temperature field and
chemical compositions in the Los Humeros geothermal field from the cooling of a magma
chamber. The results were validated by comparing the simulated temperatures with the stabilized
temperatures from actual bottom hole temperature measurements reported by Andaverde et al.
[35] and the simulated major-element chemistry with that of the most-voluminous calderaforming ignimbrite reported by Verma [36]. More recently, Verma et al. [13] also used
TCHEMSYS to understand the dependence of spatial distribution of simulated temperatures.
Thus, in the present work HEAT_FORMING module of TCHEMSYS (Figure 5) was
used to simulate temperature field in 3-D for a magma chamber underlying the La Primavera
caldera. The initial and boundary conditions as well as other information on the simulation
models of the La Primavera caldera are summarized in Table I. The input for the program comes
from three files, which contain information on boundary conditions, emplacement conditions and
mesh construction (Table I).
To simulate and compare the results of different magma chamber models, the volume of
the magma chamber was varied from 500 to 700 km3, with its top at depths varying from 4 to 7
km. Correspondingly, the depth of the centroid of the magma chamber ranged from 6.125 km to
9.875 km. These chamber volume estimates are reasonable from the geochemical modeling
reported by Verma [36] and the erupted volumes of differentiated magmas, which amount to
about 45 km3 for the main caldera-forming event and the related domes emplaced practically
during the same time at about 0.095 Ma. The radius of the cylindrical magma chamber (6 km)
was assumed to be similar to that of the caldera. Although only highly differentiated rhyolitic
magmas are emplaced within the caldera [15, 16, 26, 37], the latter is surrounded by volcanic
centers that have erupted basic magmas [16, 27, 37]. Therefore, it is reasonable to assume that the
magma chamber was initially formed by mantle-derived basic magmas whose initial temperature
6
was also assumed at about 1350°C [38]. This assumption is similar to that used for the magma
chamber in the Los Humeros caldera [13, 39].
For simulating temperature field from different models (Table II), the time of
emplacement of the magma chamber in the La Primavera was assumed to be 0.24 Ma, 0.12 Ma,
and 0.095 Ma. The depth of the top of the magma chamber was assigned values of 4 km, 5 km, 6
km, and 7 km. The volume of the magma chamber was modeled as three different values of 500
km3, 600 km3, and 700 km3. Because for changing magma chamber volume for a given depth of
the top of the chamber its diameter was assumed to be fixed, i.e., the chamber was assumed to
grow at deeper levels. Therefore, we also report the subsurface depth of chamber centroid (Table
II).
Thus, TCHEMSYS was run 36 times to simulate temperature field for all combinations of
emplacement time, magma chamber depth (either as the depth of the top of the magma chamber
or that of its centroid), and its volume. From these simulated temperatures, best-fit equations
were obtained for predicting the temperatures as a function of the emplacement time, chamber
depth and volume variables.
A second set of simulations were then carried out using the selected parameters of magma
chamber and effective thermal conductivity values of the three layers (Figure 4), which varied as
multiples of actual rock thermal conductivity data. These higher conductivity values were
necessary to take into account the contribution of geological faults and fractures as well as
varying porosity of the rocks. The actual distribution of these properties is difficult to establish,
and therefore, different combinations of the effective thermal conductivity values were used for
simulation. Besides fractional crystallization and assimilation of country rocks, an additional
petrogenetic process of magma recharge was also considered.
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5. RESULTS AND DISCUSSION
5.1. Best-fit equations
The results of temperature simulation at the base of the La Primavera geothermal reservoir
(assumed from 2 km to 3 km subsurface depths) for these different magma chamber models are
summarized in Table III. Qualitatively, for any given magma chamber depth and volume, an
increase in emplacement time (t) from 0.095 to 0.24 Ma causes an increase in the temperature at
3 km subsurface depth. For example, for magma chamber of 500 km3 volume (Vcham) emplaced at
4 km depth (top of the magma chamber, dtcham) or equivalently at 6.125 km depth of chamber
centroid (dccham), the temperature increases from about 338ºC for emplacement time of 0.095 Ma
to 360ºC for 0.12 Ma and to 400ºC for 0.24 Ma (Table III).
Figure 6 shows the results for one of the models, in which initial time of 0.120 Ma,
volume of 600 km3 and chamber depth of 4 km were assumed. Thus, it appears that the magma
chamber is still maintained at high temperatures (about 700ºC - 1100ºC), the center of the magma
chamber being at about 1100ºC.
For a given t and Vcham, an increase in dtcham from 4 to 7 km significantly decreases the
simulated temperature at 3 km depth (Table III). For example, for t of 0.095 Ma and Vcham of 500
km3, the simulated temperature decreases from 338ºC for dtcham of 4 km, to 179ºC for dtcham of 5
km, to 128ºC for dtcham of 6 km, and to 120ºC for dtcham of 7 km (Table III).
Finally, for a given t and dtcham or dccham, an increase in magma chamber volume slightly
decreases the temperature at 3 km subsurface depth. For example, for t of 0.095 Ma and dtcham of
4 km or dccham of 6.125 km, the simulated temperature at 3 km depth decreases from 338ºC for
Vcham of 500 km3 to 333ºC for Vcham of 600 km3 and to 278ºC for Vcham of 700 km3. This may be
8
partly due to our magma chamber model, in which it is assumed that the increase in chamber
volume at a given depth of the chamber top increases the depth of the chamber centroid, i.e., the
chamber is supposed to maintain its diameter and grows in the vertical direction only towards the
deeper levels.
The best-fit equations for predicting temperatures at the base of the geothermal reservoir
in terms of these parameters were obtained to quantitatively interpret the simulated data (Table
III).
Two regression equations 1 and 2 for these subsurface temperatures (denominated
T1(Z=3km) for equation 1 and T2(Z=3km) for equation 2) were obtained as follows:
T1(Z=3km)  (1110  230)  (900  900)t  (1400  2100)t 2  (1.04  0.70)Vcham 
(1.0  10 3  6  10 4 )Vcham  (402  30)dt cham  (29.92  2.73)dt cham
2
(1)
2
T2 (Z=3km)  (1284  305)  (900  900)t  (1400  2520)t 2  (2.77  0.85)Vcham 
(2.2  10
3
4
 7  10 )Vcham  (443  44)dccham  (23.04  2.74)dccham
2
(2)
2
The quality of these best-fit equations is characterized by multiple correlation coefficient
(R2; [40]) values of 0.97444 and 0.96191, respectively for equations 1 and 2. The regression
analysis and examination of errors of the coefficients reveal that both intercept and dtcham are
statistically significant 99% confidence level in equation 1 whereas intercept, Vcham and dccham are
so in equation 2. Further, the sizes of the coefficients indicate that the temperature at the base of
the geothermal reservoir shows greater dependence on both t and dtcham (or dccham) than on Vcham.
These results are consistent with similar thermal modeling of magma chamber in Los Humeros
geothermal field [13], in which the greater importance of the magma chamber depth was
suggested as compared to its volume.
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5.2. The best simulated model
These 36 simulated models used for obtaining the best-fit equations were also evaluated by
comparing the simulated temperatures with the actually measured borehole temperatures [17].
The best models are summarized in Figure 7 and Table IV. Three of these models (a), (b), and (c)
were, in fact, selected from these 36 simulations, with the additional process of magma recharge
at 0.095 Ma and modification of physical properties to take into account more efficient heat
transfer processes in the geothermal reservoir (see Figure 7 for more details on these models).
Because even these models did not fully reproduce the measured temperatures (Table IV), we
present a final model (d) (emplacement time 0.15 Ma, chamber volume 600 km3, chamber depth
4 km, magma recharge at 0.095, 0.075, and 0.040 Ma, higher conductivity both in the geothermal
reservoir and other geological structures; see Figure 7) provided somewhat better agreement
between the simulated and measured temperatures.
Finer mesh construction (e.g., 0.050 km on each side instead of 0.250 km currently used)
could provide more consistent results with the measured subsurface temperatures. Additionally,
petrogenetic processes such as fractional crystallization, assimilation, and magma mixing as well
as heat generation from radioactive elements naturally present in rocks should be taken into
account. Besides, convection processes in the geothermal reservoir will have to be simulated. We
also envision the need of running TCHEMSYS in an automatic way, which could efficiently
provide the best model(s) for each application. Unfortunately, in order to achieve these goals we
would need better computing facilities than those currently available to us.
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5. CONCLUSIONS
Using the results of simulations in 3-D, we present two equations describing the simulated
temperature at the base of the geothermal reservoir as a function of the age, volume and depth of
the magma chamber. The best model was obtained for emplacement age of the magma chamber
of 0.15 Ma, the top of the chamber at a depth of 4 km, and the chamber volume of 600 km 3. The
temperature simulation results were evaluated in the light of the actually measured temperatures
in six geothermal wells.
ACKNOWLEDGMENTS
Efraín Gómez-Arias benefited from a Ph.D. fellowship from Conacyt and Usy C. ArredondoParra did so partly from Sistema Nacional de Investigadores as Ayudantes de Investigador
Nacional nivel 3. Jorge Andaverde is grateful to his University for granting him permission to
periodically travel to Morelos and participate in this research. We thank Carlos García Sánchez
and Luis Eduardo Aguilar Pavon for help with the preparation of Figures 3 and 4.
REFERENCES
1. Spera FJ, Yuen DA, Kirschvink SJ. Thermal boundary layer convection in silicic magma chambers:
effects of temperature-dependent rheology and implications for thermogravitational chemical
fractionation. Journal of Geophysical Research 1982; 87:8755-8767.
2. Giberti G, Moreno S, Sartoris G. Thermal history of Phlegraean fields (Italy) in the last 50,000 years: a
schematic numerical model. Bulletin Volcanologique 1984; 47:331-341.
11
3. Verma SP. On the magma chamber characteristics as inferred from surface geology and geochemistry:
examples from Mexican geothermal areas. Physics of the Earth and Planetary Interiors 1985; 41:207214.
4. Tait SR. Samples from the crystallizing boundary layer of a zoned magma chamber. Contributions to
Mineralogy and Petrology 1988; 100:470-483.
5. Giberti G, Sartoris G. Evaluation of approximations in modeling the thermal history of a volcanic area.
Journal of Volcanology and Geothermal Research 1989; 36:233-240.
6. Valentine GA. Magma chamber dynamics. In: Nierenberg WA. ed., Encyclopedia of Earth System
Science, 3: Academic Press: New York, 1992; 1-17.
7. Stimac JA, Goff F, Wohletz K. Thermal modeling of the Clear Lake magmatic-hydrothermal system,
California, USA. Geothermics 2001; 30:349-390.
8. Verma MP, Verma SP, Sanvicente H. Temperature field simulation with stratification model of magma
chamber under Los Humeros caldera, Puebla, Mexico. Geothermics 1990; 19:187-197.
9. Castillo-Román J, Verma SP, Andaverde J. Modelación de temperaturas bajo la caldera de Los
Humeros, Puebla, México, en términos de profundidad de la cámara magmática. Geofísica
Internacional 1991; 30:149-172.
10. Verma SP. Heat source in Los Humeros geothermal area, Puebla, Mexico. Geothermal Resources
Council Transactions 1985; 9:521-525.
11. Verma SP, Andaverde J. Temperature distributions from cooling of a magma chamber in Los Azufres
geothermal field, Michoacán, Mexico. Geofísica Internacional 1996; 35:105-113.
12. Verma SP, Andaverde J. Coupling of thermal and chemical simulations in a 3-D integrated magma
chamber-reservoir model: a new geothermal energy research frontier. In: Ueckermann HI, ed.,
Geothermal Energy Research Trends. Nova Science Publishers, New York, 2007;149-189.
13. Verma SP, Gómez-Arias E, Andaverde J. Thermal sensitivity analysis of emplacement of the magma
chamber in Los Humeros caldera, Puebla, Mexico. International Geology Review 2010; DOI:
10.1080/00206810903234296.
12
14. Verma SP, Verma SK, Pandarinath K, Rivera-Gómez MA. Evaluation of recent tectonomagmatic
discrimination diagrams and their application to the origin of basic magmas in Southern Mexico and
Central America. Pure and Applied Geophysics 2010; in press.
15. Mahood GA. A preliminary report on the comenditic dome and ash flow complex of Sierra La
Primavera, Jalisco, Mexico. Revista del Instituto de Geología UNAM 1977; 1:177-190.
16. Mahood GA, Truesdell AH, Templos M. LA. A reconnaissance geochemical study of La Primavera
geothermal area, Jalisco, Mexico. Journal of Volcanology and Geothermal Research 1983; 16:247261.
17. Villa Merlo SJ, Chacón Franco M, Medina Orozco G. Utilización de la relación atómica Na +/K+ para
identificar zonas de mayor actividad hidrotermal en el campo geotérmico de la Primavera, Jalisco.
Geotermia Revista Mexicana de Geoenergía 1987; 3:241-254.
18. Yokoyama I, Mena M. Structure of La Primavera caldera, Jalisco, Mexico, deduced from gravity
anomalies and drilling results. Journal of Volcanology and Geothermal Research 1991; 47:183-193.
19. Maciel-Flores R, Rosas-Elguera J. Modelo geológico y evaluación del campo geotérmico La
Primavera, Jal. México. Geofísica Internacional 1992; 31:359-370.
20. Verma SP, Rodríguez-González U. Temperature field distribution from cooling of a magma chamber
in La Primavera Caldera, Jalisco, Mexico. Geothermics 1997; 26:25-42.
21. Mahood GA. Geological evolution of a Pleistocene rhyolitic center - sierra La Primavera, Jalisco,
Mexico. Journal of Volcanology and Geothermal Research 1980; 8:199-230.
22. Mahood GA. Chemical evolution of a Pleistocene rhyolitic center: Sierra La Primavera, Jalisco,
México. Contributions to Mineralogy and Petrology 1981; 77:129-149.
23. Mahood GA. A summary of the geology and petrology of the Sierra La Primavera, Jalisco, Mexico.
Journal of Geophysical Research 1981; 86:10137-10152.
24. Wright JV. The Rio Caliente ignimbrite: analysis of a compound intraplinian ignimbrite from a major
Late Quaternary Mexican eruption. Bulletin Volcanologique 1981; 44:189-212.
13
25. Mahood GA, Drake RE. K-Ar dating young rhyolitic rocks: a case study of the Sierra La Primavera,
Jalisco, Mexico. Geological Society of America Bulletin 1982; 93:1232-1241.
26. Mahood GA, Halliday AN. Generation of high-silica rhyolite: a Nd, Sr, and O isotopic study of Sierra
La Primavera, Mexican Neovolcanic Belt. Contributions to Mineralogy and Petrology 1988; 100:183191.
27. Michael PJ. Partition coefficients for rare earth elements in mafic minerals of high silica rhyolites: the
importance of accesory mineral inclusions. Geochimica et Cosmochimica Acta 1988; 52:275-282.
28. Alatorre-Zamora MA, Campos-Enríquez JO. La Primavera caldera (Mexico): structure inferred from
gravity and hydrogeological considerations. Geophysics 1991; 56:992-1002.
29. Campos-Enríquez JO, Domínguez-Méndez F, Lozada-Zumaeta M, Morales-Rodríguez HF,
Andaverde-Arredondo JA. Application of the Gauss theorem to the study of silicic calderas: the
calderas of La Primavera, Los Azufres, and Los Humeros (Mexico). Journal of Volcanology and
Geothermal Research 2005; 147:39-67.
30. White DE. Geochemistry applied to Discovery, evaluation, and exploitation of geothermal energy
resource. Geothermics 1970; spec issue:58-70.
31. Fournier RO. A revised equation for the Na/K geothermometer. Geothermal Resources Council
Transactions 1979; 3:221-224.
32. Fournier RO, Truesdell AH. An empirical Na-K-Ca geothermometer for natural waters. Geochimica et
Cosmochimica Acta 1973; 37:1255-1275.
33. Fournier RO, Potter RW. Magnesium correction to the Na-K-Ca chemical geothermometer.
Geochimica et Cosmochimica Acta 1979; 43:1543-1550.
34. McKenzie WF, Truesdell AH. Geothermal reservoir temperature estimated from the oxygen isotope
compositions of dissolved sulfate and water from hot springs and shallow drillholes. Geothermics
1977; 5:51-61.
14
35. Andaverde J, Verma SP, Santoyo E. Uncertainty estimates of static formation temperatures in
boreholes and evaluation of regression models. Geophysical Journal International 2005; 160:11121122.
36. Verma SP. Geochemical evidence for a lithospheric source for magmas from Los Humeros caldera,
Puebla, Mexico. Chemical Geology 2000; 164:35-60.
37. Mahood G, Hildreth W. Large partition coefficients for trace elements in high-silica rhyolites.
Geochimica et Cosmochimica Acta 1983; 47:11-30.
38. Nielson RL. Simulation of igneous differentiation processes. In: Nicholls J, Russell JK, Eds., Modern
Methods of Igneous Petrology: Understanding Magmatic Processes. Reviews of Mineralogy 1990,
24:63-105.
39. Ferriz H. Zoneamiento composicional y mineralógico en los productos eruptivos del centro volcánico
de Los Humeros, Puebla, México. Geofísica Internacional 1985; 24:97-157.
40. Bevington PR, Robinson DK. Data reduction and error analysis for the physical sciences. McGrawHill, Boston, 2003; 320 p.
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Figure legends
Figure 1. Location of the La Primavera caldera (P), Jalisco, in the western part of the
Mexican Volcanic Belt (MVB), modified after [36]. The abbreviations are: MAT–Middle
America Trench; MVB–Mexican Volcanic Belt; PV–Puerto Vallarta; V–Veracruz; G–
Guadalajara; Hu–Los Humeros caldera; W, WC, C, and E refer to, respectively, the western,
west-central, central, and eastern parts of the MVB. Major geological faults and fractures in the
MVB are also shown schematically.
Figure 2. Simplified surface geology of the La Primavera caldera, modified after [15, 21, 23].
The wells referred to in the text are labeled.
Figure 3. Simplified lithology from the drilling information of wells in the La Primavera
caldera. The wells (LP─La Primavera) along the approximate section are numbered as follows:
LP2 (about 2 km depth), LP9 (about 2.986 km depth), LP1 (about 1.822 km depth), LP12 (about
2.560 km depth), LP8 (about 1.861 km depth), LP5 (about 1.215 km depth), and LP4 (about
0.668 km depth), modified after [18].
Figure 4. Simplified geological model of geothermal reservoir and magma chamber in the La
Primavera caldera.
Figure 5. HEAT_FORMING module of computer program TCHEMSYS used in thermal
simulation of the La Primavera magma chamber.
Figure 6. Temperature field distribution as a function of the depth in km (vertical axis at the
right side of the diagram) or as the number of control volumes (cvn; vertical axis at the left side
of the diagram). The magma chamber is schematically shown by dotted lines. The diagram shows
the temperature distribution along a vertical line (coordinates 80, 1 in the control volume space)
of 20 km depth, at the center of the chamber (x=60 and y=60), i.e., between the surface
16
(coordinates 60, 60, 80) and the deepest part of the simulated volume (60, 60, 1). Note the
thermal anomaly due to the emplacement and cooling of the magma chamber is still observed
within the magma chamber (see filled diamonds) as well as both above and below it (see open
circles). Open triangles show the temperature field in the geothermal reservoir.
Figure 7. Comparison of simulated temperatures with the measured temperatures in La
Primavera geothermal wells LP1, LP2, LP4, LP5, and LP8 (note the approximate depths in (a),
where measured temperatures were reported, and see Figures 2 and 3 for locations of wells). The
symbols used are shown as inset in (b). The geothermal reservoir models were as follows: (a)
Magma chamber emplacement time (t), its top (dtcham) and its volume (Vcham) were, respectively,
0.12 Ma, 4 km depth and 500 km3, magma recharge volume (magr) of 5% magma chamber
volume at 0.095 Ma, assumed reservoir (2-3 km depth; ekres) effective conductivity of 10 times
the rock conductivity, and of the other two layers (upper 0-2 km and lower > 3 km depth, ekul and
ekll) of 1.5 times the respective rock conductivity; (b) Values of t, dtcham and Vcham were,
respectively, 0.12 Ma, 4 km depth and 500 km3, magr of 10% magma chamber at 0.095 Ma,
assumed ekres of 20 times the rock conductivity, and both ekul and ekll of 4 times the respective
rock conductivity; (c) Values of t, dtcham and Vcham were, respectively, 0.12 Ma, 4 km depth and
500 km3, magr of 5% of magma chamber at 0.095 Ma, assumed ekres of 20 times the rock
conductivity, and both ekul and ekll of 4 times the respective rock conductivity; and (d) Values of
t, dtcham and Vcham were, respectively, 0.15 Ma, 4 km depth and 600 km3, magr of 10% of magma
chamber at 0.095 Ma, magr of 5% of magma chamber at 0.075 and 0.040 Ma, assumed ekres of 20
times the rock conductivity, and both ekul and ekll of 4 times the respective rock conductivity
values.
17
N
21
Rivera
plate
North American
plate
PV
P
G
W
WC
C
Mexico
E
V
MVB
Pacific
plate
17
MAT
Cocos
plate
W 106
102
98
Figure 1
18
Hu
Figure 2
19
Figure 3
20
Figure 4
21
boundary_conditions.txt
emplacement_conditions.txt
mesh_construction
HEAT_FORMING
temperature.txt
Figure 5
22
200
0
60
5
40
10
Simulated temperature
Geothermal reservoir temperature
Magma chamber temperature
Location of magma chamber
20
15
20
Figure 6
23
Depth (km)
Control volume number (cvn)
80
0
Temperature (ºC)
400 600 800 1000 1200
Temperature (ºC)
0
50
100
150
200
250
300
0
0
300
LP
300
600
4
5
600
5
1
1200
900
1200
Depth (m)
100
150
200
250
300
Reported temperature
Simulated temperature
900
1500
1500
1
8
2
1800
1800
2100
(a)
50
0
2100
0
50
100
150
200
250
300
(b)
0
0
0
300
300
600
600
900
900
1200
1200
1500
1500
1800
1800
2100
2100
(c)
(d)
Figure 7
24
50
100
150
200
250
300
Table I. Initial and boundary conditions for the model of the La Primavera caldera (LPC),
Jalisco, Mexico
Physical property (units)
Emplacement of magma chamber
Boundary conditions
Surface temperature (Ts ) (°C)
Temperature gradient (Tg) (°C/km)
25
30
Emplacement conditions
3
Volume (Vcham) (km )
Radius (rcham) (km)
Depth of the top the chamber (dcham) (km)
Magma emplacement temperature (Tcham) (ºC)
500-700
6
4-7
1350
Mesh construction
Length – x (km)
Number of control volumes in x-direction
Length – y (km)
Number of control volumes in y-direction
Number of geological strata
Control volume (x , y , z) (km)
30
120
30
120
5
(0.25, 0.25, 0.25)
Geological strata (1-5)
Strata 1 (deepest layer) width (km)
Thermal conductivity (W/mK)
Specific heat (J/kg K)
Density (kg/m3)
17.00
2.60
1073
2460
Strata 2 width (km)
Thermal conductivity (W/mK)
Specific heat (J/kg K)
Density (kg/m3)
1.15
1.28
1151
2180
Strata 3 width (km)
Thermal conductivity (W/mK)
Specific heat (J/kg K)
Density (kg/m3)
0.10
2.68
1074
2460
Strata 4 width (km)
Thermal conductivity (W/mK)
Specific heat (J/kg K)
Density (kg/m3)
0.75
1.28
1073
2460
Strata 5 (shallowest layer) width (km)
Thermal conductivity (W/mK)
Specific heat (J/kg K)
Density (kg/m3)
1.00
2.08
900
2200
Time constraints
250
0.095-0.24
Time step (t) (year)
Total simulation time (t) (Ma)
25
Table II. Emplacement conditions for sensitivity evaluation of the La Primavera
caldera (LPC), Jalisco, Mexico
Physical property (units)
Depth of the top the chamber (dtcham) (km)
Depth of the chamber center (dccham) (km)
Volume (Vcham) (km3)
Thickness (Echam) (km)
Radius (rcham) (km)
Magma emplacement temperature (Tcham) (°C)
Time of emplacement (Ma)
Time Step (year)
26
Emplacement of magma
chamber
4–7
6.125 – 9.875
500 – 700
4.4 – 6.2
6
1350
0.095 – 0.24
250
Table III. Temperature at the base of the geothermal reservoirs (3 km depth) resulting
from conductive cooling of a magma chamber in the La Primavera caldera (LPC),
Jalisco, Mexico
Emplacement
Depth of chamber
Chamber
Volume
Temperature
time
top dtcham (km)
centroid dccham
Vcham
(ºC)
3
t (Ma)
(km)
(km )
0.095
4
6.125
500
338
0.095
5
7.125
500
179
0.095
6
8.125
500
128
0.095
7
9.125
500
120
0.095
4
6.625
600
333
0.095
5
7.625
600
175
0.095
6
8.625
600
127
0.095
7
9.625
600
119
0.095
4
6.875
700
278
0.095
5
7.875
700
154
0.095
6
8.875
700
123
0.095
7
9.875
700
119
0.120
4
6.125
500
360
0.120
5
7.125
500
204
0.120
6
8.125
500
138
0.120
7
9.125
500
122
0.120
4
6.625
600
357
0.120
5
7.625
600
200
0.120
6
8.625
600
137
0.120
7
9.625
600
121
0.120
4
6.875
700
306
0.120
5
7.875
700
175
0.120
6
8.875
700
130
0.120
7
9.875
700
120
0.240
4
6.125
500
400
0.240
5
7.125
500
273
0.240
6
8.125
500
189
0.240
7
9.125
500
145
0.240
4
6.625
600
402
0.240
5
7.625
600
272
0.240
6
8.625
600
188
0.240
7
9.625
600
144
0.240
4
6.875
700
366
0.240
5
7.875
700
246
0.240
6
8.875
700
173
0.240
7
9.875
700
138
27
Table IV. Reported temperature vs. temperature resulting from conductive cooling of a magma
chamber in the La Primavera caldera (LPC), Jalisco, Mexico
Well
Depth
Temperature
Simulated
Simulated
Simulated
Simulated
(km)
(ºC)
temperature
temperature
temperature
temperature
Model-a (ºC)
Model-b (ºC)
Model-c (ºC)
Model-d (ºC)
LP1
1226
256
124
168
156
182
LP1
1822
303
203
260
242
270
LP2
2000
210
230
290
272
299
LP4
668
80
72
98
92
107
LP5
690
178
74
100
94
110
LP5
1215
223
123
166
155
180
LP8
1861
287
209
266
248
276
28
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