The following Master's thesis is the same as the original except in minor ways: All pages are numbered the same as the originals but in the upper left corner End of a page is noted by _____ just above the number of the following page. Fonts have been changed Line spacing has been changed Plates and Figures are linked to the text. Tables are included with the text. Some accents on Spanish words have been omitted. Signatures of examiners on p. i have been omitted _____ i


A Thesis Submitted to the Faculty in partial Fulfillment of the requirements for the degree of Master of Arts by Richard W. Birnie DARTMOUTH COLLEGE Hanover, New Hampshire February 1971 Examining Committee: Signatures not included in this scanned copy.


Abstract......... 	iii
Acknowledgements	v
List of Tables	vi
List of Figures	viii
List of Plates	ix
I.      Introduction	 1
II.    Infrared Radiation Theory	 5
III.   Infrared Photography	14
IV.   Previous Work	18
V.    Instrumentation	22
VI.  Procedure	25
VII. Thermal Patterns	27	   
           1. Izalco from Cerro Verde	27
           2. Izalco from Lava Nueva	31
          3. San Miguel from La Placita	33
          4. Pacaya from Cerro Chino	35
          5. Pacaya from El Chupadero	44
          6. Calient from Santa Maria	47
          7. Santiaguito from BuenaVista	53            
          8. El Brujo from La Isla	57
          9. El Brujo from La Loma	60
VIII. Atmospheric Corrections	63
IX. Excess Radiant Heat Calculations	71
X,  Thermal Energy Calculation	83
XI. Emissivity Corrections	86
XII. Summary and Conclusions.	91
XIII. Appendices	94
         1.Thermal Data	95
         2. Predicted Effects of Magma Movement	110
XIV. Bibliography	115
	  A Barnes PRT-5 radiation thermometer was used to obtain apparent surface 
	  temperatures of four Central American volcanoes from land-based stations from 
	  500 to 4000 meters distant.  Isotherms of apparent surfac temperatures, drawn 
	  on photographs of the volcanic terrain under study, delineate areas of 
	  fumarolic activity and active domal upgrowth, The excess radiant heat emitted 
	  from Pacaya Volcano is calculated from apparent surface temperatures corrected 
	  for atmospheric absorption of infrared radiation and for the adiabatic cooling 
	  of the atmosphere with altitude.  The excess radiant heat data indicate that 
	  the lava flow extruded in June, 1969 had completely solidified by December,l969.  This oalculation is consistent with theoretical estimates of the cooling of an extrusive lava sheet by conduction.  Similar calculation of excess radiant heat emission shows the depth of the magma chamber underlying the Santiaguito Volcanic Dome to be 11 meters.  This depth is consistent wlth field observation.
      Conductive heat flow to the surface of Santiaguito is calculated from the 
      infrared radiation data and is an order of magnitude less than the average 
      rate of thermal energy expenditure during the growth of the dome.
	 Corrections are made for surface emissivity on Pacaya Volcano and the isotherms 
	 of real surface temperature plotted.
	  This study was financed in part by the U.S. Army Cold Regions Research and 
	  Engineering Laboratory (USA CRREL) and the National Science Foundation (Grant 
	  No S24-101).  The author is indebted to Dr. Richard Stoiber, Professor of 
	  Geology at Dartmouth College, for his tireless assistance in all aspects of 
	  the study. Help was received from the staff of the Photographic Interpretation 
	  Research Division of USA CRREL, in particular, Mr. Robert Frost, Chief of the 
	  Division, who provided the infrared radiation thermometer, and Mr. Ambrose 
	  Poulin, Research Civil Engineer.
      Excellent assistance in the field was provided by Dr. Ian Lange, Mark Nibbelink, 
      and John Valley.  Dr. Oscar Salazar of the lnstituto Geografico Nacional, 
      Guatemala, and Dr. Henry Meyer of the United Nations.  Projecto Minero, 
      El Salvador, provided vehicular support for the author while in the field.
List of Tables  														Pages						

 1 Calculation of excess radiation heat emission..........				74
 2 Calculation of geothermal gradient at Pacaya
 3 Calculation of cooling time at Pacaya.....                                                       .... .79
 4 Calculation of geothermal gradient at  El Brujo.                                       .....  .81
 5 Estimate of thermal energy of growth of El Brujo.			......	84
 6 Thermal data, Izalco from Cerro Verde, 12/16/69
 7 Thermal data, Izalco from Cerro Verde,4/3/70.				......	96
 8 Thermal data, Izalco from Lava Nueva, 4/5/70.... 
 9 Thermal data, San Miguel from La Placita 4/4/70			    	 	98  
10 Thermal data, Pacaya from Cerro Chino, l2/23/69			.....		99
11 Thermal data, Pacaya from Cerro Chino   12/30/69			  ..		100
12 Thermal data, Pacaya from Cerro Chino  3/31i70			.           101
13 Thermal data, Pacaya from El Chupadero   12/23/69			....	102
14 Thermal data, Pacaya from El Chupadero  4/1/70			.....		103
15  Thermal data, Caliente from Santa Maria 12/20/69.			... 	104 

16 Thermal data, Santiaguito from Buena Vista,  12/22/69	 ...........105
17 Thermal data, Santiaguito from Buena Vista   3/30/70	..	     .......106
18  Thermal data, El Brujo from La Isla 12/21/69.				.       107
19  Thermal data, El Brujo from La Isla 2/27/70...                                         .   108
20  Thermal data, El Brujo from La Loma 3/29/70.    

_____                                ...   
					List of Figures

 Description																   Page

 1 Sketch map of a portion of Central America.........	                		 2
 2 Spectral radiant emittance curves	             ...						11
 3 Atmospheric transmission of infrared radiation	.             . 			65
 4 Correction factors for atmospheric absorption of infrared radiation.	. ..	67
 5 Atmospheric cross section through Pacaya and Cerro Chino	               .	69
 6 Correction factors for surface emissivity.	             ..					89
 7 Apparent surface temperatures of Pacaya from Cerro Chino.....................90
 8 Real surface temperatures of Pacaya from Cerro Chino	.             .			90
 9 Excess radiant heat pattern of Pacaya Volcano from Cerro Chino.	..			90
10 Equilibration of El Brujo geothermal gradient.	             ..				112
11 Equiiibration of geothermal gradients for varying crustal thicknesses....	114
                      List of Plates

No.                   Description                                              Page 
 1  Barnes PRT-5 Precision Radiation Thermometer				...  			23
2 Vertical air photo of Izalco Volcano.	.... . 28
3  Thermal Pattern of Izalco from Cerro Yerde, 12/16/69	.......					29
4  Thermal Pattern of Izalco from Cerro Yerde	
5 Thermal Pattern of Izalco from Lava Nueva	,
6 Thermal Pattern of San Miguel from Finca  La Placita 4/4/70	......		  .34
7 Vertical air photo of  Pacaya Volcano	...... 36
8 Pacaya from Cerro Chino	 ......37
9 Pacaya from the north	...... 38
10 Thermal Pattern of Pacaya from Cerro Chino, 12/23/69.	..     40                       
11  Thermal Pattern of Pacaya from Cerro Chino, 12/30/69.	...... 41
12 Thermal Pattern of Pacaya from Cerro Chino, 3/31/70	....   		42
13  Thermal Pattern of Pacaya from El Chupadero,     12/29/69	   ... 45
14  Thermal Pattern of Pacaya from El Chupadero, 4/1/70	.
15  Oblique air photo of Santiaguito and Santa Maria.	.     	 	48
16  Santiaguito rom Santa Maria	...
17 Santiaguito from Buena Vista	.  .. 50
18  Oblique air photo of Santiaguito	.  
19  Thermal pattern of Caliente Dome from Santa Maria, 12/20/69 ...52
20  Thermal pattern of Santiaguito from Buena Vista, 12/22/69		
21  Thermal pattern of Santiaguito from Buena Vista, 3/30/70	..
22  Thermal pattern of El Brujo from La Isla, 12/2 1/69	 .
23  Thermal pattern of El Brujo from La Isla, 3/27/70	...
24  Thermal pattern of El Brujo from La Loma, 3/29/70	...

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The Central American Volcanic chain is part of the Circum-Pacific Ring of Fire. The volcanoes in this study are located along the Circum-Pacific Ring of Fire in Guatemala and El Salvador. The volcanic belt strikes northwest-southeast across Guatemala and El Salvador. Individual volcanic ridges strike normal to the major trend. A coastal plain, up to 80 km wide, lies parallel and to the southwest of the volcanic chain. Some volcanoes attain altitudes of 4000 m and provide a sharp contrast to the low coastal plain. To the northeast of the volcanic belt lies an intensely folded and metamorphosed eugeosynclinal mountain belt. The volcanic and geologic history of this region of Central America has been described by Williams (1960), MeyerAbich (1958), and Willlams and Meyer-Abich (1955). Figure 1 shows the geographic relationship of the four volcanoes discussed in this study.

Izalco Volcano is situated on the south flank of Santa Anna Volcano in western El Salvador. Lava flow commencing in 1770 make up the early history of this volcanic vent, while tephra eruptions were more significant later in its history (Meyer-Abich, 1958, p.75).

The eruptive activity continued intermittently until 1957, when the eruptions stopped (Rose and Stoiber, 1969, p. 3119). By this time, the cone had risen about 650 m above its base (Meyer-Abich, 1958, p. 76). This repose period ended in October, 1966 with a lava flow from the south flank (Rose and Stoiber, 1969, p. 3119). The Izalco rocks are augite-olivine basalt with bytownite phenocrysts (Meyer-Abich, 1958, p. 79; Rose and Stoiber,

1969, p. 3120).

San Miguel Volcano is located in eastern El Salvador, south of the city of San Miguel. This volcano is sometimes referred to by its Indian name, Chaparastique. This strato volcano rises to an altitude of 2129 m above sea level. San Miguel originated in prehistoric times at the eastern end of the main volcanic chain of El Salvador (Meyer-Abich, 1958, p. 97). Since 1856, San Miguel has experienced intermittent ash aruptions and lava flows (Meyer-Abich, 1958, p. 100). The lavas of San Miguel are augite-olivine basalt with plagioclase phenocrysts (Meyer-Abich, l958, p. 101).

Pacaya Volcano is part of a volcanic complex south of Guatemala City. The volcano is located where the two bordering faults of the Guatemala City Valley grabben intersect, All that remains of the original cone of Pacaya is a fault scarp, marked today by hot springs around the village of San Francisco and Laguna des Calderas. The Cerro Grande Dome lies along the eastern

border of the ancient caldera. Smaller and more recent domes are located at the north base of Pacaya on the shores of Lake Amatitlan. The present summit cone of Pacaya Volcano rises 2552 m above sea level. The first recorded eruptions occurred in 1565 (Meyer-Abich, 1958, p. 66). After 100 years of quiescence, Pacaya resumed activity in 1961 with lava flows from its south flank. In August, l965, eruptive activity commenced in a collapse crater to the west of the summit cone and has continued to the present. The older Pacaya lavas are hornblende-pyroxene andesite rich in olivine (Meyer Abich, 1958, p. 66), while the more recent products are olivine basalts (Rose, 1967). The geology of Pacaya and the surrounding area has been studied in detail by Eggers (Ph.D. thesis in preparation).

The fourth volcanic feature studied was the Santiaguito Volcanic Dome located 12 km southwest of Quezaltenango, Guatemala, The Santiaguito Dome lies in the 1902 explosion crater on the southwest flank of Santa Maria Volcano. The dome is made up of 14 chronologically related units, the first of which was extruded in 1922 (Rose, 1970, p. iii). Dacite is the principal rock type of Santiaguito (Rose, 1970, p. 111 and p. 237-238). The history, geology, and fumarolic activity at Santiaguito have been described by Rose (1970) and Stoiber and Rose (1969). In this paper, the Santiaguito Volcanic Dome will be referred to as Santiaguito Volcano or Santiaguito.

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All bodies with a temperature greater than absolute zero emit electromagnetic radiation. The bulk of the earth's radiant emittance occurs in the infrared portion of the electromagnetic spectrum. The infrared portion of the electromagnetic spectrum includes wavelengths from 0.72 to 1000 . The lower end of the infrared spectrum borders on visible wavelengths while the upper end borders on the microwaves. The infrared spectrum is subdivided into three regions: near infrared region, from 0.72 to 1.5 , the intermediate infrared region, from 1.5 to 20 , and the far infrared region, from 20 to 1000 (Jamieson, et al., 1963, p. 12). Infrared radiation arises from vibrational and rotational motions of the atoms and molecules in the emitting substance (Bramson, 1968, p. 5). The character of radiation depends on the physical state of the source. Emission spectra of liquids and gases are characteristically lines or bands of discrete wavelength while solids, in most instances, radiate in a broad continuous spectrum (Branson, 1968, p. 7).

Sir Frederick Ylilliam Herschel was the first person to relate the radiant energy characteristics of heat and light. His discovery of the infrared region was made

.in the spring of 1800a, p. 272) observed that "radiant heat consists of particles of light of a certain range of moments" and that "radiant heat will at least partly, if not chiefly consist...of invisible light; that is to say, of ray coming from the sun, that have such momentum to be unfit for vision." Herschel (1800b p. 291-2) noted that the heating powers of solar radiation increased beyond thevisible red boundary and reached a maximum in the invisible part of the solar spectrum. Herschel (1800b, p, 291) concludes:

if we call light, those rays which illuminate objects, and radiant heat, those which heat bodies, it may be inquired, whether light be essentially different from radiant heat? In answer to which I would suggest, that we are not allowed, by the rules of philosophizing, to admit two different causes to explain certain effects if they may be accounted by one.

The radiant emittance of a body dspends primarily on its temperature. Radiant emittance (W) is defined as the amount of radiant energy emitted per unit time (sec) per unit surface area (cm2) (Simmon, 1966, p. 12). Power is energy per unit time; therefore, radiant emittance (W) can be expressed in units of power per units of surface area (watts/cm2) (Simmon, 1966, p. 12-13. The propagation of radiant energy can be explained by either electromagnetic wave theory or quantum mechanical theory. The quantum mechanical approach sees

radiant energy transferred through space by discrete particles of matter called photons (Seigel and Howell, 1968, p. 5). Energy changes in the radiating atoms occur in discrete jumps that are constant for a given frequency of radiation. The energy (E) of the discrete quantum of radiation of certain frequency ( v ) is given by E-h v where h= Planck's Constant=6.624xlO-27 erg.sec (Ivanov and Tyapkin, 1963, p. 10). Since =c/, where c equals the speed of light and equals the wavelength of radiation, it follows that the wave length associated with a quantum of energy is given as =hc/E (Simon, 1966, p. 11).

No body is a perfect emitter or absorber of radiant energy. For the sake of deriving theory, one defines a blackbody as "an ideal body that allows all incident radiation to pass into it...and absorbs internally all the incident radiation..." (Siegel and Howell, 1969, p. 11). A blackbody is also a perfect emitter of internally absorbed radiation. At a given temperature, the radiant emittance of a real body will be less than that of a blackbody. The emissivity (E) of a real body is the ratio of its radiant emittance and the radiant emittance of a blackbody at the same temperature (W/Wb) (Simon, 1966, p. 13). The emissivity of a blackbody is unity. The ratio of radiant energy absorbed by a body to the radiant energy incident upon it is defined as the absorptance (alpha) of the body (Simon, 1966, p. 131).

For a blackbody, the absorptance is also unity. No radiant energy pases through an opaque body. The emissivity and absorptance of an opaque body are equal:

E = alpha (Simon, 1966, p. 13). For a blackbody, the emissivity equals the absorptance equals unity: E=alpha=1. The same relationship holds for each spectral component of radiation: E lambda=alpha lambda (Kruse, et al, 1962, p. 15).

Kirchhoff's Law (Simon, 1966, p. 13) states that the total radiant emittance from a real body equals the product of its emissivity or absorptance and the radiant emittance from a blackbody of the same temperature: W=EWb=alphaWb. Spectral emittance (W lambda) is defined as the amount of radiant emittance in a certain wavelength interval. Since E lambda=alpha lambda, it follows that: Wlambda= ElambdaWlambdab=alphalambdaWlambdab. It should be noted that Kirchoff's Law applies only to purely thermal radiation and not to the combination of thermal and luminescent radiation (Ivanov and Tyapkin, 1963, p. 24). For the above discussion, all radiant energy is assumed to be transmitted in a nonabsorbing medium such as a vacuum.

All radiant energy incident on a body must be either absorbed, reflected, or transmitted (Kruse, et al., 1962, p. 15). If the surface of the body is opaque, no energy is transmitted. One can view the loss of radiant energy due to the imperfect emissivity of a real body as an internal reflection of energy. Planck (1959, p. 4) describes this phenomenon:

It is true for the sake of brevity that we frequently speak of the surface of a body as radiating heat to the surroundings, but this form of the expression does not imply that the surface actually emits heat rays. Strictly speaking, the surface of a body never emits rays, but rather it allows part of the rays coming from the interior to pass through. The other part is reflected inward and according as the fraction transmitted is larger or smaller the surface seems to emit more or less intense radiations.

The manner in which radiant emittance at a given wavelength varies with temperature provides the basis for determining the temperature of a surface by measuring the intensity of its radiant emittance. Planck's Law describes the spectral relationship of the radiative properties of a blackbody. This law gives the intensity of radiant energy (Wlambdab) from a blackbody at a given wavelength and temperature (Simon, 1966, p. 14):


where h is Planck's Constant, c is the speed of light, k is the Boltzmann Constant (1.380 erg/deg), T is the temperature in K, and l is the wavelength in microns. The quantity ( 2phc2) is often referred to as the first radiation constant (Cl), while hc/k) is the second radiation constant (C2) (Simon, l966, p, 14). Planck's Law simplifies to:

Wlb =C^l/l5(exp(C^2/lT-l).

When the intensity of radiant energy is plotted against wavelength at different temperatures, a family of spectral emittance curves is obtained (Figure 2). These curves indicate that there is a large increase in radiant emittance for each increase in temperature and that the wavelength of maximum emittance shifts to shorter and shorter wavelengths as ehe temperature increases. By taking the derivative of Planck's Law with respect to and setting it equal to zero (Simon, 1966, p. 14-15), the maximum radiant emittance is shown to occur at a wavelength, max,where: lmax=2898/T This equation is known as Wien's Displacement Law (Figure 2). This shift in maximum wavelength with temperature can be visualized by the heating of a metal. As the heat is applied the metal radiates in invisible infrared wavelengths. Eventually it starts to glow a dull red. As more heat is applied, the metal glows orange and then yellow. With further heating, the metal will radiate at all the wavelengths of the visible spectrum and appear white hot. The effective surface temperature of the sun is between 5000 and 6000K (Siegel and Howell, 1968, p. 27). According to Wien's Displacement Law, the sun radiates its maximum energy in the center of the visible spectrum at about 0.5. At temperatures about 140K, maximum
radiant emittance occurs in the far infrared. It can be seen from the Wien Displacement Law that terrain surfaces which have a temperature of about 12C (285K) have peak radiant emittance at about 10 . This is in the intermediate infrared region. To determine the total radiant energy at all wave lengths, Planck's Law can be integrated from infinity to zero (Siegel and Howell, 1968, p. 27-28): Wb=C1/l5(exp(C2/lT)-1=T4 (range 0-inf) This equation is the Stefan-Boltzmann Law and a is the Stefan-Boltzmann Constant (1.354x10-l2 cal/cm2/K4/sec). The Stefan-Boltzmann Law gives a method of calculating the total radiant emittance of blackbody at a given temperature. It may be of interest to determine the radiant energy in a certain wavelength interval. For a black body, this is done by integrating Planck's Law between the desired wavelengths. Values of radiant energy for blackbodies have been tabulated and appear in the tables of Pivovonsky and Nagel (1961). For blackbodies, 75% of the total radiant energy occurs between lambdamax and infinity while 25% of the radiant emittance will occur between lambdamax and zero (Simon, 1966, p. 16). For a blackbody at terrain temperature, 12C, over 75% of the radiant emittance will occur at a wavelength greater
than 10 , and 36% of the radiant energy will occur between 8 and 14 (Pivovonsky and Nagel, 1961, p. 244).

Two important generalities should be emphasized concerning the relationship of radiant energy and temperature. The Stefan-Boltzmann Law indicates that as the temperature of a radiating body increases, the radiant energy increases in direct proportion to the fourth power of the temperature (K) at all wavelengths. Secondly, the Wien Displacement Law shows that as the temperature lncreases, the wavelength of maximum radiant intensity decreases. To view sections other than the one next following refer to Table of Contents


Infrared photography is the technique of obtaining a photographic record by using a camera lens to focus lnfrared radiation (Eastman Kodak, 1968, p. 3). Infrared photography is often confused with infrared radiation thermometry and infrared imagery. These processes are quite different and distinction must be made. The word infrared implies that infrared film has a response in the thermal or intermediate infrared region (1.5-20), but this is not true. Infrared film has a spectral sensitivity through the visible and up to about 0.9 of the near infrared region (Eastman Kodak, 1968, p. 3 and 31). For a body to emit radiation that peaks at 0.9 , the Wien Displacement Law indicates that this body must have a temperature of 3220 K. Clearly, this is out of the range of most terrestrial bodies. However, this is well within the range of radiation from the sun whose effective surface temperature is between 5000 and 6000K, Infrared film responds to visible and near infrared solar radiation that is reflected by objects on the earth. This pattern of reflected solar radiation produces an infrared photograph.
Infrared radiation thermometers respond to radiation in the intermediate infrared region. This is radiation that is emitted directly by the terrain surface and is not reflected solar radiation. It is apparent that it would be impossible to take an infrared photograph at night due to the absence of sufficient solar radiation. However, the earth is constantly radiating in the region in which infrared radiation thermometers are sensitive; and infrared thermal sensing is often carried out at night. An infrared image is a photographic display of infrared radiation thermometry data. Infrared thermal images of terrain features often appear as black and white photographs. These photographs are secondary displays of the thermal data. Infrared radiation thermometry data are inputted to a cathode ray tube, and a black and white photograph is taken of the image on the cathode ray tube. The actual photograph is a response to the thermal pattern of the terrain only as it has been detected and displayed electronically. The means of monitoring the radiation is different for infrared photography and infrared thermometry. Infrared films use normal silver halide photographic emulsions. Infrared radiation thermometers are electronic devices which employ supercooled crystals or thermally sensitive wires as the detecting agent.
The principal use of infrared film is in forestry and agriculture. Vegetative matter strongly reflects near infrared radiation, while water strongly absorbs near infrared radiation. Therefore, drainage patterns appear strongly contrasted to vegetative matter in an infrared photograph. There has been some use of infrared film for thermal sensing, but only for very hot cbjects which have sufficient radiation in the near infrared region to activate photographic elaulsions. Pollack and Hickel (1969) have described a process of infrared photographic thermometry for industrial turbine cooli-ng investigations up to 1370C. Fritz (1967, p. 1133) observed that an object heated to 650F will be recorded by infrared film if exposed for 15 minutes at f/2.0. This assumes that no other radiation is present to affect the film. Fritz (1967 , p. 1133) concludes that infrared film won't record normal terrestrial temperature differences. In summary, three important differences between infrared photography and infrared thermometry manifest themselves. The source of radiation for infrared photography is the sun; while for infrared thermometry, the source of radiation is the terrain surface. Secondly, infrared photography senses in the 0.5-0.9 band of the electromagnetic spectrum, while infrared thermometry senses in the 1.5-14 band. Finally, infrared photography uses silver halide film emulsions
as the detector, while infrared thermometry uses electronic sensors. Henceforth in this paper, infrared photography, infrared thermometry, and infrared imagery will apply to the sensing processes distinguished above.

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The first report on the ability to render a thermal pattern visible was made by Sir John Herschel (1840), the son of Sir Frederick William Herschel, the discoverer of infrared radiation. Sir John Herschel (1840, p. 51) reported:

I have discovered a way by which the calorific rays in the solar spectrum are made to leave their impress on a surface properly prepared for the purpose, so as to form what may be called a thermograph of the spectrum, in which the intensity of the thermic ray of any given re frangibility is indicated by the degree of white ness produced on a black or very dark ground...

On paper especially treated with spirit of wine, Sir John Herschel (1840, p. 53) was able to record thermal radiation emitted by the sun in the near and part of the intermediate infrared region. The sun's rays were refracted through a prism and the visible parts of the spectrum were marked. The thermal patterns were observed beyond the red end of the visible spectrum. The thermal pattern was produced by the differential evaporation rates of the spirit of wine on areas of the paper that were receiving the thermal radiation.

Since this original work, technology has advanced to the point where electronic radiation thermometers have been developed to measure the intensity of radiant

emittance at specified wavelengths or within particular spectral bands. These instruments have been made portable for use in the field and have been adapted for use in airplanes and satellites. They are capable of measuring the relatively low levels of terrestrial infrared radiation. There are many earth science applications of infrared thermometry. Among these are water resource studies (Weaver, 1969), agricultural studies (Weaver, l969), timber resource studies (Colwell, 1968), distinguishing of surface materials (Cantrel, 1964, Sabins, 1967, and Moxham, et al., 1967), forest fire detection (Wilson, 1966), sea ice studies (McLerran, 1967), and identifying tectonic and structural features (Sabins, 1967, and Moxham, et al., 1967).

Airborne infrared radiation thermometers have been used to detect thermal emissions from volcanic and geothermal areas. Work during the decade from 1958-1968 has been summarized by Friedman and Williams (1968). They report that several geothermal fields and 22 volcanoes were surveyed by infrared techniques during that period. Infrared systems recorded effusive volcanic activity at Kilauea, Etna, and Surtsey (Friedman and Williams, 1968, p. 788), Surface thermal anomalies indicated a change in the thermal regime prior to the eruption of Askja Volcano, Iceland in 1961 (Friedman and Williams 1968, p. 788).

Curvilinear fault patterns associated with the Kilauea Caldera, Hawaii (Fischer, et al., 1964, p. 735), the central crater of Taal Volcano, Philippines (Moxham and Alcara, 1966, p. 830), and the summit crater of Mt. Rainier, Washington (Moxham, et al., 1965, p. D93) have been manifested on infrared imagery. Thermal features in the Cascade Range have been summarized by Moxham (1971). Linear and en echelon fault systems associated with rift zones have been indicated on infrared imagery along the southwest rift zone of Kilauea (Fischer, et al., 1964, p. 735) and in the Icelandic rift zone (Friedman and Williams, 1968, p. 788).

Moxham (1969, p. C115) reported that the most intense thermal anomalies in the Geysers area of California coincided with the region of hydrothermally altered and steaming ground with the thermal maximum occurring over active fumaroles and hot springs. Infrared thermal sensing devices have been flown over several volcanoes along the Kamchatka Peninsula in Russia. These studies have delineated fumarolic areas and fault patterns (Shilin and Komarov, 1968; Shilin et al., 1969, and Shilin and Gusev, l969). Surface hydrothermal features have also been mapped in Yellowstone National Park (McLerran and Morgan, 1964; and Miller, 1966). Infrared surveys have been used to determine the proportion of total heat flow from a cooling body that is emitted as radiant energy. The proportion of heat

that was emitted as radiant energy was found to be about 10% at Alae Lava Lake, Hawaii (Decker and Peck, 1967, p. D175). About 4% of the thermal energy in a lava flow` on Surtsey Volcano, Iceland exited the earth's atmosphere as radiant emission (Friedman and Williams, 1968, p. 815). The Friedman and Williams study (1968) used data obtained from an lnfrared sensor employing the 3.45-4.07 band in the Nimbus II satellite. Decker and Peck (1967) used a land-based radiometer measuring in a wavelength band greater than 3 from a height above the surface of one foot. To the best of this author's knowledge, the study described herein is the first land-based attempt to remotely obtain an infrared thermal pattern of volcanic terrain.

To date, two main uses for infrared thermal images of volcanic features have manifested themselves. Infrared thermal images have depicted the relative intensity of anomalous geothermal features in a region. Secondly, infrared thermal images have been able to relate thermal anomalies to structural and tectonic patterns such as faults caused by rifting or caldron subsidence in volcanic areas. These airborne studies are purely qualitative; and in general, they merely confirm the presence of geothermal and structural features already well known from field observations. A method of obtaining quantitative information from land-based infrared surveys will be discussed in this paper.

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The radiation thermometer used in this study is a Barnes PRT-5 Precision Radiation Thermometer. The instrument is manufactured by the Barnes Engineering Company of Stamford, Connecticut. A detailed description of the specifications and electronics of the instrument appears in the instruction manual (Barnes Eng. Co. 1968). A general description of the contents of this manual is included below. The instrument measures the radiant energy emitted ln the 8-14 band by any target that fills its two degree field of view. The two degree field of view "sees" a circle about three feet in diameter at a distance of one hundred feet from the sensor. The instrument is completely portable. It operates from either a built-in battery pack or external power. The instrument has about eight hours of battery time when operating at ambiant temperatures around 25C. The instrument can operate at ambiant temperatures between -20 and +40C. The instrument consists of two units, an Optical and an Electronics Unit (Plate 1). The Optical Unit Contains an internal reference standard held at 45C 0.5C. This unit continually compares the amount

of radiant energy emitted by the target with that emitted by the internal reference standard. The Electronics Unit converts this energy difference to a voltage that is metered in terms of irradiance at the radiometer ( watts/cm^2). The time constant of the radiation thermometer is 50 milliseconds,

A thermistor bolometer is used as the radiation detector. It measures equivalent blackbody temperatures between -42C and +65C 0.5C. The thermistor bolometer is a thermally sensitive resistor. A change in resistance takes place when the resistor is exposed to varying amounts of radiant energy. There are two thermistors in a bridge configuration in the unit. The radiant energy strikes one element while the other is shielded. The bridge unbalances by an amount proportional to the radiant energy. An optical chopper alternately exposes the unshielded thermistor to the target area and the internal reference standard. The diffexence in radiation is processed by the electronics. The thermistor sensing area is a 50 square on the back of a germanium lens. Unlike quartz, germanium is transparent to radiation in the 8-14 band. The optical unit is spectrally filtered to this 8-14 band. As was pointed out earlier, 36% of the energy emitted by terrain surfaces occurs in this 8-14 band.

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This survey was land-based. Each station was chosen so as to command a view of the volcano or volcanic feature whose thermal pattern was of interest. A Polaroid photo was then taken of the area under consideration. These photos were most often taken on the day preceeding the survey. A grid representing a 2 field of view was lain over the photo. In this way, the scene was sectioned off in 2 boxes representing the 2 field viewed by the radiation thermometer. A rifle type sight is located on the Optical Unit of the radiation thermometer. With the aid of this sight, the Optical Unit was pointed at a particular area that could be located on the Polaroid photo and identified by the grid system. The Optical Unit was held fixed on a tripod while the radiant energy was read off the Electronics Unit and recorded. In this way the radiant energy at any point of the field could be measured and documented, The radiant energy at each point represented the energy integrated over the whole 2 field of view. The radiant energies were converted to equivalent blackbody temperatures according to calibration tables of the Barnes Engineering Company. The following thermal patterns are

based on apparent surface temperatures. No correction was made for the emissivity of the surface material or atmospheric absorption of infrared radiation. The recordings were taken at early dawn before the sun directly struck the scene. In this way, the influence of differential solar heating on the surface materials was minimized. The volcanic surfaces were of constant composition, so the end emissivities were considered to be constant, though not unity. Therefore, any thermal anomalies could be related to differentlal geothermal heating, not differential solar heating or differential surface emissivity.

End of this section To view the rest of the thesis pp. 27 and ff.

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1. Izalco from Cerro Verde

Thermal patterns on the northeast flank of Izalco Volcano were mapped from a station on the front porch of an unoccupied hotel on Cerro Verde (Plate 2). Cerro Verde is a small hill on the south flank of Santa Anna Volcano and to the northeast of Izalco Volcano. Apparent temperatures were measured on the early morning of 16 December, 1969 (Plate 3) and 3 April, 1970 (Plate 4). There are about 250 m of vertical relief on the cone of Izalco as seen in Plates 3 and 4. No distinct thermal pattern was observed. The average apparent surface temperatures in April 1970 were about 3C warmer than those of December 1969 (Tables 6 and 7). The apparent surface temperatures of both patterns cool upwards about 1C in 250 m. One would expect the surface temperatures to cool with altitude due to the adiabatic cooling of the atmosphere. The rate of cooling of the surface was 0.4C/100 m on the northeast flank of Izalco. There is no surface manifestation of an anomalous geothermal area on the northeast flank of Izalco Volcano in either Plate 3 or 4.

2. Izalco from Lava Nueva

The southwest flank of Izalco Volcano was thermally mapped from a station near the Lava Nueva coffee grove (Plate 2). Plate 5 shows the thermal pattern of Izalco as seen from the Lava Nueva station on the early morning of 5 April, 1970. About 550 m of relief are represented in Plate 5. The collapse feature associated with the October 1966 lava flow (Plate 2) is seen at the left of Plate 6. It was hoped that the thermal pattern on this side of the cone might show an anomalous thermal feature associated with the upper-level magma chamber of this volcano. According to Rose and Stoiber (1969, p. 1329), the center of the upper level magma chamber is 550 m below the summit crater. The upper-level magma chamber is believed to be centered under the collapse feature, placing it at about G-12 on Plate 5. Clearly, there is no thermal anomaly associated with either the collapse feature or the assumed center of the upper level magma chamber. With the exception of the sides of the volcano, the isotherms are horizontal. The apparent cooling on the sides is probably due to presence of sky in the field of view of the radiation thermometer, when it was viewing close to the edge of the mountain. Clear sky temperatures were about -1.4C. When a portion of the sky is included in the field of view, the apparent surface
temperatures of any feature warmer than the sky appear cooler than when the field of view includes only the sur face. This problem is also encountered across the top, where it can be seen (Table 8) that apparent surface temperatures drop about 4.3C between grid rows 8 and 7. The cooling rate calculated for grid rows 12 to 8 (Table 8) is 4C/430 m or 0.9C/100 m. This is close to the dry air adiabatic lapse rate of 1C/100 m (Willett and Sanders, 1959, p. 22).

3. San Miguel Volcano from La Placita

Plate 6 is a thermal pattern of the west flank of San Miguel Volcano as seen on the early morning of 4 April, 1970. This pattern was obtained from a station on the western side of the soccer field at Finca La Pla cita. This Finca lies about 14 km south southeast of the city of San Miguel. The relief in Plate 6 from the bottom of grid row 7 to the top of the volcano is about 900 m. The slope of the volcano up to the base of grid row 8 is gradual relative to the slope above grid row 8. It is estimated that the vertical relief for grid rows 7, 8, 9 and 10 is 400 m, 250 m, 150 m, and 100 m respectively. The thermal pattern of San Miguel was determined five days after an ash eruption from the summit crater. Ash was erupted to a height of 400 m above the summit crater floor and was deposited in a fan-shaped area 10 km
northwest of the volcano (Stoiber et al., 1970). The light grey ash can be seen blanketing the bare rock upper slopes of the volcano (Plate 6). It was hoped that the location of the upper-level magma chamber that fed the ash eruption would be manifested in the thermal pattern. Reference to Plate 6 shows that there is no indication of the upper-level magma chamber. Over grid columns I to L (Plate 6) the thermal contours are essentially horizontal. The cooling for the 350 m from the center of grid row 8 over grid columns I to L is 1.4C. The rate of cooling is 0.4C/100 m.

4. Pacaya from Cerro Chino.

The northwest flank of Pacaya Volcano was thermally mapped from the northwest rim of an old explosive vent known as Cerro Chino (Plate 7). This station affords an excellent view of the vent of present activity on Pacaya as well as the deposit left by a lava flow in June 1969 (Plates 8 and 9). Thermal patterns on the northwest flank of Pacaya Volcano were mapped on three occasions: 23 December, 1969 (Plate 10); 30 December, 1969 (Plate 11); and 31 March, 1970 (Plate 12). The portion of the volcano covered in the Plates 10 to 12 represents about 300 m of relief. Eruptive activity has been going on since August of 1965 (Rose, 1965, p. 1) and is centered in the collapse feature on the west flank of the volcano seen in Plate 7. The cone that has been built
up by pyroclastic eruptions is seen in profile at S-12 of Plates 10-12. Hot pyroclastics from this cone blanket much of the west flank of the volcano. The area covered by these pyroclastics is sectioned off in the thermal patterns. Irregular temperatures that were often greater than the maximum range of the radiation thermometer (65C) were measured in this area. Since temperature patterns in this area are the result of loose material on the surface and not an underlying geothermal anomaly, this area is deleted from consideration. Eruptive activity was much greater on 31 March, 1970 than the days of the two previous thermal observations. Hot pyroclastics were falling over a greater area. For this reason, a greater region is deleted from the thermal pattern in Plate 12. The general pattern of the three thermal patterns is the same. A linear-shaped hot thermal anomaly points up slope towards the eruptive vent. The difference in apparent surface temperature between the hottest area and coolest area on each of the thermal patterns ranges from 7C on Plate 11 to 9C on Plate 12. The apparent surface temperatures cool to the left and right of the thermal anomaly and up slope. The hot thermal anomaly stretches farther to the left and the cooling gradient is much sharper in Plate 12 than in Plates 10 and 11. This is due to the presence of a few hot pyroclastics covering the lower portions of grid columns 4-13. Field
observations on the morning of 31 March, 1970, indicated that occasional pyroclastics from the explosive vent were rolling down the northwest side of the volcano and coming to rest in the lower portions of the area included in the thermal pattern (Plate 12). Due to the impossible task of precisely locating the areas in this thermal pattern where hot pyroclastics were lying and quantitatively determining their contribution to the apparent surface temperatures, no inference to underlying geothermal features will be made on the basis of this thermal pattern. Reference to Plate 8 shows that the June 1969 lava flow from Pacaya's active vent is coincident with the hot thermal anomaly in Plates 10 and 11. The relief associated with this lava flow is best seen in Plate 9. The sides of the lava flow radiate infrared radiation, and the radiation strikes the lava surfaces not under lain by lava flow. For this reason, the anomalously hot area extends beyond the physical confines of the lava flow. Near the summit of Pacaya, the apparent surface temperatures are seen to increase in towards the explosive vent. This may be a surface manifestation of the hot pipe feeding the explosive vent, but is most likely due to hot pyroclastics lying on the surface near the vent.
The right side of the thermal patterns shows a cooling with altitude observed in the preceeding thermal patterns discussed earlier. The average cooling rate for the thermal patterns in Plates 13 and 14 was 1.2C/100 m for the approxiamte 200 m up grid column P from the center of grid row 10 to the center of grid row 7. There is no surface manifestation of an underlying geothermal anomaly in either Plate 13 or Plate 14.

6. Caliente from Santa Mari.

The Caliente Dome is a part of Santiaguito and is located at its eastern end about 1500 m below the summit of the present volcano, Santa Maria (Plates 15, 16, 17, and 18). The thermal pattern of the Caliente dome was mapped on the early morning of 20 December, 1969 (Plate 19) from a station on the summit of Santa Maria. The hottest part of the dome is congruent with the recent explosive vent at H-8 (Plate 19). Apparent surface temperatures are seen to increase up slope toward the explosive vent. The irregular thermal pattern across grid row 10 is due to varying atmospheric conditions while this row was being mapped. Small clouds sporadically occupied a portion of the field of view of the radiation thermometer and caused irregular, lower apparent sufface temperatures. The El Mitad Dome on the right side of Plate 19 shows uniform apparent surface temperatures of about 9
and 10C. Most of the area to the right of grid column K is bare lava, while the areaa to the left of grid column K is blanketed with a thin veneer of fine ash erupted from the Caliente vent.

7. Santiaguito from Buena Vista.

Plates 20 and 21 show from left to right the El Mitad Dome, the El Monje Dome, and the El Brujo Dome of Santiaguito as seen from La Buena Vista located on the west flank of Santa Maria Volcano (Plate 17). Santiaguito extends about 1400 m from left to right with a maximum relief of about 350 m. These thermal patterns were mapped on the early mornings of 22 December, 1969 and 30 March, 1970, respectively. It is apparent in Plates 20 and 21 that Santiaguito shows increasing apparent surface temperatures with altitude. This is a reversal of the patterns observed at Izalco, San Miguel, and Pacaya Volcanoes and is in consistent with the adiabatic cooling of the atmosphere with altitude. The top of Santiaguito is bare rock that has been gradually extruded upward with the growth of the individual domal units. Material is continually breaking off the upper slopes of Santiaguito and rolling down the lower slopes forming a thick talus blanket. This talus blanket has an insulating effect and hinders the conduction of heat out from the magma chamber to the surface. The upper levels of Santiaguito are devoid of
this insulating talus blanket and, therefore, have higher apparent surface temperatures. The apparent surface temperatures on the early morning of 30 March, 1970 (Plate 21) were on the average 2C warmer than those of the early morning of 22 December, 1969 (Plate 20). The average minimum air temperatures for the region around Santiaguito are also 2C warmer at the end of March than in December (Vasseau, 1967). Both Plates 20 and 21 show anomalously hot apparent surface temperatures in grids I-8 and P-9. It is in these regions that the Sapper and Bonis Fumaroles, respectively, are continuously emitting hot steam vapors. The hot steam radiates heat to the region around it and produces a broad hot thermal anomaly. The active El Brujo Dome is located at the far right of Plates 20 and 210 On both plates, a sharp therm al gradient is seen to stretch up and to the right across this dome. Plates 20 and 21 demonstrate the ability of remotely obtained infrared radiation thermal data to delineate areas of active domal upgrowth insofar as this growth is manifested by abnormally high apparent surface temperatures. Active fumarolic areas are also located by their local high temperature patterns.

8. El Brujo from La Isla.

The El Brujo Dome is shown to be an active thermal area in Plates 20 and 21. The north face of this dome was thermally mapped in greater detail from a station on La Isla (Plates 16 and 17) on the early mornings of 21 December, 1969 and 27 March, 1970. About 180 m of relief are present in Plates 22 and 23. It is from this vantage point that Rose (1970j p. 57) has traced the growth of the dome between February, 1967 and July, 1969. It is clear from an inspection of these patterns (Plates 22 and 23) that the center of the geothermal activity is at grid square M-5. The hottest area in the December, 1969 pattern (Plate 22) is located directly below a fresh spine that has been extruded upward. The upward growth of the north face of El Brujo is radiating from the hot spot at M-5. By MarchJ1970 (Plate 23), the sharp spine had broken off and the skyline profile was smootherO The skyline from the sharp spine in I-4 to the left showed no change between March, 1970 and December, 1969. Close inspection of the talus slope below this area shows that many of the rocks that were lying loose on the slope in December, 1969 were still present in March, 1970. The right skyllne underwent considerable change between DecemberJ 1969 and March, 1970.
The 10C and 12C apparent temperature isotherms on the December 1969 and March 1970 profiles, respectively, approximate the contact between the hard lava above and the loose talus below. From these isotherms, the apparent surface temperatures incerease sharply upward and decrease gradually downward. As is manifested in the overall thermal patterns of Santiaguito from Buena Vista (Plates 20 and 21), the apparent surface temperatures in March 1970 are about 2C warmer than those of December 1969. This is consistent with the average seasonal temperature trends in the region (Vasseau, 1967).

9. El Brujo from La Loma.

The norhtwest face of El Brujo Dome was thermally mapped on the early morning of 29 March, 1970 (Plate 24). This thermal pattern was obtained from La Loma located on the ridge abouove La Isla (Plates 16 and 17). there are about 350 m of relief on this northwest face of El Brujo in Plate 24. The hard rock outcropping at G-6 on Plate 24 is equivalent to the rock spines seen on the skyline at R-6 and S-6 of Plates 22 and 23. The isotherms of apparent surface temperatures on Plate 24 indicate the center of thermal activity is in the upper-right protion of the plate. Field observations noted a steaming lava outcrop in this area that can be seen in Plate 24 at K-5. This area was not
thermally mapped because on the early morning of 29 March, 1970, this area was covered by clouds. The clouds were induced by the large quantities of steam being emitted from this active geothermal area. Hot rocks are continually breaking off the upper slopes of El Brujo, especially in the regions of G-5 and I-4. These hot rocks roll down the talus slope out of the area covered by Plate 24 at I-12, J-12, and K-12. The active talus area is marked by distinctly lighter colored surface material in Plate 24. Apparent surface temperatures are abnormally hot in this active area due to the influence of the hot rocks rolling down slope.


The preceeding thermal patterns were based on apparent surface temperatures. Apparent surface temperatures differ from real surface temperatures in that apparent surface temperatures are calculated assuming that the surface material has unit emissivity and that there is no absorption or emission of radiant energy in the atmospheric path between the surface and the sensor. These two assumptions do not hold for a real environment. This section will consider the effects of the atmosphere in modifying real surface temperatures. The intensity of the infrared radiation arriving at the sensor differs from the intensity of the infrared radiation very near the surface due to attenuation and emission of radiation by the atmosphere (Saunders, 1967, p. 4110). If the atmosphere partially absorbs radiation at a particular wavelength, it emits radiation at this same wavelength. The atmospheric path behaves according to the following equation:
where El, al, and Tl are the emissivity, absorptance, and fractional transmission respectively of the atmospheric path at wavelength l(Yates, 1958, p. 3). If _____
the atmosphere has a fractional transmission of 0.3, the sensor will receive 30% of the radiation emitted by the surface and 70% of the radiation that would be emitted by a blackbody at the temperature of the atmospheric path (Yates, 1958, p. 4). The absorption of infrared radiation by the atmosphere depends primarily on the amount of precipitable water in the atmospheric path. The amount of precipitable water is "the thickness of the layer of liquid water which can be precipitated from the absorbing air column (Gebbie, et al., 1951, p, 87)." Figure 3 shows the atmospheric transmission of radiation in the 8-14 band over a path one sea mile long (1852 m) with 17 mm precipitable water. Planimetric integration of this curve showed the average transmission of the atmosphere in the 8-14 band to be 60%. Yates (1958, fig. lB) has plotted atmospheric transmission, against wavelength over a 1000 ft (305 m) path with 2.2 mm precipitable water. Planimetric integration of Yates'curve indicated the atmospheric transmission to be 84%. There are no data on the amount of precipitable water in the air around the volcanoes that were studied. For the sake of the followiug calculations, the atmospheric transmission will be assumed to have been 70% with a maximum variation of 14%.
The actual radiant emittance originatlng at a surface, assuming an atmospheric transmission of 70% can be calculated according to the following equation:
where Ws, Wa, and Wr are the radiant emittance originating at the surface, the radiant emittance originating in the atmosphere, and the radiant emittance arriving at the sensor respectively. The radiant emittances can be converted into apparent temperatures according to the Stefan-Boltzman Law. Figure 4 shows graphically the correction factor that must be added to the apparent surface temperatures (based on radiant emittance arriving at the sensor) for different atmospheric and apparent surface temperatures. Each of the thermal patterns that will be used in the excess radiant heat calculations in the next section are corrected for atmospheric absorption and emission of 8-14 radiation. Air temperatures for the December, 1969 patterns were recorded at the sensor stations at the time the patterns were obtained. For the March and April 1970 thermal patterns, air temperatures were not recorded. When air temperatures were not recorded, the air temperatures were estimated on the basis of regional meteorological data of the Observatorio Nacional del Servicio Meteorologio de Guatemala (Vasseau, 1967). Air temperatures are assumed to be constant for constant elevations and
to cool with alitutde according to the dry adiabatic lapse rate of 1C/100 m (Willett and Sanders, 1959, p. 22). Based on the air temperature at the elevation of the sensor and the adiabatic lapse rate, air temperatures for all the elevations were calculated. The air temperature of an atmospheric path is taken as the average of the air temperature at the sensor and the air temperature just above the surface of the volcano for the particular field of view being considered. An example of an atmospheric thermal profile is seen in Figure 5. These air path temperatures are considered accurate to 2C. The nocturnal accumulation of cold air on poorly drained surfaces has been indicated as a problem in infrared thermal sensing (Wolfe, 1968, p. 19). Cold air is apt to fill a topographic depression and provide anomalously low atmospheric temperatures. However, it is felt that the volcanic slopes observed in this study are uniformly well drained so that no local accumulations of cold air were encountered. The radiant emittance at the surface of the volcano was calculated according to the equation for the atmospheric absorption correction discussed earlier. The radiant emittance at the surface was then converted to apparent surface temperature according to the Stefan Boltzman Law. These were apparent surface temperatures corrected only for atmospheric absorption, not surface
emissivity. The atmospheric corrected apparent surface temperatures are those that would have been measured if the radiation thermometer had been just above the surface of the volcano.


It is possible to calculate the excess radiant heat emission of one surface compared to another, when both surfaces are radiating heat to a common third surface such as the sky (Decker and Peck, 1967, p. D173). This was done for six of the thermal patterns: Pacaya from Cerro Chino, 12/23/69 (Plate 10); Pacaya from Cerro Chino 12/30/69 (Plate 11); Pacaya from Cerro Chino 3/31/70 (Plate 12); El Brujo from La Isla, 12/21/69 (Plate 22); El Brujo from La Isla, 3/27/70 (Plate 23); and El Brujo from La Loma, 3/29/70 (Plate 24). The area chosen for the excess radiant heat calculation at Pacaya was free of recent hot eruptive products and included the June, 1969 lava flow (Tables 10-12). At El Brujo, the selected area covered the upper part of the dome and avoided the lower thick talus blanket (Tables 18-20). Temperatures that represent an average of the coolest apparent surface temperatures in the selected areas of each of the six thermal patterns were noted. These temperatures, corrected for atmospheric absorption, serve as a cold base and represent the temperatures of the nonanomalously hot areas. On the three Pacaya thermal patterns, the cold base is located in the upper
left portion of the selected area. On the El Brujo patterns, the cold base is across the bottom of the selected area. The cold base temperatures are considered accurate within 0.5C. In Section VIII, it was noted that atmospheric temperatures cool with altitude. This cooling of the atmosphere with altitude will tend to cool terrain surfaces as they increase in altitude. The cooling rates over nongeothermally active areas were determined for eight of the thermal patterns discussed in Section VII. The thermal patterns were Izalco from Cerro Verde, 12/16/69; Izalco from Cerro Verde, 4/3/70; Izalco from Lava Nueva, 4/5/70; San Miguel from La Placita, 4/4/70; Pacaya from Cerro Chino, 12/23/69; Pacaya from Cerro Chino, 12/30/69; Pacaya from El Chupadero, 12/28/69; and Pacaya from El Chupadero, 4/1/70. The average, cooling rate for the volcanoes was 0.9 C/100 m with a maximum variation of + 0.5C/100 m. This average cooling rate is slightly less than the dry adiabatic cooling rate of the atmosphere of 1C/100 m. (Willett and Sanders, 1959, p. 22). The cooling of the terrain surface brought about by the cooling of the atmosphere with altitude lessens the radiative transfer of geo thermal heat from the surface to the atmosphere. An adiabatic correction factor of 0.9C/100 m is added to the thermal patterns to counteract the effect
of the adiabatic cooling of the atmosphere. This correction normalizes all apparent surface temperatures to the same base altitude and permits comparison of the radiative transfer at one elevation with that of another elevation. On Pacaya, where the cold base is at the upper part of the selected area, the adiabatic correction factor (Table 1) is added to the underlying grid rows of thermal data. No correction is made to the top row, the correction factor is added to the next row under, twice the correction factor is added to the next row under, etc. At El Brujo, the cold base is at the bottom of the selected area of the thermal pattern. In the case of the three El Brujo patterns, the correction factor is added in increasing increments to the overlying grid rows of thermal data. The excess radiant heat from the selected area of each thermal pattern is calculated according to the equation in Table 1. The radiant heat emitted at the cold base of each thermal pattern is subtracted from that of each thermal data point in the same pattern. The difference in radiant heat between the cold base and each point is averaged over the selected area. The resulting excess radiant heat figures for each of the six selected thermal patterns are listed in Table 1. The temperatures on which the excess radiation calculations are based are apparent temperatures, not corrected
Table 1 Calculation of Excess Radiation Heat Emission
W= /ni (Ti4-To4)
	W=excess radiant heat loss, cal/cm2/sec
     	=stefan-Boltzman Constant=l.354xl0-12 cal/cm^2/K-4/sec
     	n=number of thermal data points
  	Ti-apparent surface temperature corrected for
     	     adiabatic cooling at each thermal data point, K
  	To= Cold base apparent surface temperature corrected for adiabatic cooling,K
Thermal Pattern  Thermal Data    A     n     To
Pacaya from		Table 10	-0.3	55	275.8	3.6x10-4
Cerro Chino

Pacaya from		Table 11	-0.4	44	274.7	2.3x10-4
Cerro Chino

Pacaya from 	Table 12	-0.3	55	279.5	8.3x10-4
Cerro Chino

El Brujo from	Table 18	0.2	66	281.0	4.2x10-4
La Isla

El Brujo from 	Table 19	0.2	66	282.1	3.9x10-4
La Isla

El Brujo from	Table 20	0.3	61	286.5	5.8x10-4
La Loma

*A=Adiabatic correction factor, K per grid row.
for emissivity. Since the calculations depend only on radiant heat emitted by the surface, there is no need to figure the surface emissivities into the calculations. The excess radiant energy figures for Pacaya and El Brujo are accurate within 61% and 40% respectively. The overall error is arrived at by taking the square root of the sum of the squares of the percentage error contributions of the individual variables involved in the excess radiant heat calculation: adiabatic cooling correction factor, atmospheric absorption, atmospheric path temperature, cold base temperature, and apparent surface temperature. The Pacaya error is greater than the El Brujo error because the difference between the atmospheric path temperatures and apparent surface temperatures at Pacaya are greater than those of El Brujo. Therefore, the excess radiant heat figures at Pacaya are more sensitive to errors in the atmospheric corrections (Section VIII) than those at El Brujo. All six excess radiant heat figures are within an order of magnitude of the 9.57 x 10-4 cal/cm2/sec figure obtained by Decker and Peck (1967, p. D173) for the excess radiant heat flow at Alae Lava Lake, Hawaii between 5:10 and 5:30 in the morning. Decker and Peck (1967) also calculated the total heat flow from Alae Lava Lake, Hawaii. Total heat flow is obtained by multiplying the thermal conductivity of the lava by the geothermal gradiant, It was observed
that the excess heat loss by surface radiation in the early morning represented about 20% of the total heat flow from the cooling lava lake (Decker and Peck 1967, p. D175). Decker and Peck (1967, p. D175) speculate that the rest of the heat was lost by "evaporation of rain, transfer by escaping gases, and conduction and convection of the contact air layer." The 3/31/70 excess radiant heat flow figure from Pacaya is anomalously higher than the 12/23/69 and 12/30/69 figures due to the presence of hot, recently erupted pyroclastics on the surface. The 3/31/70 figure is deleted from further consideration. The average of the 12/23/69 and 12/30/69 excess radiation heat figures at Pacaya is 3.0 x 10-4cal/cm^2/sec. If 20% of the total heat flow at Pacaya in the early morning was accounted for by excess radiant emission, as was the case at Alae Lava Lake Hawaii (Decker and Peck, 1967, p. D174), then the total heat flow at Pacaya was 1.5 x 10-3cal/cm2/sec. The recent eruptive products at Pacaya are basalts (Eggers, personal communication, July 1970). Since the thermal conductivity of the basalt is known, the geothermal gradient is calculated on the basis of the heat flow equation in Table 2 to be -0.4C/cm. By taking the geothermal gradient to be -0.4 C/cm, the melting temperature of basaltic lava to be 1050C (Yoder and T111cy, 1962, p. 463), and the lava surface temperature to be 15C, the depth to molten lava is calculated to
Table 2
Calculation of Geothermal Gradient at Pacaya
dQ/dA=-K dT/dZ

	dQ=heat flow=1.5x10-3 cal/sec
	dA=area=1 cm^2
	K=thermal conductivity=3.4x10-3 cal/cm/sec/C
                      (for basalt (Decker and Peck, 1967, p. D174))
	dT=temperature, C
	dZ=depth, cm

dT/dZ=dQ/dA K=-0.4 C/cm

be 26 m. Carrying on the 61% error in the excess radiant heat calculations at Pacaya, the geothermal gradient is accurate between -0.2 and -0.7C/cm and the depth to molten lava is accurate between 15 and 51 m. The excess radiant heat at Pacaya is due to the buried June, 1969 lava flow. The lava flow was no greater than 5 m thick at the time of emplacement (Eggers, personal communication, Sept., 1970). Taking this thickness as a maximum, it is possible to calculate according to the model of Jaeger (1961, p. 730) that the portion of the lava flow included within the thermal pattern had completely solidified within 59 days after emplacement (Table 3). Jaeger's model is based only on cooling by conduction and must be taken as a maximum time. If convective or radiative cooling were taken into account, the cooling rate would be faster. Therefore, it is clear that the June, 1969 flow was completely solidified in December, 1969 when the initial radiation data were taken. The radiation data taken in December, 1969 also indicate that the lava flow had completely solidified, for the calculated geothermal gradient requires greater than the thickness of the lava to reach melting temperatures. The depth required for melting temperatures is 26 m while the thickness of the lava was no greater than 5 m.
Table 3 Calculation of Cooling Time for June 1969 Lava Flow at Pacaya T=kt/d^2 (after Lovering, 1935 and Jaeger, 1961, p. 722) T=dimensionless term proportional to time of emplacement of lava flow and relates extrusive lava sheets of all thicknesses to the same set of curves=0.14 (see footnote (1) below) k=themal diffisivity=6.8x10^-3 cm2/sec (Birch, 1942, p. 253) t=time after emplacement, sec d=thickness of extrusive sheet=500 cm (maximum estimate after Eggers (personal communication, Sept., 1970) t=Td2/kk=5.1x106 sec=59 days (time for lava to solidify) ___________________ (1) Calculation of T: To=temperature of lava at time of emplacement =1250C (maximum temperature of basaltic lava observed on surface (Lee and Clark, 1966, p. 511)) T=temperature of lava at solidification=1050C (Yoder and Tilley, 1962, p. 463) therefore, T/To=0.8 at the moment of solidification according to Jaeger (1961, p. 730, fig. 11), if T/To=0.8, then the maximum possible value for T will be 0.14.
The three values of excess radiant heat from the El Brufo Dome are in close agreement (Table 1). The average of these three values is 4.6x10-4 cal/cm2/sec. If this figure represents 20% of the total early morning heat flow, as was observed by Decker and Peck (1967, p. D174) at Alae Lava Lake, Hawaii, the total heat flow from El Brujo Dome is 2.3x10-3 cal/cm2/sec. This figure is assured to apply to the whole dome, but represents observations from two angles that cover about one half of the dome. El Brujo Dome is dacite (Rose, 1970, p. 109-111 and p. 237-238). Based on the thermal conductivity of andesite, the geothermal gradient on El Brujo Dome is calculated to be 0.8C/cm (Table 4). Using 875C as the temperature change from ambiant to liquid andesite (Rose, 1970, p. 22) and a geothermal gradient of 0.8C/cm, the depth to molten rock at El Brujo Dome is calculated to be 11 m. By taking the error in excess radiant heat flow at El Brujo to be 40%, the geothermal gradient is accurate between 1.0 and 0.5C/cm and the depth to molten lava is accurate between 9 m and 19 m. On the basis of extensive field observations on and around the El Brujo Dome, Richard Stoiber (personal communication, August, 1970) and William Rose Jr. (personal communication, August, 1970) estimate the thickness of the crust over the magma chamber to be 5 and 10 m respectively. These figures
Table 4 Calculation of Geothermal Gradient at El Brujo dQ/dA=-K dT/dZ dQ=heat flow=2.3x10-3cal/sec dA=area=1 cm2 K=thermal conductivity=3.06x10-3 cal/sec/cm/C (for andesite (Birch, 1942, p. 252)) dT=temperature, C dZ=depth, cm dT/dZ=dQ/dA K= -0.8 C/cm
are also in close agreement with the 5-15 m estimate for the thickness of the crust of the Merapi Lava Dome, Indonesia (Van Bemmelin, 1949, p. 198, footnote 1). The heat flow from the selected areas on Pacaya Volcano and the El Brujo Lava Dome are three orders of magnitude greater than the average heat flow from the surface of the earth which is approximately 1.4 x 10-6 cal/cm2/sec (Lee, 1965, p. 36).


Yokoyama (1956-57) and Hedervari (1963) have described a method for quantifying the thermal energy involved in a volcanic eruption. In most cases, the thermal energy of a volcanic eruption is 10 to 1000 times greater than all other forms of energy (Hedervari, 1963, p. 375). The growth of the El Brujo Dome involved a slow extrusion of viscous lava and represents a volcanic eruption lasting years, not days or hours. The growth of the dome has been documented in detail by Rose (1970, p. 53-65). The thermal energy required for the growth of the El Brujo Dome between February, 1967 and July, 1969 is calculated in Table 5 and represents an expenditure of 3.8x10-2 cal/cm2/sec. The average heat flow from El Brujho Dome between December, 1969 and March, 1970 was found earlier to be 2.3x10-3 cal/cm2 /sec. The heat flow from the surface of the dome between December, 1969 and March, 1970 is an order of magnitude less than the themal energy input that accounted for the growth. This is to be expected, for the rocks in the upper part of the dome are still hot. The rocks involved in the domal growth have stored thermal energy. When the growth of the dome ceases, this energy will be gradually dissipated by radiative, convective, and conductive heat transfer to the atmosphere.
Table 5 Estimate of Thermal Energy Associated with Growht of El Brujo Dome: Feb. 1967-Jul. 1969. Eth=Vr(CT+B) (after Hedervari, 1963, p. 376) Eth=thermal energy, cal/cm3/sec V=rate of extrusion of rocks=1.1x105 cm3/sec (based on 8.5x10^6 m3 (based on 8.5x10^6 m3 extruded in 910 days) (Rose, 1970, p. 62 and 57-59) Eth=Vr(CT+B) (after Hedervari, 1963, Eth=Vr(CT+B) (after Hedervari, 1963, r=density of rock=2.3 gm/cm3 (based on Santa Maria rcks (Rose, 1970, p. 21-23)) C=specific heat of lava=0.3 cal/gm/C (based on basalt at 800C (Goranson, 1942, p. 235)) T=temperature of lava above ambiant=875C (based on Santa Maria rocks (Rose, 1970, p.22) B=heat of fusion=50 cal/gm (based on albite (Goranson, 1942, p. 238)) Eth=7.9x107 cal/sec surface area of new growth=2.1x10^9 cm2 (assuming average thickness of new growth to be 40m (Rose, 1970, p. 57-59) Eth=3.8x102 cal/cm2/sec
The total thermal energy expended during the growth of El Brujo dome was 6.2x1015 cal (2.6x1023 ergs). This is two orders of magnitude less than the thermal energy of the 1902 eruption of Santa Maria which has been estimated by Rose (1970, p. 24) to have been 10x1017cal (4.2x1025 ergs) and by Hedervari (1963, p. 380) to have been 12.5x1017 cal (5.3x1025ergs). 93


According to Kirchoff's Law, the spectral radiant emittance from a real body (Wlambda) equals the product of its spectral emissivity ( Elambda) and the spectral radiant emittance of a blackbody (Wlambdab) at the same temperature: Wl= ElWlb (Simon, 1966, p. 13). The apparent temperatures discussed previously were not corrected for surface emissivity. Since real body emissivities are less than one, the apparent surface temperatures must be corrected upward to represent the real surface temperatures. Daniels (1966 and 1967) has measured the spectral emittance of natural rock surfaces in the 8-14 band. Daniels (1967, p. 7) gives the emissivity of a banded andesite with feldspar phenocrysts from a lava dome to be 0.90. This rock is considered close to those of the Santiaguito lava dome. Daniels (1967, p, 7) gives the emissivity of a black, vesicular basalt as 0.91. This rock is considered close to the vesicular olivine basalt of Pacaya Volcano and Izalco Volcano. Since the emissivities of a pumiceous rhyolite and a welded portion of the Bishop Tuff are both reported as 0.91 (Daniels, 1967, p. 5 and 6), it appears that the chemical
composition of the extrusive volcanic rocks doesn't affect the surface emissivity by greater than 0.0l. This close agreement gives confidence to the values chosen for the respective volcanoes and indicates that the ash blanketing the upper slopes of San Miguel Volcano has an emissivity of 0.910.01. The Stefan-Boltzman Law states that the radiant emittance of a real body (W) equals the product of its real temperature in degrees Kelvin (Tr) to the fourth power, the Stephan-Boltzman Constant () and its emissivity (e):
Given the apparent temperatures and the emissivity of a surface, it is possible to calculate its real body temperature on the basis of the following equation:
Tr= (Ta4/e )1/4
where Tr and Ta are the real body temperature and apparent temperatures respectively and E is the emissivity of the real body. Assuming that all rocks at Santiaguito have 0.90 emissivity, a correction of between 7 and 8C should be added to all apparent temperatures to get real surface temperatures. Assuming that the emissivity of all Pacaya and Izalco rocks is 0.91, a correction factor of
between 6.5 and 7.5C should be added to the apparent surface temperatures to get real body surface temperatures. The variation of apparent and real temperatures for different emissivities is shown graphically in Figure 6. By combining the emissivity and the atmospheric corrections with the apparent surface temperatures, one arrives at the real surface temperature. This is the temperature that would be measured directly on the surface of the rock. A comparison of apparent surface temperatures and real surface temperatures is given diagrammatically in Figures 7 and 8. The general shape of the thermal patterns remain the same though the real surface temperatures are about 5C warmer than the apparent surface temperatures. Figure 9 shows the thermal pattern of surface temperatures associated with the excess radiant heat. These temperatures are apparent surface temperatures corrected for atmospheric absorption and adiabatic cooling of the atmosphere and minus the cold base surface temperature. These temperatures can be converted to radiant energy by the Stefan Boltzman Law. It can be seen on the left that the horizontal isotherms associated with the cooling atmosphere with alitutde have disappeared though the contours associated with the June,1969 lava flow are still present.


This study is a land based infrared radiation thermometry survey of volcanic terrain. The theoretical relationships between infrared radiation and surface temperatures are discussed. Mention is made of the techniques of infrared photography and how they differ from those of infrared radiation thermometry. A Barnes PRT-5 precision radiation thermometer was used to obtain fifteen thermal patterns of nine different volcanic surfaces. A time interval of three months separated five of the thermal patterns and permitted observation of time related changes in the thermal regime of the volcanoes. The thermal patterns are corrected for the effects of atmospheric absorption, surface emissivity, and the adiabatic cooling of the atmosphere with altitude. The thermal patterns indicate areas of intense fumarolic activitity and domal growth. Based on excess radiant heat calculations, it concluded that the June, 1969 lava flow from Pacaya Volcano had completely solidified by December, 1969 This conclusion is consistent with theoretical calculations on the cooling of an extrusive lava sheet by conduction.
Excess radiant heat calculations indicate that the magma chamber underlying the El Brujo Dome, a subunit of the Santiaguito Volcanic Dome, is at a depth of 11 m with maximum variation of between 9 m and 19 m. This figure is consistent with field observations in the area. These calculations are based on the fact that the excess heat radiated from Alae Lava Lake in Hawaii in the early morning represented 20% of the total heat flow to the surface during the early morning hours (Decker and Peck, 1967). Further refinement of the quantitative relationship between excess radiant flow and total heat flow under varying atmospheric and surface conditions would permit more universal use of this author's method. The extrapolation of Decker and Peck's excess radiant heat data to other areas to predict a geothermal gradient implies that the areas over which the radiant heat data were collected are the same. Decker and Peck's hot base stations were located every foot along a profile 102 feet long (Decker and Peck, 1967, p.D171), which was considered representative of the central portion of the lava lake (Decker and Peck, 19~7, p. D173) whose diameter is between 800 and 1000 feet. The areas studied in this report were between 600 and 1100 feet on a side. It may be concluded that the scale
of the feature studied by Decker and Peck is approximately equivalent to the scales of the features in this report. The repeatability of the infrared measurements is impressive. The five thermal patterns that were mapped first in December 1969 and again in March 1970 show a very similar pattern of isotherms whose absolute temperature variations are a result of different atmospheric temperatures. This high degree of repeatability is imperative if one is to undertake a series of observations spread out over time. The total thermal energy required for the domal growth at the El Brujo is calculated. The indications are that the dome still has thermal energy stored and that this energy will be gradually dissipated over time. This study has proved the feasibility and rapidity of a land-based remote infrared radiation thermometry survey to obtain valuable information on the geothermal state of a volcano. It would be possible with observations spread out at periodic intervals over longer periods of time to trace changes in the underground magma reservoir of a volcano and, from the observed changes, predict impending volcanic activity.



The following tables list the thermal data used in plotting the thermal patterns 
and in calculating the excess radiant heat flow in the preceeding sections,

Table 7.  Thermal data, Izalco Volcano from Cerro Verde, 3 Rpril 1970. Numbers 
represent apparent surface temperatures In  C.  See Plate 4 for thermal pattern.

Table 8. Thermal data, Izalco Volano from Lava ~usva, 5 April 1970.

Numbsrs represent apparent surface temperatures in C. See Plate 5 for thermal 

Table 9. Thermal data, San Miguel Volcano from La Placita, 4 April 1970. Numbers 
rspresent apparent surfacs temperaturas in C. See Plate 6 for Thermal pattern
Table 11-  Thermal data, Pacaya Volano from Cerro Chino, 30 December, 1969.

                                0~ temperatures in  C.  Area sectioned off
Numbers represent apparent~ surface radiant heat calculation.  See Plate 11 to 
lower left was used in e~oe5S for thermal pattern.

Table 12~  Thermal data, Pacaya Volcano from.Cerro Chino, 31 ~t March, 196Q.
numbers represent apparent surface temperatures in C. Area ss~ioned to lower left 
was used in excess radiant heat alculation. See Plate 12 for thsrmal pattern.

Table 13. Thermal data, Pacaya Volcano from Finca El Chupadero 28 Deaember, 1969. 
Numbers represent apparsnt surface temperatures in C. See Plate 15 for thsrmal 

Table 14.  Thermal data, Pacaya Volcano from Finca ~1 Chupadero, 1 April, 1970.  
Numbers represent apparent surface temperatures in  C..  See Plate 14 for thermal 

Table 14.  Thermal data, Pacaya Volcano from Finca El Chupadero, 1 April, lB70.  
Numbers represent apparent surface tempsratures in  C.  See Plate 14 for thermal 

Table 15.  Thermal data, Caliente Dome, Santiaguito Volcano, from Santa Maria 
Volcano, 20 December 1969.  Numbers represent apparent surface temperatures in 
C.  See Plate 19 for thermal pattern.

Table 16. Thermal dsta, Santiaguito Volcano fron~ Buena Vists, 22 December, 1969. 
Numbers represent apparent surface temperatures in C. Sse Plate 20 for thermal 

Table 17. Thermal dsta, Santiaguito Volcano from Buena Vista,

30 March, 1970. numbers represent apparent surfacetemperatures in C. See Plate 21 
for thermal pattern.
Table 18. Th~rmal data, El Brujo Dome, Santiaguito
Volcano,from La Isla, 21 Deoember,l969- Numbers represent apparent surfaoe 
temperatures in C. Area seotioned off at top was used in excess radiant heat 
oalculation. See Plate 22 for thermal pattern.

Table 19.  Thermal data~ El Brujo Dome, Santiaguito Volcano~ from La Isla, 27 March, 
l970.  Numbers represent apparernt surface temeratures in C.  Area sectioned off 
at top was used in excess radiant heat calculation.  See Plate 23 for thermal 
Table 20. Thermal data, El Brujo Dome, Santiaguito Volcano, from La Loma 29 March 
1970. Nunbers represent apparent surface temperatures in C. Area sectioned off
 at top used in excess radiant heat calculation. See Plate 24 for thermal pattern.


Predicted Effects of Magma Movement

The geothermal gradient underlying El Brujo Dome has been shown to be 0.8C/cm (Table 4). Therefore,the solidus interface of andesite is reached at 11 m depth. Let us investigate the effects of an instantaneous upward movement to magma from 11 m to 5.5 m depth. The temperature change between liquid and ambiant andesite is assumed to remain unchanged at 875C. The upward movement of magma will double the geothermal gradient to 1.6C/cm and double the total heat flow to the surface to 4.6x10-3 cal/cm2/sec. By the methods outlined in Chapter IX, this increase in total heat flow would be manifested by an increase of 3.7C in average apparent surface temperatures. Assuming no meteorological changes, the cold base apparent surface temperature would remain unchanged, It is anticipated that the thermal effects of this upward movement of magma would be seen almost immediate ly in fumaroles and fissures on the surface due to the rapid upward convection of heat, However, if the heat were allowed to make its way to the surface only by the mechanism of conduction through the solid rock,

the thermal effects would be seen on the surface much later.
The effects of the magma movement on the geothermal gradient can be seen in the equation of Carlslaw and Jaeger
(19~9, p. 100):

V=V2(X/1)+(2/~) ~ V2c-os(n~-)-sin(n~x/l)exp(-kn ~t/12)
               n=l   n

where V is the temperature (C) at depth X (cm), 1 is the thickness of rock (cm)separating the surface and the magma, V2 is the temperature difference (C) of liquid andesite and ambiant, k is the thermal diffusivity of the rock (cm2/sec), and t is the time (sec),  For these calculations, the surface
is assumed to be at 0C, and the thernal diffusivity for andesite is taken as 1.24x 10-2 cm2/sec (Birch, 1942, p. 292) and considered independent of temperature.  By taking the derivative of the above equation with respect to X, the geothermal gradient at the surface (X=O) is seen to vary over time according to the following equation:

dx=lV  (1-2exp~-klT2t/12)+2exp(-4k1r2t/12)-2exp(-9k~r2t/12 ~ ., . )
Figure 10 shows the percent equilibration of the geothermal gradient at the surface plotted against time for the case of the 5.5 m crustal thickness of El Brujo Dome.The surface shows no effects of the subsurface magma movement until twelve days after the upsurgence.
and it takes over four months for gradient to fully equilibrate. Twelve days is taken as the minimum time for the surface to thermally manifest the subsurface magma movement and as the minimum time required for the magma movement to be monitored by surface infrared radiation thermometry. Figure 11 shows the percent equilibration of the geothermal gradient for different crustal thicknesses plotted against the log of time and using an average diffusivity of.01 cm^2/sec. There is an exponential increase in time with increase in crustal thickness for the surface to register changes in its geothermal gradient following a subsurface magma movement. Unless one is dealing with a very shallow magma chamber or unless there is a transfer of heat to the surface by mechanisms other than pure conduction through the rock, it appears that considerable periods of time are required for the thermal effects of a subsurface magma movement to be thermally manifested on the surface*

*The author wishes to acknowledge the kind assistance of Francis Birch, Professor of Geophysics, Harvard University, in interpreting the equations of Carlslaw and Jaeger (1959).


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