First order leveling surveys at Cerro Prieto

Geothermtcs, Vol 8, pp 273- 274

Pergamon Press Ltd 1979 Printed m Great Britain © CNR

FIRST O R D E R L E V E L I N G SURVEYS AT C E R R O P R I E T O J R G A R C I A G. Dtrecct6n General de Estudtos del Terrttorlo Nactonal, Mexico, D F Mexico

NOMENCLATURE /~h° ~m

difference m orthometnc elevation between two points (m) difference m elevation between two points (m) OC orthometnc correction between two points (m) DC dynamic correctmn between two points (m) hm elevation of a given point above sea level (m) G referencegravity for a given point in mgal (computed using the formula proposed for the 1967 reference geodetic system) G~, averagereference grawty between two points (mgal) go~2 averageobserved gravity between two points (mgal) g' approximate mean actual gravity along the plumb hne (mgal) go observed gravity (mgal) latitude of a given point In A u g u s t 1977 the C o m l s l 6 n Federal de Electrlcldad a n d the Dlrecci6n G e n e r a l de EstudIos del TerrltorIo N a c l o n a l ( D E T E N A L ) signed a n agreement to c o n d u c t vertical c o n t r o l surveys in the area of the Cerro Prleto geothermal field The p u r p o s e o f the survey was to establish a firstorder leveling n e t w o r k to detect, between surveys, vertical g r o u n d m o v e m e n t s The route to be followed was first d r a w n o n D E T E N A L t o p o g r a p h i c maps Sites having characteristics o f p e r m a n e n c e , stability, a n d easy p h o t o l d e n t l f l c a t l o n a n d access were identified a n d selected for the location o f the p e r m a n e n t stations Concrete m o n u m e n t s were built for the fixed elevation m a r k s ; m one case the m a r k was e m b e d d e d into a c o m m e m o r a t i v e m o n u m e n t High-precision I n s t r u m e n t s were used to o b t a i n the data Relative gravity m e a s u r e m e n t s were also m a d e to d e t e r m i n e the vertical c o n t r o l m o r e accurately At least three readings were t a k e n per station Each point was properly identified by its latitude a n d longitude Three types o f elevations were d e t e r m i n e d t o p o g r a p h i c , o r t h o m e t r l c , a n d definitive T o p o g r a p h i c elevations are o b t a i n e d starting with a k n o w n elevation, which is p r o p a g a t e d to all stations, based o n the elevation differences measured in the field O r t h o m e t r l c elevations differ f r o m the t o p o g r a p h i c elevations by the parallelism existing between lsohypsometrlc surfaces Therefore, to take Into c o n s i d e r a t i o n the e a r t h ' s curvature, corrections have to be m a d e to t o p o g r a p h i c elevations These corrections determine the difference between a h o r i z o n t a l surface a n d a n lsohypsometrlc surface All points o n an lsohypsometrlc or e q u l p o t e n t l a l surface are p e r p e n d i c u l a r to the p l u m b line (local attraction) In other words, all the points have the same gravlmetrlc p o t e n t m l H e l m e r t ' s o r t h o m e t r l c correction was used, 611° = A h " + O C

where OC = DC + hi

G

-

h:m

(,-o) g2

273

G

274

J R Garcia G g" ° 1 2

DC

=

--

GI2

G,2

Ah

l 2m

g ' = go + 0 0424 h m G = 978,031 8(1 + 0 0053024 sin 2 + - 0 0000059 sm 2 2+) Defimtlve elevations were calculated using a least-squares method to correct or adjust existing closure errors due to instrument or human errors To adjust the o r t h o m e t n c elevations Cholesky's method was used This method can be apphed to two types of problems (1) observation equations where the number of equaUons ~s greater than or equal to the number of unknowns, and (2) c o n d m o n equations where the number of absolute equations is less than or equal to the number of unknowns In the two cases the normal equations are set up differently but the method of solution ~s the same once the equations have been formulated The set of normal equations can be written as

I x } = {8}, where [N] = matrix of normal equations, {X} --- esumated solution vector, and {B} -- assocmted constant vector The solution of the system of equations yields final values for the connection pomts that form the network (F~g 1) The benchmark elevatmns of the network were computed using the adjusted elevations of the connection points

~4L.K X ~ 0 T 1~4

•

Reference bpnchmark

C') Connection point

Fig 1

First-order levehng network