Interim report on a regional RCM-network in Friuli, Italy

J Geodynamtcs Vol 18, Nos 1-4, pp 59-70, 1993

Copyright© 1994ElsevierScienceLtd Printed m Great Britain All rights reserved 0264-3707/93 $6 00+ 0 00

Pergamon

INTERIM REPORT ON A REGIONAL RCM-NETWORK IN FRIULI, ITALY A. B E I N A T , 1 R. JA, G E R , 2. C. M A R C H E S I N I 1 and G. SCHMITF 2 Dipartimento di Geonsorse e Territono, Umverslth & Udme, Udme, Italy 2Geodatlsches Inst~tut, Umversitat Karisruhe, Englerstrasse 7, D-76128, Kadsruhe, Germany

Abstract--The paper gives a report on geodetic activities in the epicentral region of the North Italian earthquake of May 1976 situated in the town of Gemona. The Gemona network was installed in 1989 as a regional monitoring network with seven points and an extension of 10 x 10 km. It is shown how this regional network is connected with other local networks in the Friuli region and how it ~s integrated into the GPS-Alps-traverse. The paper outlines the method for combining GPS and terrestrial data types in a 3-D concept, as well as for transforming and mapping GPS-results for a respective combination with terrestrial data in a classical (2-D, I-D) concept. The accuracies which could be realized by combining GPS and terrestrial data and some respective sensitivity studies are described, also stressing the comparison of GPS against classical terrestrial data types. Finally the paper presents the deformation analysis results, which have been evaluated with the hitherto available data.

1. T H E G E M O N A N E T W O R K AND ITS I N T E G R A T I O N IN A R E G I O N A L AND AN O V E R - R E G I O N A L GPS-FRAME OF NETWORKS IN THE ALPS

The Gemona network consists of seven points and covers the region of the town of Gemona and a few neighbouring villages. The network is situated above the epicentre of a strong earthquake, which destroyed the original town of Gemona on 26 May 1976. By means of a so-called regional Friuli 'GPS frame-network' (Crosilla et al., 1990) including also the terrestrial Caneva (Beinat et al., 1993) and the Fella-Gail network, the Gemona network becomes part of the GPS-Alps-traverse established in 1990 and observed in 1991 and 1992 (Leinen et al., 1991). Figure 1 shows the GPS-Alps-traverse crossing all interesting disturbance zones in the Eastern Alps in the context with the Friuli GPS framenetwork and the local networks included. Figure 2 shows details of the GPS frame-network with respect to sets of each three connection points for the local Caneva, the Gemona and the Fella-Gail networks as well as the connection points of the GPS frame-network to the GPS-Alps-traverse and the structure of the seven-point Gemona network. While the three networks included in the * To whom all correspondence should be addressed 59

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A BE1NATet al.

I HohenpeissenbergFRG -I-

STRIA

,

"-L / \

Trieste Ftg. 1 The Gemona network as part of the GPS-Alps-traverse (left, as silhouette in the geological profile) and of the regional Friuh GPS frame-network (dotted)

Friuli GPS frame-network were originally constructed for pure terrestrial observations linked by GPS to the regional frame, Sections 2 and 3 show that for the 10 x 10 km range of the Gemona network GPS is equal or even superior in accuracy and deformation sensitivity.

2. DATA PROCESSING CONCEPTS AND RESULTS FOR THE GPS-COMBINED GEMONA NETWORK

2.1. Available data, combined 3-D adjustment and accuracies Table 1 shows that a complete set of 3-D terrestrial observations and GPS exists only for the 1st epoch. In the other epochs only slope distances were measured and GPS has been performed only on the points 1, 4 and 7 to integrate the Gemona network into the Friuli GPS frame-network (Fig. 2), and subsequently into the GPS-Alps-traverse (Fig. 1). The mainly 2-D character of the observations is in accordance with the intention to perform in the highest priority a pure 2-D deformation analysis for the Gemona network and the other terrestrial networks included in the Friuli regional GPS frame-network as well as for the GPS-Alps-traverse with respect to the detection of fault-movements and the determination of strain-rates. The extensive 3-D terrestrial data and a complete GPS occupation for the 1st epoch (Table 1) however suggested a combined 3-D adjustment together with a

Regional RCM-network

61

• Points of the Alps-Traverse @ Pure Frame-Network Points

FELLA -

GAIL

Fig. 2 The regional Fnuh GPS frame-network (dotted) m its hnk to the GPS-AIps-traverse and including the terrestrial and partly GPS-combmed networks Caneva, Gemona and Fella-Gall

variance component estimation for all data types, which was performed with the software-package NETZ3D for the 1st epoch (Crosilla et al., 1990). For GPS the variance component estimation revealed that the external accuracy of the covariance-matrix C~,e is by a factor f2 = (3.5)2 worse than the covariance matrix Cgps,, of the internal accuracy, which resulted from the GPS-software processing (POPS software-package). The final result of the 3-D adjustment of the terrestrial data combined with GPS led to an average point accuracy of 6.7 mm and is shown in Fig. 3. Table 1 Avadable data for three epochs between 1989 and 1991

Epoch No.

T~me

1

April 1989

2

March 1990 April 1991

3

Terrestnal data

GPS-(WILD) 2-frequency

MES000-distances, directions, slmuitaneous zenith angles ME5000-distances

On all seven points

MES000-distances

Only on three points (1,4,7)

Network status Combined 3-D Data. 3-D adjustment and variance component-estimation

-"2-D data" "2-D data"

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A. BEINAT et al

2

4

11 Fig 3. Final result of the 3-D GPS-combmed adjustment of the 1st epoch

About the same scaling-factor f2 between the external and the internal accuracy was found for the (X,Y,Z)gps coordinates of the 1991 GPS-campaign for the frame-network (Fig. 2), which was processed with the Bernese Software-Package 3.3. The external accuracy was determined by performing a common adjustment and variance component estimation of the daily GPS session coordinates. The range of discrepancies between the accuracy C~s., and the 'true' external accuracy Cgps,e of GPS is known from practical experience and can be explained theoretically by the effects of neglecting correlations in the raw phase measurements and remaining unmodelled systematic errors (J/iger, to appear; Jiiger and Leinen, 1992). At least a scaling of Cgps,, towards Cgps,e is necessary for any further processing and interpretation of GPS coordinates, but it is only a first and rough approximation of the true external accuracy Cg~,e. In the correct sense Cu,s,~ has to arise from an additive modification of C~,,, which implies a complete change of the inner structure of C~.~ compared to Cgps,, (Leinen et al., 1991; J/iger and Leinen, 1992).

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63

S t a n d a r d ellipses

I

I

I

0

5

10

3km I

I

.... - -

GPS Terreltrlal

[7

Fig. 4 Comparison of the 2-D accuraoes between the terrestrial distance network (trd = 0 5 mm + 0 5 ppm) and GPS in the 'tuner datum'

The final external accuracy of GPS after scaling due to the above variance c o m p o n e n t estimation and after the conformal mapping (Section 2.2) of the (X,Y,Z)gps to plane (y,X)gps-Coordinates is shown in Fig. 4. For the pure terrestrial observation components the variance c o m p o n e n t estimation gave ad = (0.5 m m + 1.5 ppm) as accuracy of the ME5000 distances, and 0.0003 gon and 0.00045 gon for the direction and simultaneous zenith-angle measurements respectively in the 1st epoch. In the 2nd and 3rd epoch the distances turned out to be better, namely ad = (0.5 m m + 0.5/0.7 ppm).

2.2. Transforming and mapping of GPS and classical terrestrial observation types for a common 2-D adjustment and analysis concept As explained in the context of the data in Table 1 the G e m o n a network aims, as the other concerned regional and over-regional networks, in a first priority at a 2-D deformation analysis. It is familiar that the mapping of a point from space to a plane namely to 2-D coordinates (x,y) based on a rotational ellipsoid (axis a,b) is described by mapping functions x = x(B,L,a,b) and y = y(B,L,a,b) referring to the latitude B

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and longitude L, by omitting the ellipsoidal height h. As the mapping-functions also define curved parameter-lines x = const, and y = const, on the ellipsoid, the set ( X , Y , Z ) in space is consistent with (x,y,h). As soon as x = x ( B , L , a , b ) and y = y(B,L,a,b) are not assumed as a parameter-substitution on the ellipsoid but as Cartesian 2-D coordinates and referred to a plane Euclidian geometry we have to do with "mapped" coordinates (v,x). In geodetic applications conformal mapping-functionsmsuch as the transverse Mercator projection, delivering the UTM- or Gaul3.--Kr/iger coordinates--are the most important as the angle included by two geodesics on the ellipsoid is preserved after the mapping. The idea of combining GPS and terrestrial observations in a 2-D concept, which starts with a conformal mapping of the GPS space coordinates (X, Y,Z)~s according to the flow diagram in Table 2 was first published by Schmitt et al. (1991) and has meanwhile found great acceptance (Hofmann-Wellenhof et al., 1992). In case no other differently oriented and parametrized local ellipsoidal system than the GPS system is required, the similarity transformation, which separates steps 1 and 2 is omitted. On starting in step 1 with the stochastic model represented in the covariance-matrix C~s of the coordinates ( X , Y , Z ) g p s , the functional model of the complete mapping process (Table 2) has to be accompanied by a stepwise propagation of the covariance matrix of coordinates to preserve the mathematical strictness for any further use of the final result (y,X)gps, e.g. in the context of a combined adjustment and deformation analysis. A corresponding software-package T R A V A R carrying out the transformations and mapping of Table 2 together with a respective error propagation for the covariance matrix of coordinates is presented by Schmitt et al. (1991). As concerns the Gemona network, the GPS-system and the corresponding WGS84 reference-ellipsoid were kept for the 2-D conformal mapping with respect to a transverse Mercator projection (GauB--Kriiger coordinates). The plane GPS-coordinates (y,x)~ resulting from (X, Y,Z)gps w e r e combined with the classical terrestrial distance and direction observations. For combining the 2-D mapped GPS coordinates (y,x)~ with the terrestrial observations the standard reductions for the transverse Mercator projection (GroBmann, 1976) have to be applied to the distancemand direction-observations.

Table 2. Flow diagram for transforming 3-D GPS-coordmates to a local datum and for mapping to a plane 2-D system GPS-system 3-D Step 1 Cartesian coordinates (X,Y,Z)u,~ ~

Local ellipsoid system 3-D Still 3-D Step 2 Step 3.1 Step 3.2 Cartesian coordinates (X,Y,Z)~ ~

Similarity transformation

"Map" (2-D, l-D) Step 4

Curved coordinates and eUipsoldal heights

(x,y)~

~(B,L,h)~ ~---~(x,y,h)le ~

Parameter transformation

~h

Mapping

3.2 taken as plane 2-D coordinate 1-D eUips heights

Regional RCM-network

65

2.3. Characteristic results from the single epochs Figure 4 shows the accuracy of GPS after a conformal 2-D mapping (Section 2.2) in comparison with the accuracy of the distance network. Point No. 7 served as fixed reference-point for the processing of GPS-coordinate differences in epoch 1. The average accuracy of these coordinate differences was in the range of 4 mm according to the above variance component estimation. An accuracy of 3-4 mm for the 2-D mapped GPS coordinates of the GPS frame-network linking points 1, 4 and 7 in the 3rd epoch was determined by a session-wise adjustment and a respective variance component estimation. It is evident that the accuracy of GPS and the ME5000 distance network (in best case situation of t7d = 0.5 mm + 0.5 ppm) lie in the same range with a mean point accuracy of 2-3 mm, whereas both networks are represented in the so called 'inner' datum. It is remarkable that the GPS-network is more isotropic, which will also become important for the network-sensitivity (Section 3.3).

3. D E F O R M A T I O N ANALYSIS F O R T H E G E M O N A N E T W O R K

3.1. Height deformations The range of ellipsoidal 'height-deformations' determined by GPS between the 1989 and 1991 GPS-epochs for the three points 1, 4 and 7 linking the Gemona network to the GPS frame-network were in an average range of only 5 mm! This was evaluated by a simple 1-D Helmert-transformation between the epochs. Due to these small discrepancies there is no need to prove by an additional strict statistical testing that the heights are identical. For this, the ellipsoidal heights h of the points of the complete GPS-occupation in the 1st epoch (Table 2) were used hitherto for the reductions of the slope distances in the context of the 2-D conformal mapping in all epochs.

3.2. Visualization of 2-D deformations Figure 5 shows the discrepancies between the adjusted coordinates of the pure terrestrial networks in the single epochs and GPS in the 1st epoch. The residuals for GPS in the 3rd epoch against the terrestrial epoch 2 in the points 1, 4 and 7 (not presented here) are in an average range of 4 mm. Although the visualization of the residuals of a simple Helmert transformation is sometimes useful to trace out a more sophisticated deformation model, it suffers from the lack of a statistical strictness (due to the neglected correlation of the coordinates and due to the ignorance of the variance of the r e s i d u a l s ) briefly, it is no substitute for the strict mathematical model of a coordinaterelated deformation analysis (for this see J~iger and Drixler, 1990). In this context it turned out that applying a strict deformation analysis related to a more sophisticated generalized Helmert-transformation (Section 3.4), the large residuals in point 5 are not at all significant while those in point 1 are significant centring-errors.

66

A. BEINAT et al [] Identical points

5 km

GPS-I

O Non-identical points

!

Terr-3

s

I c,,,

315"~ ~4

5

6

q,

,

Terr-3 Ftg 5. Left: residuals of a standard Helmert-transformatton of adjusted coordinates of the terrestnal network epochs 1 and 2 Right. residuals of terrestrial epoch 3 and GPS-1 referred to the terrestnal network epoch 2

3.3. Sensitivity analysis of GPS against classical terrestrial data types The analysis and comparison of the sensitivity of the Gemona network for the terrestrial and for the GPS network, respectively (both in the 2-D concept described in Section 2.2) is reterred to the model of a movement of one single point relative to a stable reference, which consists in the left points. For an mpoint network in two epochs the deformation model implies a common free adjustment with (m - 1) common points taken as datum-points and the introduction of epoch-coordinates for the point of interest with respect to its 2-D deformation vector d (Heck, 1983). The sensitivity of a network due to this basic deformation model is given by the range of that 2-D single point-deformation, which is in the case of occurrence, to be detected with the probability fl (usual fl = 80%) on testing d on an error level a (usual a = 5%). The strict sensitivity domain for the coordinate difference vector d is given by the equation d T ' C 0 d -1 ° d-----A(F2~,

a, fl), Cdd m _ c o v a r i a n c e _ m a t r i x of d

(1)

(Heck, 1986), where the non-centrality parameter 2 of the F2.®-distribution depends on the chosen power fl for a given a. For a = 5% and fl = 80% we have 2--9.7. For the described deformation model of a single point movement, the sensitivity domain (1) for d is just the relative standard ellipse between the two epoch positions of the single point to be scaled by the factor V~2 = 3.1 in its axes. As for the sensitivity of GPS it is like the GPS-accuracy (Fig. 4) in the range of the terrestrial network, but GPS shows a more favourable isotropic character. Besides this, Fig. 6 reveals that the residuals between the epochs (see Fig. 5) for point 5 may be quite in a statistical accordance (random-like) with the low sensitivity in the corresponding direction holding for the terrestrial network; this low sensitivity could also not be improved by additional direction-measurements (see Fig. 6). For this reason it was warned above not to take too much attention

Regional RCM-network

67

Sensitivity ellipses (e~5% I~=80% ~ 9 . 7 ) cm t

t

0

1

i

i

i

2 34

i

5

3kra

I

....

GPS TerreJtrial

I

~

Additional directions

t7

Ftg 6. Comparison of the sensitivity between GPS and the terrestnal dtstance-direct~on network

and/or interpretations from the residuals of a standard Helmert-transformation in the context of deformation analysis, and it is stated, that deformation analysis should always be referred to a strict statistical concept. As a general remark it is mentioned, that the range of a 2-3 m m network accuracy (Fig. 4) decreases down to a 1.3 cm-level concerning the networks sensitivity. Although this a m o u n t of discrepancy is of a principal nature and may turn out even more severe in complex deformation models or with respect to taking additional systematic errors into account (Leinen et al., 1991), the quality of deformation networks is unfortunately too often related to the accuracy and not to the sensitivity of a network.

3.4. Deformation analysis and results by combining GPS and terrestrial observations The deformation analysis refers to the mathematical model of a combined adjustment of 2-D m a p p e d GPS-coordinates xgps., or coordinate differences Axgps., and classical terrestrial observations it, , (see Table 1) as the observation

68

A. BEINAT et al.

sets in the ith epoch. The basic adjustment model for combining these observation types is given in J~iger and van Mierlo (1991) and reads: Stochastic models

Functional models [It -[- Vt] t = [l(x)]t,

el, t

(2a,b)

[xg~ + vm],= [,u.Rl,.x + It],,

Cm,,

(3a,b)

[ A x ~ + vAgp~],= [u-R],.Ax

CAggs.,

(ha,b)

The epochwise scale parameters p,, the rotation matrices R, and the translationvectors t, refer to different orientations and scalings of the GPS-networks in the epochs. For coordinate differences Axgps (4a,b) such as occurring in epoch i = 1, no translation vector t, is to be introduced. The FORTRAN-77 software-package N E T Z 2 D (Oppen and J~iger, 1991) of the Geodetic Institute of the University of Karlsruhe is suited for the adjustment and network-analysis according to the mathematical models (2a--4b) after a common 2-D mapping of the data (Table 2). In the context with a pointwise statistical testing the models (3a,b) and (4a,b), both implied in N E T Z 2 D , provide a strict deformation analysis (see J/iger and Drixler, 1990). These formulas represent at the same time the generalization of the so-called (simple) 'Helmert-transformation', which was for example applied as a tool for the visualization of point-discrepancies in Section 3.2. In application of N E T Z 2 D to the Gemona data (Table 1), the first step of the deformation analysis treats the basic question for global congruence of the network in all epochs. For this the common least squares adjustment of all n = 3 epochs over all data sets is carried out, minimizing the sum of squares f2c n

~'~c=

E

-1 • vt,, + vT~ , , • Cgp~,, -1 • v~, ,) = Min ( vTt.," El.,

(5)

i=l

on introducing a common set of coordinates for all points. The congruence test then reads (Heck, 1983; J/iger and Drixler, 1990):

,6a, 1=1

where £~, is the sum of squares from the adjustment of the ith epoch. The degrees of freedom b are in the case of a 2-D network concept b = 2.(n - 1).m - z - d

(6b)

where n is the number of epochs, m the number of common points, z the number of additional parameters (e.g. GPS-/EDM-scales, rotation-/translationparameters for GPS or a centration-error parametrization) and d the defect of the free network.

Regional RCM-network

69

Due to the strict statistical test (6a,b) the Gemona network was proved to be congruent in all epochs and with respect to the combination of all terrestrial and GPS data sets (Table 1) on a significance level of 95%. The discrepancies at point 5 (Fig. 5) were not significant, perishing in the bad sensitivity (Fig. 6) of the terrestrial network in this direction. The discrepancies at point 1 were proved to be significant, but are related to centring-errors due to unfortunately occurring simple screw-adaptation problems for point 1, which was also noted in the field books for the respective epochs.

4. CONCLUSIONS

The paper presents a network compound, established for the detection of recent crustal movements in the Eastern Alps. It is built up in a large scale frame by the GPS-Alps-traverse as a profile through all interesting disturbance zones of the Alps. In the Friuli region the GPS-Alps-traverse is linked to the so-called GPS frame-network, which includes three terrestrial and partly GPS-combined classical networks. In application to the Gemona network, as one of these terrestrial networks, the paper points out the concept and respective results for mapping 3-D GPS coordinates due to a combined 2-D adjustment and a deformation analysis together with classical terrestrial data types. The importance of evaluating the external accuracy for the GPS-component, e.g. by a variance component estimation is pointed out. For the 10 x 10 km Gemona network the external accuracy for GPS turns out to be in the range of the accuracy of 'precise' ME5000 distances, whereas GPS is even superior on showing a more isotropic accuracy characteristic. The importance of evaluating and comparing the respective sensitivity instead of taking the accuracy as an indicator for the quality of deformation network, e.g. for the amount of detectable deformations, is made clear. In the context of the deformation analysis it is pointed out that the usual visualization of epoch-coordinate residuals due to a standard Helmert transformation between the epochs is only a weak or even a dangerous indicator with respect to the presentation of significant 'deformations'. The mathematically strict coordinate-related deformation analysis has to refer to the more sophisticated generalized Helmert-transformation realized in NETZ2D together with a respective 2-D residual test. The final statistically strict deformation analysis of the GPS and the terrestrial observations in all three epochs, performed with the software-package NETZ2D in the 2-D concept described, proves the congruence of the network in the three epochs between 1989 and 1991. This means, that no significant deformations occurred in this time-span, and also no errors remained undetected in the data or in the applied mathematical model.

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A. BEIr,IAT et al REFERENCES

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