Precision Survey & Deformations Monitoring

PRECISION SURVEY AND DEF. MON.

Teoria

UNIMOREUniversità degli Studi di Modena e Reggio Emilia

Filippo RibesNOTEWAVE_RF

Autore degli appunti: Filippo Ribes

Gli appunti sono stati scritti sulla base delle lezioni svolte dalla Professoressa Cristina Castagnetti e delle sue dispense.

Per dubbi, chiarimenti o altro, mi trovi su Instagram:ig: NoteWave_RFig: fil_ribes

In matrix form:

σ2=JCxyJ

where:

J=∂f(x,y)∂x∂f(x,y)∂y Jacobian matrix

C_xy=σx2σyxσxyσy2

Variance-covariance matrix of x and y

The variance covariance of a variable is always increased with respect to the original variances

Normal law of probability (1-dimensional variable)

One-dimensional variables being only affected by random errors, follow the normal or Gaussian distribution law probability.

The measurements belong to distribution N(μ, σ) where μ is the mean and σ is the variance → random errors belong to the normal distribution N(0, σ)

f_x=12πσ2e(-x-μ)22σ probability density function

Properties: μ = x, the value with the highest probability

PRECISION GEODETIC SURVEY TECHNIQUES

• Conventional horizontal positioning techniques
• Equipment (total station);
• Combined triangulation and trilateration: interconnected triangles in which all the angles and all the distances are measured (ensure redundancy);
• Traverses: series of straight lines connecting successive established points along the route of a survey, limited use in precision surveys since it is incapable of providing sufficient redundancy;
• Intersection: method providing the coordinates of unknown points based on the measurements made from at least 2 other points;
• Resection: method used in determining the position and height of an instrument to at least 2 points whose coordinates had been previously determined;
• Geodetic vertical positioning techniques
• The geodetic vertical positioning surveys consist of establishing the elevations of points with reference;
• Differential leveling or precise leveling: is a precise leveling technique for providing vertical control with high precision (standard deviation < 1 mm/km);
• Equipment (digital levels and mirror rods):
• Observable types
• Setting of the instrument
• Closing error computation

Monitoring network goals:

Its purpose is to monitor natural phenomena or man-made structures, like their displacements and their evolution with the time (like monitoring a bridge). They may be based on integration of multiple sensors.

Service network goals:

Their purpose is to provide surveyors during their daily work actively, with real-time corrections.

RTK (Real Time Kinematic) survey:

It is obtained by receiving corrections by a single CORS station → single base solution.

NRTK (Network RTK) survey:

It is carried out by receiving corrections by multiple CORS stations → multi base solution.

The advantages for surveyors are:

• cost saving;
• reduction of time and cost of a survey;
• coordinates always referred to the same reference frame.

Time series of observations:

It’s a series of observations collected over time. On x axis: we have time; on y axis: we have values of the variable being observed over time.

Monitoring applications usually provide observations over time:

periodic monitoring systems → they provide a small number of observations → they require longer time.

ETRF (European Terrestrial Reference Frame):

It was established in Europe, coincident with ITRF and fixed to the stable part of the Eurasian Plate, namely the European Terrestrial Reference System 1989 (ETRS 89).

It can be used as ITRF, but in Europe zone only.

GEODETIC DEFORMATION MONITORING APPROACH

Introduction:

Deformations are usually 3D but it’s common to measure the vertical and the horizontal deformations separately for higher accuracy.

The goal is to determine changes in positions to the object. This is one of the most important activities in surveying.

Factors causing deformations

• Tidal effect, changing groundwater level, mining activities.

Characteristics of geodetic deformation monitoring techniques?

• Based on a ground surface network of points interconnected.
• Usually provides redundant observations for detecting errors.
• Provide deformation trend aspect reference point.
• Fully automated mode setup is possible for continuous monitoring.

Possible problems?

• Intervisibility is required between observing stations but that's not always easy to do.
• Environmental influences.

Absolute vs Relative network:

There are 2 fundamental types of monitoring network:

• Absolute: Some of the network points are not moving over time and some are moving within the deformable area. The points that are not moving are usually outside the undergoing deformation and are used to establish the reference network. They are called reference points. The points that are moving are called monitoring points. Stability is not easy to determine a priori.
• Relative: All the network points are located...

HORIZONTAL DEFORMATION MONITORING AND ANALYSIS

Horizontal deformation monitoring:

• Slope distances:

Each distance is measured twice (2 directions), 3-5 repetitions are recommended correct distances for atmospheric refraction.

• Angles:

3 repetitions are recommended. Minimize effect of refraction. In vertical the refraction is larger than in horizontal.

z₁ = z₂ + _{(∆hᵢ sin(α₁))^d} + _{(∆x sin(α) + ∆y cos(α))^R} - _z²^2R

∆h₁ distances height instrument and target;

∆x, ∆y coordinate difference;

d measured distance;

R mean radius of the earth.

• Reduce zenith angles to their mean to mean equivalent.
• Correct zenith angles for the non perpendicular to local vertical.
• Correct zenith angles for the earth curvature effect only if ∆h are computed starting from zenith angles.

What is the goal?

Compute horizontal displacement of points between different epochs. We have 2 methods:

1. 2 epochs approach:

Least square adjustment of single epoch measurements and the single epoch results are compared to determine possible deformation.

2. Observation differencing approach:

By subtracting the model equation for epoch 1.

a point that does not pass the F-test or Chi-square test is found to be unstable and can be added to the unstable object points for further analysis.

If the test passed, then model the stable points as a fixed reference block. The stable points are used to define the datum for the determination of the final X_i and Y_i as well as the corresponding Q_d and Q_e by means of least square adjustment using minimal constraint to determine the displacement of the object points.

So the whole process is:

deformation measurements → statistical trend analysis → deformation modelling

Graphical trend analysis:

consists of plotting network points displacement vectors and their corresponding error ellipses as a graphical representation of the significance of any movement of the points.

The plot shows the spatial trend over time intervals between these two epochs.

If a displacement vector extends outside the error ellipse, the movement is significant at the specified level of significance. The associated point is considered to be unstable.