16.2 Survey Control, Instruments, Traverses & Error Adjustment

Mine surveying controls where holes are drilled, headings advance, benches are cut, volumes are paid, and hazards are located. A centimeter-level observation tied to the wrong datum is a precisely wrong result. Every survey should state coordinate reference system, projection, units, vertical datum, control source, date, instrument, method, and expected accuracy.

Instruments and Fit

Total Station

A total station combines horizontal and vertical angle measurement with electronic distance measurement. It computes coordinates from an occupied station, backsight orientation, instrument height, target height, slope distance, and vertical angle. Verify prism constant, atmospheric inputs, collimation, compensator, centering, and backsight. A reflectorless shot may hit vegetation, water, or an unintended surface.

GNSS

Survey-grade GNSS can establish surface control using static, rapid-static, or real-time kinematic methods. Accuracy depends on satellite geometry, correction link, observation time, multipath, canopy, ionosphere, and reference coordinates. GNSS generally does not provide reliable underground positioning, so control is transferred through portals or shafts by conventional survey and gyro or orientation methods.

Differential Level

A level and graduated staff transfer elevation. Balanced backsight and foresight distances reduce collimation error. Close the loop on a benchmark and compare observed closure with the allowable tolerance for the survey class.

Traverse Computation

For line length $L$ and azimuth $\theta$ measured clockwise from north:

$Latitude=\Delta N=L\cos\theta$

$Departure=\Delta E=L\sin\theta$

Apply signs by quadrant. Sum the coordinate increments. In a closed traverse, ideal $\sum\Delta N=0$ and $\sum\Delta E=0$. Linear misclosure is:

$e=\sqrt{(\sum\Delta N)^2+(\sum\Delta E)^2}$

Relative precision is total traverse length divided by $e$, expressed as 1 in $N$. A 2,000-m traverse with 0.10-m closure has 1:20,000 relative precision. Acceptance depends on the required survey class and task; do not assume one ratio suits legal boundary, production pickup, and preliminary mapping.

Bowditch Adjustment

Where distance and angle observations have comparable precision, the Compass or Bowditch rule distributes closure by line length. For line $i$:

$C_{N_i}=-(\sum\Delta N)\frac{L_i}{\sum L}$

$C_{E_i}=-(\sum\Delta E)\frac{L_i}{\sum L}$

Add corrections to observed latitude and departure. Adjustment does not make bad fieldwork good. Investigate gross error, wrong station, transposed digits, prism height, backsight, and datum before distributing a closure.

Angular Closure

For a closed polygon with $n$ interior angles, theoretical sum is $(n-2)180$ degrees. Compare the observed sum, verify tolerance, then distribute angular correction according to method and observation precision before computing bearings. A wrong initial azimuth rotates an otherwise closed traverse, so orientation needs an independent check.

Underground Control

Protect stations from blasting, convergence, vehicle damage, and poor visibility. Use redundant wall or roof stations outside likely disturbance. Advance control with check shots and close loops when geometry permits. For shaft plumbing, account for wire oscillation, air movement, water, and depth. Gyroscopic orientation can transfer azimuth where direct surface connection is unavailable.

Error Sources

• instrumental: collimation, zero, compensator, prism constant;
• personal: centering, pointing, reading, heights, booking;
• natural: temperature, pressure, refraction, curvature, wind;
• computational: units, quadrant, projection, scale factor, datum transformation; and
• operational: disturbed station, wrong design revision, mislabeled point.

Use two-face observations, reciprocal measurements, repeated sets, independent control, and closure. Store raw observations, adjustment, residuals, metadata, and final coordinates.

Safety Scenario

A breakthrough heading is designed to connect with an existing airway. Survey closure, independent orientation, and last-hole probing are critical because a positional error can cause missed connection or unintended breakthrough into water, gas, or active workings. The surveyor communicates uncertainty and exclusion controls; the mine does not treat the design coordinate as exact merely because software displays three decimals.

Level-Loop Example

A benchmark has elevation 100.000 m. Backsight is 1.425 m, so height of instrument is 101.425 m. A foresight of 2.115 m gives the turning-point elevation $101.425-2.115=99.310$ m. Continue using the height-of-instrument or rise-and-fall method consistently and close on a known benchmark. The arithmetic check compares total backsights minus total foresights with final minus initial elevation. A closure inside tolerance is then adjusted according to the survey procedure; outside tolerance requires investigation or re-observation.

Projection Trap

Grid distance and ground distance can differ through scale factor and elevation. High-accuracy legal or control surveys require the specified combined scale treatment. Never apply a generic correction without knowing whether coordinates and distances are grid, ground, or already localized.

Adjustment Does Not Cure Bad Observation

A traverse adjustment distributes an acceptable residual under a stated weighting model; it must not conceal a blunder, wrong station, prism constant, centering error or coordinate-system mismatch. Review field closures first, isolate outliers through evidence, preserve raw observations, then adjust and report both pre- and post-adjustment statistics. Compare achieved uncertainty with the set-out or volume decision, not merely a generic precision label.