Geology

Attitude of linear and planar geological objects with Brunton

Although most geologic structures are generally either curvilinear or curviplanar, they can be approximated as either linear or planar at specific scales or domains. For example, a primary linear structure such as the crest of ripple marks or flute casts on a bed may be folded around the axis of a fold. At the scale of a large fold, these linear objects are curved, i.e., have a systematically distributed orientation (e.g., small circle or great circle distribution). However, within each limb of the fold (a domain), the orientation of these structures may be homogeneous, that is, the flute casts or ripple crest are subparallel to parallel. On each limb, the fabric data of minor folds may have a homogeneous distribution.

The attitude of both linear and planar objects has two general components: bearing and inclination. Bearing is the horizontal angle between a line and a specified reference (N or S). The "line" either is the horizontal projection of an inclined linear object, or a horizontal line on an inclined plane. Bearing is a scalar feature, i.e., it just is a number (e.g., 045o or N45oE). Inclination, on the other hand, is the vertical angle between a linear or planar object and the horizontal. The convention for direction of inclination is down, i.e., we measure the angle from the horizontal down (not up), especially when we process the data on the lower hemisphere, equal area projection (mineralogists also use the upper hemisphere for crystals). Inclination is a vector, meaning that it has two components: an amount (angle below the horizontal), and an orientation specifying the direction to which the planar feature is inclined down (e.g., 30oNW).

Attitude is too general, and its two components: bearing and inclination, take different meanings when dealing with linear and planar element. For planar features such as bedding (the boundaries of a bed), fault, and foliation, the bearing and inclination become strike and dip. Note that strike is a scalar, and dip is a vector. Strike is the bearing of a horizontal line on an inclined plane. Since strike is the bearing of a horizontal line, we can read the bearing of either of its ends; thus, 000o and 180o are the same strike. Dip is the inclination of an inclined plane. For linear fabric such as hingeline, axis, or lineation, we use trend and plunge to represent the bearing and inclination. Notice that horizontal planes don't have any strike because they don't intersect the horizontal along a line.

Trend is the bearing of a linear object measured in the direction to which the line is inclined down. Plunge is the amount of the inclination of the linear feature. Thus, both trend and plunge are scalars; together they define the line vector. For example, a 060o, 30o (also written as 30o, 060o, or 30o, N60oE) is a pair of trend/plunge (direction/magnitude) or plunge/trend, which means that a line plunges 30o down below the horizontal in the 060o direction. Linear objects can also be defined by their pitch on a specific plane. Notice that vertical lines don't have any definable trend, and that the trend of a non-horizontal linear object must be read from a reference (e.g., N) to the direction that the line plunges. Thus, a trend of 000o and 180o are not the same thing (contrast this with strike!). In practice, it is extremely difficult, if not highly error-prone, to measure the trend of steeply plunging linear object; in such cases we use pitch. Notice that the trend of any line on a vertical plane is the same as the strike of that plane (a useful geometric fact). Pitch is the acute angle measured on a plane, from the strike of the plane that contains the line, toward the line (the sense is important!). For example, a pitch of 40oSW (read as: 40o from SW) means that the line is pitching 40o from (not to!) the SW end of the strike line of a plane that contains the line. Notice that pitch generally is not a horizontal or vertical angle, except for horizontal and vertical planes containing linear features. Pitch is an alternative to trend and plunge, although, sometimes, it is the only practical way of measuring a line correctly, especially if the line is steeply plunging.

Measuring the attitude of linear objects

Measuring trend and plunge: If the linear object is below our line of sight, open the sighting arm and the lid, and align the open, long slot of the arm parallel to the linear feature. If the linear feature is above our head (e.g., on a bedding above us), stand under the object and align the linear feature with the black axial line on the mirror on the lid of the compass. In either case, level the bull's eye, round level while aligning. If the linear object is plunging, only one of the needles (the north-seeking or the south-seeking) indicates the true trend of the linear feature. This is a case where many inexperienced geologists can make a common, critical mistake! Some people have the habit of only reading the north-seeking (white) needle of the compass, or vice versa, which is an error-prone practice. When using the Brunton compass we should be color-blind, and only read the direction of the needle that is correctly indicating the direction to which the line is plunging (down, not up!). Thus, the trend of only one of the needles is correct when reading a line. To figure out which one, we should be aware of the local geographic directions, that is, know the direction of north or south in the field at all times. For example, if we are measuring a linear object plunging down to the south (S or somewhere in the SE or SW quadrants), we must read the trend indicating any one of these southern directions (e.g., 120 o or S60 o E), and not the diametrically opposite northern directions (i.e., 300 o or N60oW) indicated by the opposite end of the needle. For a plunging line, 120 o and 300 o are not equivalent; only one is the true down direction (120 o or S60 o E in this case). The true direction of the trend may be indicated by the white or the black needle; the color depends on how we hold the compass (sighting arm away or toward our body), and on which way we are facing in the field (looking north or south). Therefore to avoid a common mistake, no matter how you are holding the compass or which way you are facing; just know where the geographic N or S is in the field, and ask yourself this question: Which way is the line going down (i.e., plunging)? If it is plunging to around the N, then read the needle (white or black) that points to N or in the NE or NW quadrants and not the opposite directions. This is the easiest and most practical way of correctly measuring a line. Of course, if a linear feature is non-plunging (a special case), we have the freedom of reading either the white or the black needle, because the line is horizontal (both ends are the same).

Example: We are measuring the crest of a ripple mark which is roughly trending somewhere around north (we know which way is N in the field because we have the compass!). The crest of the ripple mark is plunging, and lies on a bedding, which is dipping. Align the compass's sighting arm with the crest and then read either the direction indicated by the white or the black needle that points somewhere to the north. Thus, if the black needle points to N20oW and the black needle points to the S20oE, we must read the black needle. Don't wrongly assume that the white needle gives you the north readings; a common misconception.

Measuring vertical angles, height, and distance

To measure vertical angles, fold the lid and use the compass as was described for measuring the plunge of lines, i.e., with the clinometer. The vertical angle (q) can then be used to calculate the height (h) of an object (e.g., wall, tower, mountain peak) using the equation h = x tanq, if we know the distance (x) to the object. We can also use the trigonometric functions to calculate the horizontal distance (x) from point A to an object located at point B as follows. Walk from point A to another point C such that AC is perpendicular to line AB. This is done by taking a bearing at 90o to the bearing of AB with the compass. Use a tape or a measured pace (if pace spacing is known). In practice, we define AC to be 10 meters; or walk from A to C by 10 meters with our pace. Read a bearing from point C to point B. Subtracting the two bearings gives the angle b between AB and CB. Now we have a right angle triangle ABC with AC = 10 m, AB = x, and a known angle b. Use the equation tanb = AC/AB = 10m/x, and calculate x in meters.

If the linear object of interest is steeply plunging, it is better to use pitch instead of the trend and plunge. Measuring pitch is only possible if the linear feature lies on a physical plane. For example, if a set of slickenlines (striations) plunges (e.g., around S) on a fault, we measure the striations as follows. First, measure the plane (i.e., fault) that contains the linear features (see next section for this). Next, measure the pitch of the striations on the fault plane as follows. The Brunton compass has a circular, high relief ring on its back, which is designed for measuring pitch. Open the compass (the arm and lid opened completely) and align the edge of the lid and box with the line while the whole ring on the back of the compass touches the fault. If the clinometer, barrel-shaped level is not centered in this position, gently move the box off the plane and slightly turn the clinometer, and lay the box back on the plane while aligning the edge with the line. If the clinometer is not centered, repeat these steps several times until the clinometer is leveled while the edge of the box is parallel to the line, and the circle behind the compass is completely lying on the plane. This is a trial and error process that requires some practice to master.

Using the compass as hand level on a Jacob Staff

The compass can be used as hand level, mounted on a Jacob Staff to measure the true stratigraphic thickness of a lithostratigraphic unit (e.g., member, formation) as follows. Measure the true dip of the layers and set the clinometer at that angle. Mount the compass vertically (as in reading the plunge) on the Jacob Staff with the lid half closed; making sure that the clinometer is set at the measured dip angle. Start at the lower contact of a stratigraphic unit. Tilt the staff in the direction of the dip of the beds, and look inside the mirror until the clinometer level is centered. At this position, look through the sighting tip and through the sighting window. Identify a point (e.g., a brush, a piece of rock) on the ground where the line of sight intersects the ground. Move the base of the Jacob staff to that point. Use a counter and register the number of times (n) it takes to go from the basal contact of the lithostratigraphic unit to its top. At the upper contact, multiply the length of the Jacob Staff, which is 1.5 meter, by 'n', to get the true stratigraphic thickness of the unit.

Measuring the attitude of planes

If the plane is flat, smooth, and non-magnetic, the easiest way to measure the strike and dip of the plane is to touch the edge of the box (not all the rectangular side!) with the plane while centering the circular, bull's eye level. This will generate a horizontal line parallel to the edge of the box on the plane of interest. We have the freedom of reading either of the two needles; it does not matter which one we read! (e.g., 140o and 320o are the same strikes). This is the strike of the plane; we can mark the strike line on the plane with a pencil drawn parallel to the edge of the box. In special cases such as when taking oriented samples of rock for structural analysis, we need to distinguish and mark only one of these two ends of the horizontal line with an arrow (preferably with half arrow tip).