There may be times when a G&G interpreter, somewhat unfamiliar with gravity or magnetic interpretation, will look at a gravity or magnetic contour map of a frontier area and wonder whether the anomalies represent shallow or deep source bodies. The interpreter understands that anomaly amplitudes are related to source body density or magnetization, not depth, and that short-wavelength anomalies have shallower sources than long-wavelength anomalies with deep sources. But how shallow is shallow, and how deep is deep? The answers may reveal whether the contour map represents a prospective area and whether the map provides some insight into the area’s geology. Before deciding on whether to spend the money for a detailed quantitative gravity or magnetic interpretation, the interpreter can quickly make his/her own rough “rule-of-thumb” depth estimates from time-honored techniques. Then, if the preliminary estimates were favorable, a more sophisticated interpretation would be well-justified.

**Learning Objectives**

After completing this module, you will know how to:

- Select key anomalies from a gravity or magnetic contour map
- Determine the characteristic anomaly signature of 9 types of geologic bodies or structures
- How to extract appropriate profiles across those mapped anomalies
- Determine diagnostic points along the profiles
- Apply appropriate formulae to obtain “rule-of-thumb” depth estimates to the source body. Most of the formulae used below are appropriate for gravity interpretation where the initial estimate is to the
__center of mass__of the source body. Magnetic depth estimates are normally estimates to the depth of a magnetized surface, which is usually equivalent to depth to the top of the source body. Some basic techniques for magnetic depth estimation can be found in Mod PF 126 Depth Estimation Techniques.

**“Rule-of-Thumb” Procedures**

**Step 1. Examine the contour map. It may be a paper map or on a computer screen **

Choose a prominent gravity or magnetic anomaly and decide whether it is generally circular or is elongate. Let us consider the different anomaly patterns that one can identify:

** Case 1** If the anomaly is circular, the contours relatively gentle, and the anomaly is a gravity minimum, it usually represents a hemisphere-like, deep-seated salt dome.

** Case 2** If the anomaly is either a gravity or magnetic maximum, it usually represents a deep-seated dome of high-density sediments or basement.

** Case 3** A circular negative anomaly with steep contour gradients is the signature of a relatively shallow salt plug.

** Case 4** A circular positive gravity and/or magnetic anomaly is the signature of a relatively shallow igneous plug.

** Case 5** If the anomaly is elongate with relatively gentle, equal flanks and has a negative gravity value, that is the signature of a salt anticline.

** Case 6** If it has a positive gravity and/or magnetic value, then that is the signature of a sedimentary or basement anticline

** Case 7** If the flanks of a negative gravity anomaly are steep, then that is a common signature of a salt wall

** Case 8** If the flanks of a positive gravity and/or magnetic anomaly are steep, is a common signature of a igneous dike.

** Case 9** If contour values are significantly more positive on one side of the anomaly then the profile would have an s-shape, which is the signature of a vertical step or fault.

**Step 2. Extract one or more profiles across the anomaly. If the map is on a computer screen, you will need software that can extract and analyze profiles. If the map is paper, you only need some graph paper.**

The profiles should cross the center of a circular anomaly or cross normal to the axis of an elongate anomaly. The profiles should extend well off each flank to a point where the contours flatten out. The map-scale -/+** X** distance in feet or meters between those points will be the wavelength of the anomaly; the relative amplitude value (

**) of the anomaly at those points will be set at zero. Next, plot the anomaly profile using contour values where they intersect the line of profile. The anomaly’s relative minimum or maximum value**

*A***will depend on the number of contours crossed from the zero value to the center of the anomaly. Now, the**

*A***value directly over (or under)**

*X*

*A**will be considered*

**. The**

*X*_{0}**value (in feet or meters) directly over (or under) the point on the anomaly curve where**

*X***is half its maximum or minimum value has an important diagnostic value known as the half-max distance or**

*A***.**

*X*_{1/2}__Gravity, Case 1____ (salt dome) or Case 2 (igneous or high-density sedimentary dome)__

If the Bouguer anomaly is a minimum, we assume the body is a deep salt dome. The depth ** Z_{s}** to the

__center__of mass of the anomalous body equals 1.305 times

**. That would be the deepest the body could be; depth to the**

*X*_{1/2}__top__of the body would depend on an estimated radius of the hemisphere such that

__depth to the top__. An estimate of that radius

**would equal depth to the center minus the radius***Z*_{t}**can be made by using the anomaly amplitude and an assumed density contrast ∆σ between the anomalous body and surrounding sediments in simple formulae:**

*R*_{s}** Z_{s} **= 1.305*

*X*_{1/2}Let ** F_{s} **= where

**and**

*F*_{s}**are in kft (thousands of feet),**

*Z*_{s}**is in mgals, is the density contrast gm/cc**

*A*** R_{s} **= ∛

**where**

*F*_{s}

*R**s*and

**are in kft (thousands of feet)**

*F*_{s}The formulae can be found in many references (e.g., Nettleton, 1971). An estimate or calculation of the radius ** R_{s}** is dependent on the value of

**and an assumption of density contrast (∆**

*A***σ**) between the hemisphere and the surrounding sediments.

The profile is slightly asymmetric, so we will take an average ** X_{1/2}** = 10 kft.

Then ** Z_{s}** = 1.305*

**kft = 13.05 kft Depth to center of spherical dome**

*X*_{1/2}If ** A** = 5 mGals and ∆

**σ**= 0.2, then and

**= 38.29 kft**

*Fs*** R_{s}** = 3.37 kft Radius of dome

** Z_{t}** = 9.62 kft (i.e., 13.05-3.37 kft).

** R_{s}** can also be estimated by measuring the horizontal distance between the center of the anomaly and the map distance to the steepest contour gradients on its flank. If there are several anomalies to be estimated, it would be efficient to make some theoretical tables or nomograms using different values of

**,**

*A***, and ∆**

*X*_{1/2}**σ.**

For Case 2, if the anomaly were a maximum, the same procedures and formulae would be used.

**Figure 1. Bouguer anomaly map**

**Figure 2. Profile A-A’ with diagnostic points marked**

**Figure 3. Salt dome modeled as sphere with critical dimensions calculated**

__Gravity, Case 3 (salt plug) or Case 4 (igneous plug)__

Our next example assumes that the Bouguer minimum shown as Figure 1 might be sourced by a salt plug with very steep flanks. Cross section A-A’ remains the same as Figure 2 but the depth calculations will be different. The depth ** Z_{p}** (kft) to the top of a salt or igneous plug with deep roots is equal to 0.78 times the half-max wavelength (

**) of the anomaly profile. If the anomaly amplitude**

*X*_{1/2}**= 5 mgals,**

*A***= 10.0 kft**

*X*_{1/2}**and the density contrast**

*,***= 0.2, then depth and radius**

*∆σ***(kft) of the plug can be calculated:**

*R*_{p}** Z_{p}** = 0.78*

**= 7.8 kft**

*X*_{1/2}Let* F_{p} =* (

*A***)**

*Z*_{p}**where**

*/*5.75*∆σ***is in kft and**

*Z*_{p}**is in mGals**

*A*Then* F _{p}*

*=*(5.0*7.8)/5.75*0.2 = 33.91 kft

And ** R_{p} **= √

**= 5.82 kft**

*F*_{p}This could also be estimated by measuring the map distance between the center of the anomaly and the location of steepest contour gradients on its flanks.

For Case 4, if the anomaly were a maximum and the body were an igneous plug, the same procedures and formulae would be used.

**Figure 4. Bouguer anomaly map**

**Figure 5. Profile A-A’ with diagnostic points marked**

**Figure 6. Salt plug modeled as vertical cylinder with critical dimensions calculated**

__Gravity, Case 5 (salt anticline) or Case 6 (basement or high-density sedimentary anticline)__

If the Bouguer anomaly is a minimum, we assume that the body is a salt anticline. The depth, ** Z_{a}** to the

__center of mass__of the anomalous body equals 1.0 times the half-max distance (

**). An estimate or calculation of the radius**

*X1/2***is dependent on the value of**

*R*_{a}**(mgals) and an assumption of density contrast (∆**

*A***σ**) between the anticline and the surrounding sediments.

__The depth to its top__

**would equal depth to its center***Z*_{t}**minus its estimated radius***Z*_{a}*R*._{a}Since the profile is asymmetric, we will average the ** X ½** distances as 10.0 kft.

Let ** F_{a}** =

**/12.77∆**

*A*X*_{1/2}**σ**where

**is in mGals and**

*A***is in kft**

*X*_{1/2}Then ** R_{a} **= √

**where**

*F*_{a}*radius*

**is in kft**

*R*_{a}And ** Z_{t} **=

**–**

*Z*_{a}**Depth to top of anticline**

*R*_{a}For example, if ** A**=10 mgals,

**=**

*X*_{1/2}**10 kft at**

*Z*_{a}=**, and ∆**

*A*_{1/2}**σ=**0.2, then

** F_{a} **= 10.0*10.0/12.77*0.2 = 39.15

** R_{a}** = 6.26 kft Radius (width) of anticline

** Z_{t} **=

*3.73 kft (i.e.,10-6.26 kft). Depth to top of anticline*

An approximation of the radius can also be made by measuring the map distance between anomaly crest and the zone of steepest contour gradient on the flank of the anomaly.

For Case 4, if the anomaly were a maximum and the body were a basement or sedimentary anticline, the same procedures and formulae would be used.

**Figure 7. Bouguer anomaly map**

**Figure 8. Profile A-A’ with diagnostic points marked**

**Figure 9. Salt anticline modeled as horizontal cylinder with critical dimensions calculated**

**Gravity, Case 7 (salt wall) or Case 8 (igneous dike)**

The depth ** Z_{w}** to the

__top__of the wall or dike equals 0.32 the half-max distance (

**) if the wall or dike is narrow relative to its depth and its top is shallower than 5 times than its base.**

*X*_{1/2}** Z_{w}** =0.32

**Width=**

*X*_{1/2}**/9.36∆**

*A***σ**

For example, if A=10 mgals, ** X_{1/2}**=10 kft at

**and ∆**

*A*_{1/2}**σ=**0.2, then

**=3.2 kft if the width is not excessive. Let’s check.**

*Z*_{w}Width=10/9.36*0.2=5.5 kft, and the dike is too wide to fit the simple formula.

If the anomaly is elongate but has only one steep flank, extract one or more profiles crossing the anomaly normal to its gradient zone (fault, steeply tilted dike). The +/- ** X** distance along the profile is determined by the map-scale distance from both points of contour flattening (normalized zero values). The maximum amplitude of the anomaly is determined by the contour values between an assumed zero value and the value at the center of the anomaly. These three points on the profile determine some of the diagnostic lengths for estimating depth.

__Gravity, Case 9 (vertical step or fault)__

Locating the center of a fault zone and estimating its throw requires the measurement of two more diagnostic values on the anomaly profile: ** X_{¾}**, and

**. The zero**

*X*_{¼}**value of the profile is set directly under its maximum (or minimum) amplitude value**

*X***. The**

*A**X*distance along the profile lies directly under

_{¾}**and**

*A*_{3/4}**lies directly under**

*X*_{1/4}**. The half max distance**

*A*_{1/4}**is of course under**

*X*_{1/2}**.**

*A*_{1/2}The horizontal location of the center of the fault zone is under ** X_{1/2}** and can often be approximated by locating the zone of steepest contour gradient on the contour map. The vertical distance

**to the center of the faulted slab equals half the horizontal distance from**

*Z*_{f}**and**

*X*_{3/4}**. Estimating the thickness (**

*X*_{1/4}**) of the faulted slab and depth to its top**

*T***requires an assumption of density contrast (∆**

*Z*_{t}**σ)**between density of the slab and density of the adjacent formations. For example, using the formula:

** Z_{f} **= 0.5(

**) Where**

*X*_{3/4}– X_{1/4}**is in kft**

*Z*_{f}** T**=

**/12.77∆**

*A***σ**Where

**is in kft and**

*T***is in mGals**

*A**Z _{t}*=

*Z*–

_{f}*T*

Then if ** A**=10 mGals,

**= 0.5* 10.0 kft and ∆**

*Z*_{f}**σ=**0.4,

** T** = 1.96 kft

** Z_{t}** = (5.0-1.96) = 3.04 kft Depth to top of the faulted slab

As with **Cases 1** and **2**, if the contour map showed several areas of fault-type contouring, it would be efficient to construct reference tables or charts using a range of values for ** A** and ∆

**σ.**

**Figure 10. Bouguer Gravity Anomaly map**

**Figure 11. Profile A-A’ with diagnostic points marked**

**Figure 12. Vertically faulted high-density slab with critical dimensions calculated**