**Overview**

A qualitative interpretation of magnetic data can be a very fast and useful approach to making a general evaluation of regional geologic structure, but it does not provide adequate information about the depth of key components of the structural features. In fact, the qualitative approach can lead to a somewhat subconscious, but erroneous, concept that anomaly amplitude rather than anomaly wavelength is a reflection of the magnetic body’s depth. On the other hand, a quantitative magnetic interpretation, especially if integrated with other data (well data, surface and subsurface geology, seismic), can provide significantly more useful information about basement depth and configuration as well as depth and location of intrasedimentary igneous material (dikes, flows, plugs).

The amount of detail, time, and cost of a quantitative magnetic interpretation can vary widely depending on the geologic problem to resolve and the time/cost budget available for the project. Sometimes when there is a large dataset to be interpreted, automated methods of depth estimation and contouring are used by some firms to reduce manpower needs and to increase output. However, automation cannot yet fully substitute for a human’s experience and judgment in evaluating depth estimates and interpreting them in the form of a geologically reasonable contour map.

The primary purpose of this module is to discuss 2D interpretation along magnetic profiles since that is where there the bulk of industry effort is concentrated. However, this module will also touch on some special applications of 3D magnetic interpretation.

**Learning Objectives**

After completing this module, you will:

- Understand the benefits of making a quantitative magnetic interpretation
- Understand the data required and how to select optimal profiles to analyze
- Understand the fundamentals of different techniques for depth estimation
- Understand how to evaluate depth solutions
- Understand the benefits vs. pitfalls of automated depth solutions

**Magnetic Depth Estimation Techniques**

The depth estimation process starts with an examination of the Total Magnetic Intensity map to determine the location, orientation, and general wavelength of the anomalies present. If the dataset to be interpreted includes digital flight-path or ship-track magnetic profiles, then the next step is to locate or to plot a flight-path/ship-track map to see whether the magnetic profiles cross normal to the gradient zones of the most significant anomalies. Normal is the preferred orientation and provides the most accurate depth analysis. If the survey lines are at odd angles to the anomaly alignments, then strike corrections must be made to the depth analyses. Otherwise, pseudo-profile lines with optimal strike directions must be extracted from a magnetic data grid. In some respects the pseudo-profile line approach is easier than making strike corrections but there is a danger, depending on the data gridding interval, of losing some of the short-wavelength information critical to depth estimation techniques.

The interpreter must always remember that the initial calculated depth estimates are really a measurement of distance between the magnetometer and the magnetic source body, not depths relative to some datum such as sealevel. Many interpretation maps are contoured using a sealevel datum, so before contouring the depth estimates, they must be corrected to the datum in use. In practice, such corrections are often ignored for surveys flown at barometric altitudes less than 1000 ft, but must be made when interpreting data from surveys at higher altitudes.

The number and accuracy of depth analyses to be made must be balanced against number of useful anomalies in the area of interest as well as time and cost factors allotted to the interpretation. The type of survey and the nature of the target must also be considered. If the survey is detailed with lines at 500 m spacing or less and there are numerous shortwave-length anomalies of interest, then it may be necessary to interpret every profile line. If the targets are deeper and the anomaly wavelengths are longer, then interpretation of every other or every third profile line might suffice. But that is not a hard-and-fast rule—sometimes the overall interpretation requires that two or three adjacent lines be interpreted and others can be skipped. If the magnetic survey is semi-regional, with profile lines at 2 km spacing or more, then efforts should be made to interpret each profile. In more extreme cases where time and cost are critical, then only those profiles crossing key anomalies and having an optimal direction (Module #16 – Optimal Profile) would be selected for interpretation.

Total Magnetic Intensity (TMI) data is preferable for the quantitative profile analysis. While the use of Reduced to Pole (RTP) profile data would essentially eliminate the anomaly distortion and position shift inherent in TMI data (caused by the earth’s magnetic field inclination and declination), the gridding and the convolution necessary for RTP processing can subdue the short-wavelength components of an anomaly and thus degrade the accuracy of depth estimation.

Anomaly amplitude is more dependent on magnetization of a geologic source body than on its depth. Source body depth is estimated from the anomaly frequency content or wavelength. The example shown on Figure 1 illustrates the anomalies of two magnetized bodies identical in dimension and depth but of varying susceptibility (magnetization). Depth estimates shown were calculated by 2D spectral and Werner algorithms. The depth estimates obtained for the two bodies are the very similar.

**Figure 1. Susceptibility vs. depth estimate and amplitude comparison. Raw Werner depth estimates are shown as blue crosses; 2D spectral estimates as orange bars.**

**Selecting Suitable Anomalies and Profiles**

To make an effective depth estimate, the first critical decision is the selection of an anomaly for analysis. A suitable anomaly is one that is isolated from the effect of other anomalies. If no isolated anomaly exists but an estimate is desired, that estimate would be valid only if care is taken to choose the flank of that anomaly which is not significantly influenced by a nearby anomaly. Separation or isolation from interfering anomalies can often be achieved by data enhancement or residualization techniques (see Modules #18 and 19). Interference can be a problem in magnetic analysis and can cause the depth determinations to be either too deep or shallow, depending on the interference pattern.

Other anomalies to avoid, except for special circumstances, are those derived from sources of limited depth extent and/or finite strike-length because these characteristics violate the basic assumptions of many depth determination methods. Most analytic methods assume the magnetic body to be semi-infinite in thickness and/or be two-dimensional in strike direction. However, bodies with thickness at least twice their depth or strike lengths at least three times their width will usually provide useable basement depth estimates. Thin flat-lying magnetic bodies can be considered as thin sheets, or in geologic terms, intrasedimentary sills or flows if relatively shallow. If deep, near basement level, they can be considered as suprabasement structures that have little or no magnetization contrast with the underlying basement. These structures and associated anomalies are often overlooked but can provide important depth control points for basement interpretation.

Once one or more anomalies are selected, the data profiles across them must be evaluated. The profiles best suited for analysis are perpendicular to the contour gradients and as nearly through the center of an anomaly as interference effects will permit (see Figure 2). In general, the least desirable place for a profile is near the end on an anomaly where contours are nearly perpendicular to strike because the depth estimates from those profiles include large uncorrectable errors.

Figure 2 illustrates a case of why depth estimates should be made with the aid of an anomaly map (in this case an RTP map) rather than blindly making depth from profiles with no evaluation of profile position or orientation. The solid black line shows a data profile correctly located for depth interpretation of a primary anomaly. The dashed black line shows a data profile placed over the tail of that anomaly, but poorly located for depth interpretation. The solid purple line shows a data profile correctly located over a secondary anomaly, sufficiently distant from the primary feature to avoid interference. The dashed purple line shows a tie line across the anomaly but along strike, hence unreliable.

**Figure 2. Reduced-to-Pole (RTP) magnetic anomalies and selected data profiles.**

**Typical Magnetic Sources and Profile Anomalies**

Figure 3 illustrates several types of anomaly-producing magnetic source bodies. Some (sill, flow, dike, or plug) are intrasedimentary but are important to recognize for any exploration program. Sometimes wells have been drilled on such features because the magnetic data were not correctly interpreted (or not interpreted at all!). Anomalies produced by basement horsts or uplifts, basement intrusives, or basement lithologic contacts or discontinuities are commonly interpreted as top of igneous basement. Intrabasement intrusives such as batholiths or deep ultramafic bodies typically produce high-amplitude anomalies.

In Figure 3, red indicates basement of felsic or intermediate composition and not highly magnetic. Blue indicates features with mafic or ultramafic composition which are normally strongly magnetic.

Note that the frequency content of the magnetic profile anomalies decreases with source body depth. Since each anomaly along such a profile can relate to a magnetic source depth, it is apparent that those depths cannot all be mapping the surface of magnetic basement. It is up to the interpreter’s experience and judgment to sort out how those depths must be analyzed and mapped.

**Figure 3. Typical igneous source bodies with their magnetic anomalies**

**Computer-Driven Magnetic Depth Estimation: Windowed vs. Batch-mode Analysis**

Numerous companies make magnetic depth estimates using computer-assisted analysis of digital magnetic profile anomalies. Several versions of software exist, each offering analysis by the computer alone or by interaction between interpreter and the software. Each algorithm will normally produce a cloud of solutions for each anomaly analyzed. The interpreter must examine every cloud and determine where in that cloud to select the most reliable solution; normally that would be the area with the tightest group of solutions. That reliability can be influenced by solutions from other clouds; i.e., similar depth solutions for the same or adjacent anomalies but made from different algorithms will increase the reliability factor. Some software provides a correction function for non-optimal profile directions and/or non-two-dimensionality of the anomaly. Some software allows the interpreter to assign and store a reliability grade, if desired, for each chosen solution. If that software option is not available, the interpreter should record his/her own solution list with grades.

Software may contain options for windowed and/or batch-mode analysis.

__Windowed Analysis, Profile Data__

Magnetic depth estimation is essentially an analysis of the frequency content or wavelength of a specific anomaly or set of magnetic anomalies. A magnetic profile normally contains an assemblage of frequencies or wavelengths similar to those of the illustrated seismic wavelet. For convenience, we will use spatial domain (wavelengths) to discuss the analysis. The width of the analysis window or gate for a Werner or 2D Euler algorithm will determine the range of magnetic source depth estimate(s) for the anomaly wavelength(s) contained within the window. However, depth estimate overlap or scatter can occur when a long window causes aliasing of short-wavelength anomalies (making them seem deeper). A short window can make erroneously shallow depth estimates from the short-wavelength components, or deep depth estimates from the near-linear components, of a long-wavelength anomaly. The most accurate depth estimation (within limitations of the software used and algorithm chosen) for a given anomaly requires that its specific wavelength content be analyzed (Ku, 1983; Li, 2003). The process for doing that is to make a sequential windowing (isolation) of anomalies along the magnetic profile. Windowing consists of selecting bounds (e.g., bounding minima or maxima) for each chosen anomaly. It allows for close inspection of that anomaly for noise contamination or anomaly superposition (Hartman, 1971). The quality of the resulting estimation can be immediately judged by the interpreter by the solution cluster tightness, or later by the consistency of solutions along-line or line-to-line. Windowed analysis requires time and study since each anomaly is examined individually.

__Batch-mode Analysis, Profile Data__

Depth estimation for a series of magnetic anomalies along a profile can also be made by means of batch-mode analysis (Jain, 1976) using a selected algorithm such as Werner or 2D Euler. The interpreter starts with a given analysis window length which will then be applied to all anomalies along the profile, regardless of their actual wavelength. The set of depth estimates to be calculated are governed by that selected window or assumed wavelength. Multiple passes, using wider and wider windows, must then be made to cover all expected anomaly wavelengths on the profile. As noted above, this procedure can result in clusters of both real and spurious depths for short-wavelength (by aliasing) and long-wavelength (by partial component) anomalies (Goussev et al, 1998). Other problems occur when there is a smear or overlap of depth solutions obtained from different processing runs, unless some special color or symbol code has been used to identify solutions for each run.

Batch-mode might be a useful approach, a sort of depth filtering, to quickly derive only those solutions for some desired depth range; e.g., a shallow horizon, by selecting a very short window, or a deep horizon by using a very long window. However, results for mid-range depths would be very ambiguous because of possible aliasing, uncertain anomaly wavelengths and solution overlaps. An interpreter, after significant experience with batch-mode processing, may find it necessary to make slope-type estimates “by hand” to correlate with the batch-mode clusters in order to select the most reliable ones. Furthermore, profiles must be pre-selected before processing to ensure that only those with optimal contour crossings are used, or if all profiles are processed en masse, then the solutions must then be evaluated and graded. Either way, time and effort saved on the front end of the batch-mode approach must be spent later on selecting and grading results.

**Depth Estimation Algorithms, Profile Data**

Before the advent of computer analysis of magnetic anomalies, it was common to use simple analog “rules-of-thumb” approaches to magnetic depth estimation. We will touch on three of them: one because it is extremely simple, and two of them because they have stood the test of time and have been automated. All are primarily for use with vertical field anomalies, but they are effective for total field anomalies in high magnetic latitudes. As used in these simple formulas, the half-width (W/2) is defined as the horizontal distance between the maximum anomaly and the half-maximum anomaly (See Figure 4).

The very simplest depth estimates are based on the estimated shape of the magnetic body and the half-amplitude width of its anomaly along an optimal profile (Module #16 – Optimal Profile).

**Figure 4. Half-width definition: W/2 is the distance at the half-amplitude point A/2**

Anomaly shape (map view) |
Geologic Body |
Depth Rule |

Circular | Plug, stock, volcanic spine, intrabasement mass | Depth=1.305xW/2 |

Narrow, elongate | Thin dike, mineralized or intruded fault zone | Depth=1.0xW/2 |

Broad, elongate | Thick dike, dike swarm, intrabasement mass | Depth=0.7xW/2 |

The next generation of analog depth estimation methods involved the use of nomograms based on critical wavelength indices and amplitudes along a magnetic anomaly profile. Some were quite accurate but were slow and cumbersome to use. Three examples would be the ITI, Bean, and Koefed methods. A few, such as the Vacquier straight-slope and Peters half-slope, were simple but sufficiently robust to warrant retaining in many computer-driven depth estimation programs.

**Vacquier Straight-slope Method**

The straight-slope rules for depth estimation are based on studies by Vacquier et al of measurable horizontal dimensions of the magnetic effect of 2D or 3D tabular bodies with a flat top and prism-shaped sources in varying magnetic fields. These rules enjoy wide-spread application, providing effective results in the hands of the experienced interpreter. They rely on measurements that are generally insensitive to the relative size and attitude of the source and that avoid significant interference from overlapping anomalies, but the straight-slope method is most commonly used with 2D source bodies. The method is particularly advantageous because it does not require estimation of a base level. Base level may be difficult to evaluate where anomalies are subject to significant interference from other anomalies or are affected by gradients from regional anomalies derived from deep, broad sources with high magnetization contrast with the adjoining rock formations.

The straight-slope method is based on the optical illusion that the anomaly curve approximates a straight line near its inflection point. Mathematically, the anomaly has no straight slopes, but the steepest part of the anomaly curve is very nearly a straight line (see Figure 5). In practice, a tangent (blue) is drawn to the steepest gradient of an individual magnetic anomaly on a section of profile. The horizontal distance (h) over which the tangent line is coincident with the anomaly profile is measured. This horizontal distance (h) is considered to be related to the depth of source. A depth estimate is obtained by multiplying the horizontal distance (h) by a factor (a) which usually falls in the range of 0.6-0.8 (0.8 index for prisms, 0.6 for plates). Thus, the formula for Straight-Slope (SS) depth estimation is SS= a x h. As a reminder, the profile must be measured along a line at right angle to the strike of the anomaly or else the depth estimate must be multiplied by the cosine of the intersection angle.

Many currently-used computer programs designed for depth estimating will help in measuring the tangent to the curve. If the selected anomaly is noisy or if there is an interfering anomaly, a small low-pass filter may help eliminating the noise and obtaining the correct tangent. The factor

(a) is usually selected before measuring the tangent.

**Figure 5. Vacquier straight-slope measurement: h is the horizontal distance for which the anomaly curve approximates a straight line**

**Peters’ Half-slope Method**

This fairly robust method was developed and tested by a Gulf Oil geophysicist named Peters. It is based on the mathematical expression for the vertical component of the magnetic anomaly due to the 2D vertical-sided infinite prism (dike) of width w and depth h.

To implement the half-slope method, the interpreter draws a tangent (blue) to the profile at the point of the steepest slope (like in Straight Slope method). Two more tangents (red) are drawn at the half-slope (not the half-angle!) of the blue tangent line (see Figure 6). The two points at which the half-slope (red) lines are tangent to the anomaly curve are found by eye or with a parallel ruler, and the horizontal distance between them (h) is measured. The distance (h) is divided by 1.6 to give a rough depth to the top of the source body. Peters’ method relies on model studies that show that the true factor generally lies between 1.2 and 2.0, with values close to 1.6 being common for thin, nearly-vertical bodies of considerate strike extent. The formula for half- slope is HS= 1.6 x h. The profile must be either measured along a line at right angle to the strike of the anomaly or else the depth estimate must be multiplied by the cosine of the intersection angle.

**Figure 6. Peters’ half-slope: the blue line approximates the straight-line portion of the curve. Red lines have half the slope of the blue line; h is distance between points of tangency.**

**Spectral Analysis**

Spectral analysis is used in a variety of ways in the analysis of magnetic anomaly data. It can be used in the design and application of filters of various types to isolate or enhance particular attributes of anomalies and it can also be used in the inversion of individual or groups of anomalies. The method has been especially useful in determining the average depth to an ensemble of magnetic sources observed on either profiles or maps. The sources of magnetic anomalies within a region are assumed to average out so that spectral properties of an ensemble of sources are equal to those of the average of the ensemble. This methodology is advantageous because it is statistically oriented, averaging source depths over a region containing complex patterns of anomalies. It is also less affected by interference effect due to overlapping anomalies and high wave-numbers noise than other methods.

2D Depth Estimation

One of the early papers describing the use of 2D spectral analysis for magnetic depth estimation was by Spector and Grant. The method has been automated, but some software is not always successful in estimating depth to a single windowed anomaly of finite wavelength. Most software does work well in assigning an average depth to a suite of anomalies along a profile.

The method consists of computing the 2D log spectrum of either a single windowed anomaly, a set of anomalies, or all anomalies along an entire magnetic profile. The power spectrum of the selected anomaly (or anomalies) is then plotted as a graph (Figure 7) with the vertical scale representing log power and the horizontal scale representing frequency in radians. The long-wavelength, low-frequency, values represent deep-source anomalies and are plotted on the left side of the graph; those of the shallower bodies are to the center and right side. The steepest slope (black line) of the blue curve provides a depth value for the longest wavelength anomaly (or anomalies) within the computation window of the magnetic profile and the shallower slope (green line) provides the shallow depth value. Some anomaly complexes may provide three or more depth estimates.

**Figure 7. Log spectrum plot for analysis of anomalies along a magnetic profile. Straight-line approximations (black and green lines) of the spectrum curve provide depth estimates.**

3D Depth Estimation

Most magnetic depth estimation methods consider a magnetic anomaly as generated by a magnetized source body in the shape of a vertical prism. If the prism has great vertical dimension, its top surface will represent the top of an igneous plug, top of magnetic basement, or top of an intrabasement intrusive. The base of the prism will also have a magnetic surface which forms a magnetic discontinuity with the material below it. If the deeper material is essentially non-magnetic, the base of the prism will approximate the Curie point which in turn may approximate the Mohorovicic discontinuity, or Moho. Determining the depth and surface configuration of the Moho has important considerations for heat flow and regional tectonics.

However, there are few data points other limited seismic refraction surveys to provide Moho control. The application of 3D spectral analysis could provide additional data points. Several papers have been published describing the use of 3D spectral analysis of magnetic data to estimate Curie depths.

**Werner Deconvolution**

The Werner deconvolution method is based on mathematical analysis of simultaneous equations arising from the magnetization formulae for thin magnetic sheets in any position or orientation. From the perspective of magnetic anomalies along profiles, lateral margins or contacts between subsurface magnetic sources of anomalies can be interpreted by the collective effects of thin sheet-like bodies. One of the first papers describing the solutions to the equations and plotting of the solutions was published by Hartman, Teskey, and Friedberg.

Werner deconvolution is not only effective for determining the position, depth, dip and magnetic susceptibility contrast times thickness product of thin vertical or dipping sheets, but can also be employed to determine the characteristics of 2D contacts or interfaces of prismatic bodies. The latter is based on the equivalence of the horizontal gradient of an interface anomaly and the anomaly of a thin dike. Horizontal derivatives may be observed in gradiometer data, but more commonly they are calculated from the difference in total intensity values at a prescribed horizontal distance.

Figure 8 is an illustration from the Hartman paper showing results from a fully automated use of Werner Deconvolution. The process produces multiple solutions from analysis of the total magnetic intensity (upper) profile and from the horizontal gradient (lower) profile. The solutions, which appear as patterns of strings and clusters, are the result of several passes of the convolution operator, using different window sizes, along the input data. Interpretation of the profile is difficult without significant experience with Werner and a suite of model solutions with which to compare the survey solutions.

**Figure 8. Raw Werner Deconvolution depth solutions for total field and horizontal gradient aeromagnetic profile data (after Hartman et al)**

**Figure 9. Summed Werner Deconvolution depth solutions for total field and horizontal gradient aeromagnetic profile data (after Hartman et al)**

Figure 9 illustrates a magnetic basement interpretation of the Werner solutions by an experienced interpreter. Note that the raw depth estimates from Figure 8 have been summed into triangles (interface solutions from horizontal gradient analysis) and squares (thin sheet solutions from total intensity analysis). The magnetic profile is that of a north-bearing line at magnetic inclination of 5º N, therefore the central basement graben has a positive magnetic anomaly.

In theory, Werner horizontal gradient solutions should be used for depths to magnetic interfaces or very wide bodies, whereas depths for other bodies are commonly taken from the total intensity solutions. In practice, the total intensity solutions are used the vast majority of times.

**Euler Deconvolution**

The Euler deconvolution technique can be used to help speed interpretation of any potential field data in terms of depth and geological structure. The method may be applied to survey profile data or gridded data. It operates on a data subset extracted using a moving window. In each window, Euler’s equation (see reference Hood, 1965) is solved for source body coordinates. The source body geometry is specified by a Structural Index (SI) ranging between 0 and 3, as shown in the table below.

Source body |
Magnetic Structural Index |

Dipole (sphere, small, compact body) | 3 |

Thin pipelike body (vertical>kimberlite, horizontal>pipeline); thin bed>fault | 2 |

Thin sheet edge (dyke, sill) | 1 |

Contact of great depth extent | 0 |

Intermediate bodies have non-integer Structural Indexes and the Euler formulation is only approximate. The method does not require any assumptions about direction of exciting field, direction of magnetization or the relative magnitudes of induced and remanent magnetization of sources. Euler deconvolution is only valid for homogeneous fields. These are only obtained from particular idealized bodies with integer SI. The fields of most real bodies do not meet this strict criteria and the method is therefore an approximation in practice.

Euler solutions can be interpreted without rejecting any solutions, by simply relying heavily on the skill of the interpreter to discriminate between reliable and spurious solutions, since this method generates a solution for each window position, regardless of the presence (or lack) of any nearby magnetic sources. It assumes that the effects of only one source are present in any window without considering interference from other sources. A more mathematically rigorous technique to discriminate between reliable and spurious solutions is preferable, such as the use of estimates of the standard deviations of model parameters from the least squares inversion

The 3D Euler method is quite popular because it can compute and post anomaly source depths on an interpretation map. However, the interpreted depths are dependent on the grid spacing chosen for input to the program and also on the assumption of the SI factor chosen. A number of depth estimation programs include a 2D Euler option within a window chosen by the interpreter. As with depth solutions from Werner, for example, the quality of the Euler solution is highly dependent on the tightness of solution clusters and their relation to solutions from all other depth estimates.

Figure 10 illustrates a 3D Euler interpretation. Here the depth estimates are represented by circles: the small circles represent a depth of 1 km, the medium size represents 2 km, and the large circles represent 3 km. Some presentations use color-coded symbols to display the different depth solutions. The solutions are aligned along magnetization boundaries, so the Euler map provides useful information about the location and shape of the magnetic source bodies.

However, a detailed contour map of a surface such as magnetic basement would be extremely difficult to produce.

**Figure 10. 3D Euler Deconvolution depth solutions from total intensity magnetic data grid (after Reid et al)**

**Summary of Methods and Factors Used in Magnetic Profile Interpretation:**

- Werner (primarily TI for dike-like bodies, some HG for interfaces)
- 2D Euler (1.0 index for dike-like bodies, 0.5 for interfaces)
- Straight-slope (0.8 to 1.4)
- Half-slope (1.6 to 1.0)
- 2D Spectral