The boundary between the Earth’s crust and the mantle has been defined as the Mohorovičić discontinuity or known for short as the Moho. This boundary interface involves a large change in both velocity measured directly using refraction data and density contrast measured using gravity data. Due to this contrast, undulations in the Moho surface generate anomalies of regional scale producing gravity gradients that can conceal and hide geological features of interest. Therefore, gravity anomalies sourced within the sedimentary section must be enhanced by: 1) removing the gravity effect of the Moho surface, and 2) attenuating the gravity effect of shallow topographic features; and what remains is a crustal model that reflects gravity anomalies of exploration significance from the Earth’s surface to the base of the crust.

The surface which separates the Earth’s crust from the mantle can be configured by seismic or gravimetric methods. The seismic method is expensive and suffers the scarcity of available seismic data. On the other hand, the gravity method is less costly and regional gravity public domain data sets are easily accessible. The interpretation of the surface using gravity is carried out in three steps:

a) compute an estimated depth-to-Moho surface using Airy-Heiskanen model,
b)incorporate the surface as a layer in a regional 3D gravity EarthModel, then invert on the Bouguer gravity field, and
c) calibrate and adjust the inverted depth surface to available refraction or reflection data sets.

Learning Objectives:

After completing this Module, you will be able to:

  • Describe the isostasy principal.
  • Describe the gravity crustal model.
  • Describe a Depth-to-Moho surface
  • Describe a calibrated and adjusted Depth-to-Moho Surface.
  • How to generate an isostatic residual map.
  • Identify the anomaly zone of interest: from earth surface to the base of crust.
  • Example area is used to illustrate the procedure.

Crustal Model-Moho

As a reminder, the Earth’s concentric four prime layers are: the crust, the mantle, the outer core and the inner core. These layers or shells differ in depth, volume and density. The densities vary both laterally and with depth. The volumes are as follow: crust 2%, mantle 80%, outer core 17% and inner core 1% of the Earth’s volume. The crust is composed of oceanic and continental crusts. The oceanic crust is about 6-12 km thick, and the continental crust averages about 36 Km with a maximum thickness of 90 km in Tibet. The 2% crust floats on the mantle by virtue of the isostasy principle.

Isostasy Principle

Understanding the nature of isostatic mechanism has been an endeavor for Geoscientists since the concept of crustal balance had been introduced along with the term “Isostasy” to accompany it. The word “Isostasy” means equal pressure in the Greek language. In brief, the principle of isostasy states that the lighter crust floats on the dense underlying mantle. When a certain area of lithosphere reaches the “state of isostasy”, it said to be in isostatic equilibrium. The depth at which isostatic equilibrium prevails is called the compensation depth. The principal also provides an explanation to why longer wavelengths of the Bouguer gravity field correlate inversely with the longer wavelengths of the topography; the principle suggests that loads on Earth surface caused by topographic features are supported at depth by deficiencies in mass as if the crust is floating on a denser material. These deficiencies in mass under topographic loads are referred to as compensating masses or roots. This can be visualized as the mass of the topography above sea level must equal the mass deficit caused by the root below the average crustal thickness. A good first approximation of the average crustal thickness is the depth to the base of the local crust where the overlying topography is at or near sea level.

Gravity Crustal Model

A gravity based crustal model may be defined as a waveform model where long-wavelengths caused by either thick or deep seated sources and short wavelengths associated with thin or near- surface sources have been attenuated. This is a structure model where gravity effects of both water/sediment (bathymetry) and crust/mantle (Moho) interfaces have been isolated and removed.

In geological terms, the gravity crustal model is the structure of a floating slab of material between the Earth’s surface and the Mohorovicic discontinuity (Moho). The slab is an amalgamation of soft and hard sediments, igneous intrusions, upper and lower crust and upper mantle.

Calibrated and Adjusted Depth-to-Moho Surface

The primary objective of this module is to show how to derive a calibrated and adjusted depth configuration map of the crust/mantle discontinuity (Moho). The steps required to achieve this goal are:

  1. to compute a first-pass depth-to-Moho configuration using the Airy-Heiskanen equation,
  2. to adjust this first-pass Moho structure configuration by calculating a 3-dimensional inversion using the Bouguer gravity field, and
  3. to calibrate the result with available refraction/reflection data sets.

An example of this procedure to calculate and interpret a crustal model follows for an area in Tanzania (onshore and offshore).

A. Example Area: Tanzania

The example area covers roughly 2,000,000 square kilometers. Latitude and longitude bounds range from 15° to 0 ° South and 35° to 50° East respectively. The Index Map (Figure 1) shows the area that encompasses major onshore and offshore basins. Selous-Ruvu-Tanga, Ruvuma and Mandawa represent the main onshore basins. Mafia, Pemba, Songo-Songo and Zanzibar are among major offshore basins. The area also includes the Cosmolido group, Comoros islands and the Wilkes rise.

Figure 1: Index Map


B. Database

The Primary input data consisted of public source Free-air satellite-derived gravity (version 20.1) and bathymetry/topography (version 15.1) grids. The grids were obtained from Scripps Institution of Oceanography, La Jolla, CA.

C. Free-Air Gravity

Scripps Oceanographic Institute (Sandwell et al) has been providing the industry with satellite- derived marine gravity data which has been collected through several satellite missions, such as ERS-1, Geosat and Topex/Poseidon. These datasets are periodically reprocessed and enhanced to provide the scientific community with better products. For this Moho interpretation example, we are using version (20.1) based on 1×1 arc-minute spatial grid resolution.

The Free-air gravity anomaly map (Figure 2) contains major anomalies generated by the large density contrasts of the topography and the water/sea bottom interface as well as at the top of the crust/mantle interface. These anomalies are often of regional scale and strong enough to distort or overwhelm other anomalies that can provide a useful structural interpretation. Therefore, anomalies sourced by geologic features within the sedimentary section or basement must be enhanced for interpretation by attenuating gravity effects of water/sea bottom and crust/mantle interfaces. The gravity effect of water/sea bottom is removed by converting the Free-air gravity to Bouguer gravity (Module #22 3D Bouguer Correction) and the crust/mantle effects by removing the gravity effect of the Moho. Both procedures are discussed below.

Figure 2: Free-Air Gravity Anomaly (mGal)


D. Bathymetry & Topography:

The bathymetry/topography data (Figure 3) was collected concurrently with the satellite-derived marine gravity data. Scripps Institution of Oceanography has also reprocessed and enhanced the data to provide an essential understanding of mantle conviction patterns, plate boundaries and distribution of volcanoes. Version (15.1) is used here.

Figure 3: Bathymetry/Topography (Meter)


E. Airy-Root Calculation

According to Airy-Heiskanen hypothesis, the Earth’s lighter crust floats on the denser mantle, and there are light roots under mountains and heavy anti-roots under oceans. The hypothesis also presumes a local compensation, and a static equilibrium between buoyancy forces acting on the floating crust and the weight of the displaced mantle material. The method determines the depth to the bottom of the roots and anti-roots and provides an estimated depth to the Mohorovicic discontinuity (Moho). The method also requires the assumption of the depth of compensation and the density contrast of the crust/mantle interface. For our project area, the topographic/bathymetric configuration is used as the key element to derive an estimation of the crustal thickness in conjunction with the other two essential assumptions: the density contrast of 0.55 g/cc, and a crustal thickness at the coast line value of 34 km. These two parameters have been determined based on an intensive literature search. We have used Airy-Heiskanen formula to calculate the root or the initial depth-to-Moho surface onshore (Figure 4-a) and offshore (Figure 4-b), then we merged the two surfaces to obtain (Figure 4).

Figure 4-a Depth-to-Moho (Airy-root Onshore Calculation) (Meter)


Figure 4-b Depth-to-Moho (Airy-root Offshore Calculation) (meters)


Figure 4: Initial Depth-to-Moho (Airy-root Calculations added but unsmoothed) (meters)


F. 3D Gravity Inversion

Prior to the 3D Bouguer gravity inversion, two important steps have to be taken: a) conversion of Free-air gravity field to Bouguer gravity, 2) building of a simple 3D EarthModel to carry out the Bouguer gravity inversion.

1. Bouguer Gravity Anomaly

The Free-air Gravity anomaly contains anomalies caused by topographic/bathymetric features. Therefore, Bouguer reduction correction of the Free-air gravity corrects for or attenuates these gravity anomalies, and the resultant Bouguer map best represents anomalies from real geologic sources below datum.

Bouguer reduction or combined corrections require elevation and/or bathymetric data plus knowledge of, or a good estimate of near surface density. Poor quality elevation/bathymetric data or a poor density estimate will degrade the final Bouguer gravity.

The objective is to minimize the effect of high relief bathymetric features present in the Free-air gravity offshore, similarly to correct for the effect of topographic features within the free-air gravity onshore Kenya, Tanzania, Mozambique and the islands of Comoros, Cosmolido group, Mafia and Zanzibar. A Bouguer correction of 2.75 gm/cc was assigned to the islands due to the underlain known oceanic rock, an average Bouguer density of 2.67 gm/cc was assigned to the sediments present on the sea floor, and a Bouguer correction of 2.67 gm/cc to onshore Kenya, Tanzania and Mozambique. In order to correct for the excess of gravity onshore Kenya, Tanzania, Mozambique and the islands, computed Bouguer corrections 2.67 g/cc and 2.75 g/cc respectively were subtracted from the Free-air gravity, and to minimize the effect of high relief bathymetric features Bouguer correction 2.67 gm/cc offshore was added to the Free-air.
Consequently, the final merged 3D Bouguer gravity grid includes two variable densities; 2.67 gm/cc onshore and offshore and 2.75 gm/cc on the islands due to the presence of the underlain oceanic rock (Figure 5). For further details see Module #22 3D Bouguer Correction.

Figure 5: Merged Bouguer Gravity Anomaly (mGal)


2. 3D EarthModel:

Due to data access limitations and scarcity of depth layers for constraints, the 3D EarthModel was built using four simple density layers. In order of depth they are:

  • Water/topography: The layer’s upper surface is sea level and the lower surface is controlled by the Sandwell (Version 15.1) bathymetry grid. The density assigned to this layer is 2.67 gm/cc.
  • Sedimentary layer/Upper crust: The upper limit of this layer surface is the Sandwell bathymetry surface and its lower surface represents an estimated lower crust surface. This layer contains an aggregate lithological composition and heterogeneous structures. The infill consists of claystones, continental and lacustrine rocks, and marine deposits. The density value for this layer is estimated to be 2.7 gm/cc.
  • Lower crust: this layer has been introduced into IGC’s 3D EarthModel as an oceanic/lower crust boundary of homogenous composition (mafic). The upper boundary is the sedimentary/upper crust layer and the lower boundary is the initial Moho configuration computed using the Airy method. An average density of 2.75 g/cc was assigned to the layer.
  • Mantle: The upper mantle layer is a high-density, high-velocity layer between the earth’s crust and its core. The layer’s upper surface is the Moho interface; its configuration was computed using the Airy method. The lower surface was set at 60 km subsea. Density of the mantle was selected to be 3.3gm/cc.

The location of a NW-SE profile is shown on (Figure 6), and its corresponding cross section from the 3D EarthModel is shown on (Figure 7). The shown Moho surface is the uncalibrated unadjusted Moho surface prior to the gravity inversion.

Figure 6: NW-SE Profile location (Airy-Root)


Figure 7: Profile through Initial 3D EarthModel. The mantle is shown colored brown. The Moho surface shown is unadjusted and the observed Bouguer gravity curve is shown.


G. Moho Gravity Inversion and Adjustment

The Bouguer gravity based inversion was carried out using the simple four-layered 3D EarthModel defined above. The inversion adjusted the initial Airy-root Moho surface until a regional and suitable fit between the observed and the calculated Bouguer gravity fields was obtained. The initial inversion generated a surface with numerous short wavelength anomalies. Analysis of the radial power spectrum of the surface shown on Figure 8 indicated that a 150 km wavelength (0.01 Nyquist) filter was adequate to reduce the short wavelength noise while preserving Moho anomalies of geologic interest. The filter was therefore applied to produce an improved map of the computed surface. Figure 9 shows the profile of the final model after smoothing using the 150 km low-pass filter.

Crustal Model-Moho

Figure 8: Radial Power Spectra of Moho Surface


Crustal Model-Moho

Figure 9: Profile through 3D EarthModel after five iterations


H. Moho Calibration to Reflection/Refraction Data Sets:

Twenty-three seismic derived mantle depth solutions over the project area have been utilized to constrain the inversion. These depths were the product of the study of the wide-angle reflection and refraction acquired during R/V Vema legs V3618 and V3619 in the Western Somali basin (Figure 10).

Crustal Model-Moho

Figure 10: Mantle Depth solutions Location Map


Final Depth-to-Moho Surface

The calculated crust/mantle interface surface (Moho) has been mapped using a contour interval of 1,000 meters below sea level (Figure 11). Shallow mantle ranging between approximately 8000 – 14000 meters (bsl) and is located seaward east of the Davie Ridge. The Bouguer gravity (Figure 5)shows the highest gravity field in the Comoros islands, Cosmolido group and the Wilkes rise.As expected these features of high gravity correlate well with the shallowest Moho, which wasderived by gravity inversion and calibrated to refraction and reflection mantle depths deduced fromthe sonobuoy experiment along the Somali Basin. Deepest mantle ranging between approximately14000 – 43000 meters (bsl) is located shoreward west of the Davie Ridge. The map (Figure11)shows a portion of the Mozambique belt where Moho depths range between 37000 – 42000 meters (bsl). The Moho depth of the Mandawa basin, Ruvu basin and Seous basin ranges from 24000 to 29000 meters (bsl).

Crustal Model-Moho
Figure 11: Final Depth-to-Moho


Isostatic Residual Gravity Map

The isostatic residual gravity map (Figure 13) is essential for interpretation of the geology, the map reveals enhanced anomalies of geologic interest removing the effect of Moho surface undulations. The undulations generate strong gravity anomalies or gradients that conceal anomalies sourced within the basement or the sedimentary section. The map is generated by removing the gravity effect of the Moho (Figure 12) from the Bouguer gravity anomaly field. The gravity effect of the Moho has been computed based on a forward gravity calculation using the 4-layered EarthModel described above, where a density contrast of 0.55 g/cc has been assigned to the crust/mantle interface and 0.0 g/cc density to the remaining layers.

Crustal Model-Moho

Figure 12: Gravity Effect of Moho

Crustal Model-Moho

Figure 13: Isostatic Residual Gravity


The isostatic residual gravity map could be enhanced by using data enhancement techniques (Module #15 data Enhancement Techniques). The enhancement method we have selected for our onshore/offshore Tanzania project area is a band-pass filter. Our aim is to isolate and target more anomalies of interest and to produce a resultant map sufficient for general interpretation and correlation with regional geologic features.

Band-Pass Filtered Isostatic Residual Gravity:

A band-pass filter can be designed for any gravity dataset to remove: a) unwanted short wavelengths anomalies due to instrument noise or bad recording, mis-positioning of the data point, poor terrain corrections, or abrupt changes in near surface density, and b) unwanted long- wavelength anomalies due to regional gradients that obscure or distort the anomalies of immediate geologic interest. Therefore, we have determined that a 75 – 225 km band-pass filter was appropriate to isolate anomalies of interest that correlate with the available geological features for our sub-set area outlined by the box on (Figure 14).

Crustal Model-Moho

Figure 14: Band-Pass Filtered Isostatic Residual Gravity.
The subset outlined in black is discussed in the following section.


Band-Pass Filtered Isostatic Residual Gravity with Geologic Overlay

The sub-set area outlined on (Figure 14) is an area with an extensive presence of oil and gas- prone source bed of Middle Jurassic to Late Cretaceous age. The area contains major basins with an average sedimentary section depth between 6,000 – 10,000 meters. There are four types of basins -with a brief decription below- as shown on the band-pass filtered isostatic residual gravity overlaid by regional geologic features assembled from various published articles (Figure 15):

  • Inland basins delineated by Selous and Ruvu basins
  • Coastal basins represented by Ruvuma, Mandawa, Dar-es-Salaam and Rufuji basins
  • Shallow offshore Songo – Songo basin in territorial waters up to 200 meters in depth
  • Deep offshore basins in territorial waters more than 200 meters in depth such as Pemba-Zanzibar and Mafia basins.

Crustal Model-Moho

Figure 15: Isostatic Residual Gravity with 75-225 Km Band-Pass &Geologic Overlay


Final Comments

  • The Mohorovicic discontinuity or (Moho) generates gravity anomalies of regional scalethat conceal geological features of interest.
  • The gravity 3D EarthModel and the refraction/reflection data are critical to the calibrationof the initial Airy-Heiskanen calculation of the root or depth-to-Moho surface.
  • The conversion of Free-air gravity to Bouguer gravity corrects for anomalies caused by topographic/bathymetric features.
  • Gravity effects of both the Moho and of shallow geologic features must be attenuated from the Bouguer gravity field to produce a preliminary crustal model.
  • The crustal model is a structure or a floating slab material between the Earth’s surface and the Mohorovicic discontinuity (Moho).
  • The final isostatic residual gravity eliminates both gravity effect of the Moho and gravity effect of shallow topographic features and it is essential to first-hand gravity interpretation.
  • The filtered isostatic residual gravity map onshore and offshore Tanzania correlate with published regional geology.
  • Gravity data provides an initial step to interpret anomalies sourced within the sedimentary section but may be enhanced by seismic and other data sets as well.