Crustal Structure of the Namibian Continental Margin and the Walvis Ridge: Results from 3D Gravity Modeling. Bachelor of Science Thesis

Crustal Structure of the Namibian Continental Margin and the Walvis Ridge: Results from 3D Gravity Modeling Bachelor of Science Thesis by Wilken-Jon von Appen May 15th, 2007 Supervisors: Prof. Dr. Vikram Unnithan 1, Prof. Dr. Joachim Vogt 1, Dr. Wilfried Jokat 2, Dr. Mechita Schmidt-Aursch 2 1 Department of Geosciences and Astrophysics, Jacobs University Bremen (formerly International University Bremen), Bremen, Germany 2 Department of Geophysics, Alfred-Wegener Institute for Polar- and Marine Research (AWI), Bremerhaven, Germany

CONTENTS Contents List of Figures 3 List of Tables 3 1 Introduction 4 2 Regional Geology 4 3 Theory 7 3.1 Gravity as the surface expression of subsurface mass distributions.. 7 3.2 Gravity anomalies measured from satellites............... 8 4 Data 11 4.1 Satellite Gravity.............................. 11 4.2 Satellite Bathymetry........................... 13 4.3 Sediment Maps.............................. 15 4.4 Seismic Refraction Profiles........................ 17 5 Modeling 18 5.1 Modeling with the Interactive Gravity and Magnetic Application System..................................... 18 5.2 Model Setup................................ 21 5.3 Choice of densities............................ 23 6 Results 25 6.1 Structure of Southern Part........................ 25 6.2 Structure north of the Walvis Ridge................... 27 6.3 Structure below the Walvis Ridge.................... 28 6.3.1 Scenario 1: no underplate.................... 28 6.3.2 Scenario 2: underplate at 15 km depth............. 30 6.3.3 Scenario 3: underplate at 18 km depth............. 30 6.3.4 Scenario 4: underplate at 21 km depth............. 32 6.4 Residuum................................. 32 1

CONTENTS 7 Discussion 34 7.1 Assessment of different scenarios..................... 34 7.2 Assessment of volume of underplate................... 35 7.3 Possible existence of extrusive volcanic material............ 37 8 Summary 38 9 Acknowledgments 38 References 40 A Appendix 42 2

LIST OF FIGURES List of Figures 2.1 Elevation of South Atlantic....................... 5 4.1 Gravity anomaly of region........................ 12 4.2 Elevation of region............................ 14 4.3 Sediment layers 1 and 2......................... 16 4.4 Sediment layers 3 and 4......................... 16 4.5 Sediment layer 5............................. 17 4.6 Bauer et al. (2000) velocity profiles of transects 1 and 2........ 19 4.7 Bauer et al. (2000) density profile of transect 1............. 20 5.1 Model setup................................ 22 5.2 Density related to p-wave velocity.................... 24 6.1 Model plane -300km........................... 25 6.2 Modeled thickness of oceanic crust for scenario 1............ 26 6.3 Model plane +350km........................... 27 6.4 Model plane +200 km for all four scenarios............... 29 6.5 Modeled depth of moho for scenario 3.................. 31 6.6 Residuum in scenario 3.......................... 33 7.1 Modeled thickness of underplate for scenario 3............. 36 A.1 Model plane +200km, Scenario 1.................... 42 A.2 Model plane +200km, Scenario 2.................... 43 A.3 Model plane +200km, Scenario 3.................... 44 A.4 Model plane +200km, Scenario 4.................... 45 List of Tables 5.1 Model densities.............................. 23 3

Introduction 1 Introduction The exact nature of so-called mantle plumes has not been satisfactorily clarified. Their interaction with passive continental margins prior, during, and after the breakup of continental crust is a further topic of current interest. Elucidating these issues is the aim of a proposed priority program. The focus of the priority program is the South Atlantic featuring the hotspot trace with its current position Tristan da Cunha and the passive continental margins of southwest Africa and southeast America. Several geophysical investigations have been carried out offshore of Namibia. Commercial seismic reflection surveys were shot in 1989 and 1991 and Stewart et al. (2000) have compiled sediment maps from those. The Alfred-Wegener Institute for Polar and Marine Research, Bremerhaven (AWI), the Bundesanstalt für Geowissenschaften und Rohstoffe, Hannover (BGR), and the GeoForschungsZentrum, Potsdam (GFZ) have shot three seismic refraction profiles in 1995 and Bauer (2001) and Schinkel (2006) have analyzed them to obtain two dimensional velocity distributions along the profiles. The general crustal structure that has been observed by these seismic refraction profiles features the extended continental crust, a transitional zone including the continent-ocean boundary, and relatively thick oceanic crust. The crustal thickness of the oceanic crust is found to be around 12 km. Additionally, a high velocity body below the oceanic crust is found. This so-called underplate is a remanence of magmatism associated with a mantle plume. The is thought to have contributed to the breakup of Gondwana and the resulting rifting of South America and Africa. This project uses the refraction seismic data sets as well as the global marine gravity anomaly maps from satellite altimetry (Sandwell and Smith, 1997) to carry out a three dimensional density modeling in the marine part of the region from 8 E to 15 E and 17 S to 25 S. The Interactive Gravity and Magnetic Application System (IGMAS) (Schmidt, 2004) is used for the 3D gravity modeling. The results provide valuable information about the depth structure that will help to define the setup of possible later seismic refraction surveys. The AWI has been chosen as a location for this off-campus guided research project due to the existing knowledge about the region (Jokat et al., 2003; Schinkel, 2006) and the modeling method and software (Schmidt-Aursch and Jokat, 2005a; Schmidt- Aursch and Jokat, 2005b). 2 Regional Geology Figure 2.1 shows the elevation of the South Atlantic and Southern Africa. The elevation data set used is ETOPO2 (Sloss, 2001). Labeled geological features are described below. 4

Regional Geology Figure 2.1: Elevation map of South Atlantic and Southern Africa. Geological features of interest are labeled as well as location of refraction seismic surveys. 5

Regional Geology The regional geology of the southwest African continental margin is governed by the Panafrican orogeny leading in the formation of Gondwana, by the rifting event breaking up Gondwana and opening the South Atlantic, and by the mantle plume responsible for Walvis Ridge and the Parana-Etendeka floodbasalts which is now located at Tristan da Cunha. The supercontinent Rodinia drifted apart some 1000 Ma ago. Then among other the Rio-de-la-Plata craton (now in South America) and the Congo and Khalahari cratons (now in southern Africa) joined to form the supercontinent Gondwana. During this process the so-called Adamastor ocean was destroyed and parts of it can be found as folded oceanic crust both in Africa and South America. The process of formation of Gondwana is called the Panafrican orogeny and it is thought to have occurred roughly 575-505 Ma ago. The rifting leading to the eventual opening of the South Atlantic was preceded by a basin and range extension which allowed for the 3000 m thick permian-jurassic Karoo-sediments to form in a shallow marine environment. In general there is still disagreement on the time of the breakup of Gondwana. Jokat et al. (2003), based on magnetic investigations, find the initial volcanism starting 200-180 Ma ago which is 40-20 Ma before they find the first oceanic crust formed. On the other hand, the Parana floodbasalts in South America and the Etendeka floodbasalts in Africa have been dated to 137-124 Ma by Milner et al. (1995). It is thought that these floodbasalts were formed by a mantle plume that is now located somewhere in the proximity of Tristan da Cunha and Gough Island which both exhibit active volcanism today. The exact position of the plume cannot be identified as it is most likely rather diffused. The plume is also held responsible for the Rio Grande Rise and the Walvis Ridge which stretches from Africa to Tristan da Cunha with age increasing with distance from Tristan da Cunha. Stewart et al. (2000) assumed the onset of the rifting 137 Ma ago for their synrift sediment maps. At that point South America, Africa, and Antarctica started to move into different directions and with different speeds. Jokat et al. (2003) have determined that unidentified fluid dynamic effects in the mantle have resulted in an asymmetric motion of the continents with South America spreading at a speed of 0.9 cm per year while Africa has been moving at 1.8 cm per year since that time. Today, the continental shelf off Namibia is between 100 km and 200 km wide and it exhibits the generic transition between oceanic and continental crust found at passive continental margins. A question frequently addressed is to identify the regions along a cross slope profile occupied by oceanic crust, by the continent-ocean transition (often a rather large region), by transitional igneous crust, by extended and intruded continental crust, and finally by unaffected continental crust. An additional feature are basalt layers that were surfaced during the Kudu 9A-1 drilling in the Orange basin. They have been interpreted as seaward dipping reflectors (SDR) which were formed from subaerial or shallow marine lava flows dipping seaward as a result of subsidence. Austin and Uchupi (1982) have identified these SDR along the entire Namibian coast and both Stewart et al. (2000) and Bauer et al. (2000) have shown SDR in their studies. 6

Theory 3 Theory 3.1 Gravity as the surface expression of subsurface mass distributions Newton s law of gravity gives the gravitational force F G between two point masses m 1 and m 2 as F = G m 1m 2 r 3 r (3.1) 11 Nm2 where r is the vector pointing from m 1 to m 2 and G = 6.67 10 is the kg 2 universal constant of gravity. The gravitational acceleration g of an extended mass distribution is defined by the integral ρ g = G r dxdydz (3.2) r3 where ρ( r) is the density distribution of the mass distribution. The gravitational potential U can also be defined such that the negative gradient of the potential is the gravitational acceleration: U = g (3.3) It can be seen that the gravitational acceleration decreases as 1 with the distance r 2 from the causing body while the gravitational potential decreases as 1 with the r distance. The gravitational field measured at any location on earth has several different masses as causing bodies for variations on a variety of length and time scales. The main component, however, is due to the earth being an oblate spheroid. Therefore the most prominent variation from the mean of 9.81 m s 2 is latitudinal with gravity increasing by a summand varying as sin 2 φ from the equator to the poles where φ is the latitude. The deviation of any gravity measurement from the gravity predicted by the oblate spheroid for the latitude of the measurement is called the gravity anomaly. Gravity anomalies are a result of subsurface geologic features that differ from the surrounding. These anomalous features can be small scale on the order of meters to continent wide on the order of thousands of kilometers. Correspondingly, appropriate measurement intervals are chosen. An isolated anomalous body with density ρ a in a surrounding with density ρ has a so-called excess density ρ = ρ a ρ and corresponding excess mass that distinguishes it from its surrounding. The surface 2D gravity signals of generic geometric objects can be analytically determined as functions of their dimensions. In general, 3D objects are attempted to be described by an arrangement of spheres whose gravity signal is generically known. Similarly, 2D objects are described by infinite cylinders, and 1D objects are described by infinite horizontal slabs. There are also techniques that analyze the signals in order to retrieve information about the dimensions of the object as well as the maximum 7

Gravity anomalies measured from satellites distance the object can be away from the measurement points (e.g. Kearey et al., 2002). In comparison to other geophysical exploration techniques, gravity has some aspects that greatly complicate the interpretation of measurements. While seismic surveying is a direct technique, both gravity and magnetics are potential field techniques. Therefore they are inherently ambiguous and a theoretically infinite number of mass distributions could yield the observed gravity field. In comparison to magnetics, the limitation of gravity is that the signal is very weak due to the fact that the densities of most common rock types are in the range (1 10) 10 3 kg/m 3 and hence the maximum density contrast never exceeds an order of magnitude. This compares to magnetics where the susceptibilities of different rock types span orders of magnitude. A consequence is that several disturbing signals have to be subtracted, a process called gravity reduction. For this the exact position of a measurement is required. For local surveys on land, the latitude has to be known to less than 10 m and the height to less than 10 mm. In deep marine surveys, only the freeair gravity correction has to be applied correcting for the elevation of a measurement point with respect to a datum, usually the sea surface. Marine gravity from satellites is already reduced to the freeair gravity anomaly. In land surveys and surveys combining land and shallow water areas, the Bouguer and terrain corrections account for the gravity effect of present or not-present rocks between the measurement point and the datum as well as for other terrain effects. In addition to this the solid earth tides have to be corrected for by analytically available formulas which have a period of twelve hours and lack significantly in phase behind the ocean tides. The drift correction takes care of instrument drift due to temperature effects or non-elastic effects in the measurement device. The Eötvös correction removes accelerations due to a moving measurement device such as a ship or an air plane and it is highly sensitive to the speed and heading of the motion. This multitude of gravity corrections significantly decreases the accuracy of land measurements while the effect for marine surveys is not as drastic. 3.2 Gravity anomalies measured from satellites In general, there are two techniques to measure gravity anomalies by satellite missions. The twin satellite model implemented in the Gravity Recovery and Climate Experiment (GRACE) directly measures the gravitational field, but it can only resolve the field down to a scale of 300 km. The other technique employs radar altimetry satellites. Their resolution can get down to scales of 20 km, but the calculation of the gravitational acceleration from the measured sea surface height requires certain additional information about the longer wavelength features. Therefore products combining the data from both types of satellite missions achieve the best resolutions that can be used for regional and local geophysical applications. The GRACE mission launched in March 2002 consists of two identical satellites that 8

Gravity anomalies measured from satellites orbit in the same orbital plane. The distance between the satellites is roughly 240 km. The principle used to measure the gravitational acceleration directly observes the effect that the gravity has on the mass of the satellites. When the leading satellite enters a region of higher gravitational acceleration, it will be pulled away from the trailing satellite. A short time later, the trailing satellite will also enter this region of higher gravitational acceleration and hence it is pulled toward the leading one. This effect is measured by a K-band microwave ranging system that can determine the distance between the satellites to less than 1 µm. In addition, high precision accelerometers on the satellites measure the non-gravitational accelerations acting on the satellites that are mainly due to atmospheric drag and solar radiation pressure. On their orbits, the satellites are also constantly tracked by the Global Positioning System (GPS) to an accuracy of less than 1 cm. The initial orbit altitude of the mission was 500 km above the 6370 km reference sphere which has decreased to 480 km by the end of the five year mission. Consider a geological feature 4 km below the sea surface. The difference between the gravitational effect at the sea surface and in the 500 km orbit scales as the inverse square 1 of the distances: (504km) 2/ 1 1. This means that the gravitational effect (4km) 2 15000 that GRACE can detect is only a one fifteen-thousandth of the effect detectable at the sea surface. Another limitation of the resolution is that the mission has only produced four years of synthesizable observations up to now and that the orbits are chosen such that they repeat every 30 days in order to be able to detect time variable effects. Reigber et al. (2003) describe the entire GRACE mission and they also give the errors of the EIGEN GRACE02S which is solely based on the GRACE mission. For wavelengths greater than 600 km they give an error of the geoid height of less than 1 mm and for wavelengths greater than 275 km they give an error of less than 1 cm. However, the regional to local small-scale study undertaken in this project has extensions of roughly (3*275 km) 2. This would mean that all the features of interest would not show up in the the gravity field provided solely by GRACE. Reigber et al. (2003) come to a similar conclusion stating that the GRACE gravitational field products supply the geodynamics community with reliable boundary conditions for large- and medium-scale, but not for small-scale modeling efforts. The radar altimetry satellites have started operating in 1993 and more than six satellites have been successfully operational. Their greatest limitation is that they can only determine the gravity above the ocean and not on land or land-locked lakes. A radar beam is sent down from the satellite, reflected on the sea surface and then again detected by the satellite. The travel time of this beam is measured and using the speed of light the distance between the satellite orbit which is only influenced by the low order components of the gravitational field and the sea surface is determined up to a resolution of centimeters. However, the sea surface is not equal to the geoid and the difference of up to a few meters is due to oceanic and atmospheric processes. The effects of winds, tides, density changes due to temperature variations, and non- 9

Gravity anomalies measured from satellites stationary currents can be eliminated by appropriate long time averaging, but the steric height due to stationary geostrophic currents cannot be eliminated by time averaging. The radar altimetry satellites can obtain a significantly higher horizontal resolution than the GRACE mission due to the fact that they measure the effects of the subsurface mass distribution at the surface and not in the 500 km high satellite orbit. However, the technique of obtaining the gravitational acceleration from the geoid height is a local technique that can only resolve short wavelength components of the gravitational field. In addition, it requires the geoid height and not the height of the sea surface. This is the point where the combination with the GRACE results greatly improves the accuracy of the radar altimetry derived gravity compared to the routines used before GRACE was operational. The geoid height determined by GRACE is subtracted from the sea surface height measured by radar altimetry to obtain the anomalous sea surface height. The only oceanic or meteorologic features remaining after appropriate time averaging are the stationary geostrophic currents. Hence, they can be directly determined to be the long wavelength features in the anomalous sea surface height. After the elimination of the geostrophic currents, the short wavelength undulations of the geoid due to the subsurface mass distribution remain. This global marine data set is chopped to regional grids of roughly 2000 km by 2000 km and passed to the procedure described by Sandwell and Smith (1997). The following summary follows Sandwell and Smith (1997) Appendix A, which should also be consulted for the detailed formulas. The vertical gradient of the gravitational acceleration can be computed from a rectangular grid of geoid height using the second order partial differential equation known as Laplace s equation which relates the second partial derivative of geoid height in x-direction and the second order partial derivative of the geoid height in y-direction to the vertical gradient of the gravitational acceleration. This only yields the vertical gravity gradient, but it can be carried out right until the border of the domain. However, to obtain the gravitational acceleration directly, the existing grid of geoid height has to be Fourier transformed in 2D in order to transform Laplace s PDE to an algebraic equation relating the horizontal gradients of geoid height to the gravity anomaly. Then, an inverse Fourier transformation yields the gravity anomaly. The major disadvantage is that Fourier transforms produce edge-effects or so-called ringing at discontinuous steps in the Fourier transformed function or at the boundary of the domain. Since the sea surface is the domain of the geoid height measured by radar altimetry satellites, the edge-effects associated with the boundary of the domain occur at each coastline and greatly increase the error close to the coast. Further complications arise from the fact that the satellite tracks rarely cross perpendicularly. Sandwell and Smith (1997) describe in their Appendix B how they transform along track gradients with a very high resolution to regular rectangular grids. 10

Data 4 Data Mainly the five distinct geophysical exploration techniques of seismic reflection surveying, seismic refraction surveying, ship depth soundings, radar altimetry from satellites, and gravitational field measurement by twin satellites have been used to obtain the four distinct data sets used in this project. The individual data sets are described below. 4.1 Satellite Gravity The satellite gravity is a combination product of radar altimeter data from the TOPEX/Poseidon (1992-2002), Jason-1 (2002 till present), ERS-1 (1992-1993, 1995), ERS-2 (1996-2003), and ENVISAT (2003 till present) satellite missions and the GRACE (2002-2007) twin satellite mission. The long wavelength undulation of the geoid measured by GRACE are subtracted from the altimeter data to expose influences from oceanic currents in geostrophic balance and short wavelength undulations. The steric height due to the oceanic currents is identified as the long wavelength difference between the GRACE and the radar altimeter data. It is subtracted and then the gravitational acceleration at the sea surface is computed as described in Subsection 3.1 and in Sandwell and Smith (1997). As mentioned, this involves interpolation between satellite tracks. Version 15.2 (Sandwell and Smith, 2005) used here interpolates onto a grid that has cell dimensions of 2 min in longitude and cosine of latitude by 2 min in latitude (Mercator projection) so that cells are equidimensional but vary in size with latitude, being 3.7 km at the equator and 1.1 km at ±72 (Sandwell and Smith, 1997). To enhance the data set, values from shipboard and landbased gravity campaigns are included as boundary conditions at particular locations. The values at other locations are determined from the difference in gravitational acceleration given by the radar altimeter with respect to the boundary conditions. Gravity anomalies are usually given in milligal (mgal) where 1 mgal = 10 5 m/s 2. Figure 4.1 shows the marine gravity anomaly surrounding the region of interest as well as the three seismic refraction profiles described in Subsection 4.4. The continental slope can clearly be seen as a positive anomaly of roughly 50 mgal stretching along the coast line at a distance of roughly 200 km. The Walvis Ridge shows up very prominently extending from northern Namibia south-westwards. The ridge is characterized by a broad positive anomaly and a thinner negative anomaly south of the main positive anomaly. The contrast between the positive and the negative anomaly is very pronounced with +100 mgal to -100 mgal. Shorter wavelength positive anomalies such as the Vema seamount at 8 E 23 S can also be seen in the figure. 11

Satellite Gravity Gravity anomaly off Namibian coast 0 2 4 6 8 10 12 14 16 18 20 22 24 18 20 22 24 26 28 Landstations OBH BGR 95301 BGR 95302 Namibia Landstations 18 20 22 24 26 28 30 OBH BGR 95303 Oranje 30 32 Oranje basin 32 34 34 36 36 0 2 4 6 8 10 12 14 16 18 20 22 24 100 80 60 40 20 0 20 40 60 80 100 Gravity anomaly [mgal] Figure 4.1: Marine gravity anomaly based on Sandwell and Smith, 2005 grid in Version 15.2. The three seismic refraction profiles of 1995 are indicated as BGR 95301, BGR 95302, and BGR 95303. The red circles indicate the ocean bottom hydrophones (OBH) and the blue circles indicate the land stations. 12

Satellite Bathymetry 4.2 Satellite Bathymetry Marine surface gravity anomalies over the 15 km to 200 km wavelength band are caused primarily by topographic variations on the ocean floor (Smith and Sandwell, 1997). This band lies between the flexural wavelength of the lithosphere and 2π times the mean water depth. At greater wavelengths, isostatic compensation plays a role and at shorter wavelengths, the exponential upward continuation of the topographic signal diminishes the signal below noise level already below the sea surface. A two dimensional transfer function using the slope and amplitude of the gravity anomaly is used to compute the bathymetry for the above wavelength band. The details are described by Dixon et al. (1983). The transfer function needs the gravity to topography ratio (in mgal/meter) which is mainly a function of mean water depth reflecting the fact that topography closer to the sea surface will have a steeper gravity effect than more distant topography. The ratio has to be determined by ship echosoundings for each region of the ocean. For the final product by Smith and Sandwell (1997), thousands of ship tracks have been digitized. The Foundation Seamounts are given as an example of a remote region with rough topography. The next ship soundings were roughly 160 km away. A comparison by Smith and Sandwell (1997) showed that the marine topography from satellite altimetry was able to recover roughly 70% of the topography signal of ship soundings used as a control. In more acurately ship-surveyed regions, the data set is predicted to be able to recover significantly more than 70% of the signal. Sedimentation is an effect complicating the calculations as is tends to bury topography by filling deeper areas. In regions with significant sedimentation, the topography associated with a gravity anomaly signal would be over-estimated. Therefore Smith and Sandwell (1997) have attempted to remove sediment effects where their nature is known. The final resolution of the satellite bathymetry is identical to the 2 min resolution of the satellite gravity quoted in Subsection 4.1. Figure 4.2 shows the elevation based on ETOPO2v2 (Sloss, 2006) which uses Smith and Sandwell (1997) for the marine part of the earth s surface. Even though the resolution is quite appreciable, artifacts are also visible such as the lines of depreciated topography converging toward Cape Town. Those lines are a result of ship track coverage in the region acting as a boundary condition to the bathymetry along the ship tracks. The typical values of the water depth on the continental shelf are between 0 m and 500 m. The continental shelf south of the Walvis Ridge is roughly 200 km wide which is significantly wider than the less than 50 km that are observed north of the Walvis Ridge. The water depth in the deep ocean beyond the continental slope is shallower than 4000 m south of the Walvis Ridge while it is significantly deeper than 4000 m north of the Walvis Ridge. The fine structure of the Walvis Ridge can also be seen very well and it becomes evident that the Ridge is comprised of a wide track with significantly shallower water depths as well as individual seamounts with 13

Satellite Bathymetry Elevation of southwest Africa 0 2 4 6 8 10 12 14 16 18 20 22 24 18 18 20 Landstations 20 22 OBH 22 24 26 28 Walvis Ridge BGR 95301 BGR 95302 Namibia Landstations 24 26 28 30 OBH BGR 95303 Oranje 30 32 Oranje basin 32 34 34 36 36 0 2 4 6 8 10 12 14 16 18 20 22 24 6000 4000 2000 0 2000 4000 6000 Elevation [m] Figure 4.2: Elevation map based on the ETOPO2v2 grid (Sloss, 2006). The three seismic refraction profiles of 1995 are indicated as BGR 95301, BGR 95302, and BGR 95303. The red circles indicate the ocean bottom hydrophones (OBH) and the blue circles indicate the land stations. 14

Sediment Maps nearly circular shape. The Walvis Ridge is also not a straight line, but there seems to be a discontinuity in the direction roughly at 6 E 22 S. 4.3 Sediment Maps The sediment maps compiled and provided by Stewart et al. (2000) are based on seismic reflection surveys. On the search for hydrocarbon deposits, Exploration Consultants Ltd and Halliburton Geophysical Surveys in 1989 and 1991 commercially mapped some 14,000 km of the continental shelf and slope off the northern coast of Namibia. Hydrocarbon deposits can only form in sedimentary environments and they cannot be in igneous rocks. Hence, the commercial campaigns did not attempt to look deeper than the oldest sediment layer and the maximum depth resolved by the seismic reflection survey is 7 seconds two way travel time which corresponds to roughly 15 km depth. Stewart et al. (2000) define five mega sequences and their ages identified from interface reflections of the different sediment layers: basement (124 Ma), Aptian (100 Ma), Turonian (77 Ma), base Tertiary (33 Ma), seafloor (present). The depth of the youngest part of each layer can be seen in Figures 4.3 to 4.5. This means that the direct reflection also measures the depth of the seafloor independently from the ETOPO2 satellite bathymetry. The original surveys had a 10 to 30 km separation between the individual lines. In order to preserve the continuity at the borders of the individual data sets, the data has been filtered with a 75 km (roughly corresponding to 40 minutes) half-width Gaussian filter. The result is that small scale features might have been lost. This study only uses the bathymetry obtained from the sediment maps and does not use the ETOPO2 global grid. The reason is that there are some differences between the sediment maps and the ETOPO2 grid in the interpolation mechanisms used and the wavelengths retained. Since this study also uses the sediment maps and the resulting sediment thickness maps, using ETOPO2 for the bathymetry and the sediment maps for the deeper layers, there would be a mismatch in the wavelength bands that are present in the data. This could possibly make it impossible to model some of the features only present in the respective higher resolution data set. Since this study only aims to do large scale modeling, the short wavelength information is not of interest and may be lost by using the larger wavelength data set. The figures show generally very thick sediments on the continental shelf and slope with sediment cover of more than 2000 m at some parts. Especially the basement shows two major depressions of roughly circular shape just north of the first transect and at the very bottom of the map. These depressions have depths of the basement of roughly 8000 m while they are completely covered by sediments such that the structures are not present anymore in the seafloor map. The sediment coverage as expected is smaller in the deep sea at a distance from the coast. It accounts for sediments of 1000 m. Contrary, there is close to no sediment cover present on top of the Walvis Ridge which is probably due to the fact that it is an elevated ridge 15

Sediment Maps Depth of layer 1 (Basement) off Namibian coast Depth of layer 2 (Aptian) off Namibian coast 8 10 12 14 16 8 10 12 14 16 18 18 18 18 20 20 20 20 Landstations Landstations 22 OBH 22 22 OBH 22 BGR 95301 BGR 95301 24 24 24 24 BGR 95302 BGR 95302 26 8 10 12 14 26 16 26 8 10 12 14 26 16 0 2000 4000 6000 8000 10000 Depth of layer [m] 0 2000 4000 6000 8000 10000 Depth of layer [m] (a) Basement (b) Aptian Figure 4.3: Depth of youngest part of sediment layers Basement (124 Ma) and Aptian (100 Ma) (adapted from Stewart et al., 2000). Depth of layer 3 (Turonian) off Namibian coast Depth of layer 4 (base Tertiary) off Namibian coast 8 10 12 14 16 8 10 12 14 16 18 18 18 18 20 20 20 20 Landstations Landstations 22 OBH 22 22 OBH 22 BGR 95301 BGR 95301 24 24 24 24 BGR 95302 BGR 95302 26 8 10 12 14 26 16 26 8 10 12 14 26 16 0 2000 4000 6000 8000 10000 Depth of layer [m] 0 2000 4000 6000 8000 10000 Depth of layer [m] (a) Turonian (b) Base Tertiary Figure 4.4: Depth of youngest part of sediment layers Turonian (77 Ma) and base Tertiary (33 Ma) (adapted from Stewart et al., 2000). 16

Seismic Refraction Profiles Depth of layer 5 (seafloor) off Namibian coast 8 10 12 14 16 18 18 20 20 Landstations 22 OBH 22 BGR 95301 24 24 BGR 95302 26 8 10 12 14 26 16 0 2000 4000 6000 8000 10000 Depth of layer [m] (a) seafloor Figure 4.5: Depth of the sediment layer seafloor, i. e. water depth (adapted from Stewart et al., 2000). with respect to its surrounding. Water masses flowing over the ridge would suspend possibly present sediments on the ridge and rather deposit it north or south of the ridge depending on the prevailing current direction. 4.4 Seismic Refraction Profiles Seismic surveys facilitate the wave field of sound waves sent through the subsurface to obtain information about the subsurface. In order to be able to compute the complex 3D structure of the wave field, the approximation that the scale of the gradient of velocity changes is much smaller than the wave length used is employed to get the so-called eikonal equations. These equations allow to describe the wave field in terms of rays. Seismic refraction surveys, also called wide-angle seismics, attempt to use refraction of rays from interfaces between different sound velocities as well as refraction from velocity gradients. Wide-angle seismics is used for long distances (on the order of hundreds of kilometers) and great depths (on the order of tens of kilometers) reaching down to the crust-mantle boundary (Moho). This is one distinction from seismic reflection surveying which in general looks downwards into the sediments. In the marine environment only pressure waves (p-waves) can be excited and received. Shear waves (s-waves) only exist when they are converted from p-waves. Therefore, 17

Modeling the intensity of the s-wave ray traces is usually orders of magnitude smaller than that of p-waves and only p-waves are taken into consideration for wide-angle seismics. Analysis of seismic data yields p-wave velocity profiles of the investigated region. These profiles contain both interfaces with discontinuous steps in the velocity profile between different geological layers and a continuous increase of p-wave velocity with increasing depth due to the increased pressure leading to compaction of the geological material and higher p-wave velocities. A combined onshore-offshore multichannel and wide-angle seismic survey was carried out in December 1995 by AWI, BGR, and GFZ. Three profiles perpendicular to the continental slope were shot: BGR 95301 and BGR 95302 in the north and BGR 95303 in the south (confer Figure 4.2). These profiles specifically attempted to look deeper than the sedimentary layers by resolving the continental and oceanic crusts down to the Moho which occurs between 15 km and 40 km depth for these profiles. Seven ocean bottom hydrophones (OBH) and 25 onshore 3-component-seismometers were positioned in a line and shots were carried out by ship on a track line above the OBHs. The average ship speed was five knots and the shot interval was 60 seconds leading to a spacing between the individual shots of roughly 150 m. The standard techniques of seismic interpretation involving migration and ray inversion (e. g. Kearey et al., 2002) were used to obtain the 2D p-velocity distribution along the profiles. Profiles 95301 and 95302 were analyzed and presented as a PhD project (Bauer, 2001) while profile 95303 was analyzed and presented as a diploma project (Schinkel, 2006). Figure 4.6 shows the modeled velocity profile for transects 1 and 2. A two dimensional gravity modeling along transect 1 was also carried out and the result can be seen in Figure 4.7. The underplate has been modeled with density values between 3.0 and 3.2*10 3 kg/m 3. 5 Modeling 5.1 Modeling with the Interactive Gravity and Magnetic Application System The method employed for this project is forward three dimensional gravity modeling. The specifics of the modeling technique are presented below. For the modeling a particular 3D mass field is assumed, the resulting gravitational acceleration at the surface is calculated and compared to the measured data in order to be iteratively improved. The region of interest is represented by a rectangular 3D cuboid. If there is a direction along which the density field most likely does not change drastically, it is desirable if the y-direction of the cuboid is aligned with this direction. The x-direction would then be in the direction of most rapid change. In the case of Namibia, the y-direction would be along the coast, as the transition ocean-slope-shelf-land is to a first order 18

Modeling with the Interactive Gravity and Magnetic Application System Figure 4.6: Interpreted crustal depth sections along transects 1 (a) and 2 (b), combining P velocities, floating reflectors, and depth converted line drawings. Solid black lines represent P velocity discontinuities of first order, while dashed lines are isovelocity lines. The isovelocity lines are drawn fainter in regions where uncertainty is high due to the lack of small-offset and reversed observations onshore. COB, continent-ocean boundary; TNOB, transitional-normal oceanic crustal boundary. (Figure adapted from Bauer et al. (2000), Plate 1.) 19

Modeling with the Interactive Gravity and Magnetic Application System Figure 4.7: Density model for transect 1 with velocity corrections. M2 and M4 are magnetic anomalies used for dating. (Figure adapted from Bauer et al. (2000), Figure 14.) approximation self-similar along the coast. In order to avoid edge-effects on the boundary of the region of interest, i. e. an underestimation of the gravitational acceleration due to a mass deficit outside the region of interest, the model cuboid is extended with a constant density by at least 300 km in each horizontal direction beyond the region of interest. The density model is defined by an arbitrary, but fixed number of parallel xz-planes at different y-values. The spacing in y-direction can be arbitrary, but it should be similar and only in regions where strong changes are expected from the gravity or topography, the spacing should be chosen smaller. For the model, layers of different, but constant density are defined. Since the system for 3D modeling due to its inverse character has already a large number of degrees of freedom, too many different layers would just lead to an increase in the number of possible modeling results, but not necessarily result more closely representing reality. The modeling procedure involves manual and subjective steps. A start model based on previous information about the region is constructed. The model is then iteratively adjusted based on the information from the modeled gravitational acceleration at the surface. During each iteration step the model will be improved to increase the correspondence between the measured and modeled gravity anomalies. This model only attempts to calculate long wavelength features that are due to the large scale crustal distribution. Therefore, the spacing between parallel xz-planes is chosen accordingly to be able to resolve those features. This, however, also means that smaller scale features cannot be resolved and will lead to a discrepancy between the model and the observations on short wavelengths. In the absence of this limitation, the goal of a modeling effort should be to have a residuum distribution peaking around 0 and only a small standard deviation. However, there might be small geo- 20

Model Setup logical scale features such as an intrusion that might lead to a locally huge residuum and thereby distorting the residuum distribution. Since the model does not attempt to model such short wavelengths features, the deviation from a normally distributed residuum may be kept and specifically explained in the discussion section. An important limitation and error source of the above method, especially when bodies extending over many kilometers depth are to be modeled is that this method assumes that there are only a very small number of layers with constant density. However, lithostatic pressure from the overlying material will compact deeper material more than shallower material. The process is similar to the concept of potential temperature and density in oceanography. The result is that the same geological layer with the same potential density will have different in-situ densities depending on its depth. The effect might be significant and account for differences up to 0.2 10 3 kg/m 3. The above method working with constant densities does not take into account this effect and will significantly overestimate the mass at the top of a large body and under estimate the mass at the bottom. Therefore large and important bodies, e.g. the continental crust, are broken down into two or three different layers each with its own constant density. The Interactive Gravity and Magnetic Application System (IGMAS) is a 3D gravity and magnetic modeling program. The development mainly followed Götze and Lahmeyer (1988) and the current documentation can be found at Schmidt (2004). This project only used the gravity modeling capacities and magnetic modeling was not attempted. The Generic Mapping Tools (GMT) developed by Wessel and Smith (1991) have been used for grid calculations and data visualization. 5.2 Model Setup The model has been set-up as 17 vertical planes that can be seen as black lines in Figure 5.1. The vertical planes have been oriented east-west. Their extension is 1600 km and they go down to a depth of 40 km. The distance between parallel vertical planes is 50 km. Two additional planes are situated at model kilometer +800, and -800 respectively. With this an area of 1600 km by 1600 km is defined. Out of this area, only an area of 800 km by 800 km actually comprises the region of interest. The additional 400 km in each direction beyond the region of interest allow the model to continue smooth in all direction and not to introduce artificial edge-effects in the modeled gravity anomalies. The rectangular Lambert projection used is centered at 11.5 east 21 south. This defines a plane at model kilometer 0 and 21 south. Respectively, 8 planes are at positive model kilometers and 8 at negative negative model kilometers. Beyond the 1600 km by 1600 km by 40 km model block, a reference density is set such that a gravity anomaly can be calculated with respect to the reference. The reference has been chosen to be 2.90*10 3 kg/m 3. This value reproduces the level of 21

Model Setup Figure 5.1: Setup of model with the 17 east-west oriented vertical planes. The black parallel lines are the individual east-west oriented vertical planes starting from model kilometer -400 and ending with model kilometer +400. The inclined black lines in the south east show the position of the two seismic refraction profiles. The black dots indicate points at which IGMAS interpolated the gravity anomalies of the model. Since the IGMAS only calculates gravity anomalies at positions where measurements are available, the black dots coincide in position with the filled color contours that show the measured marine gravity anomaly in mgal. White dots are positions where the gravity anomaly is more than 65 mgal or less than -65 mgal. 22

Choice of densities the average gravity anomaly that has been measured in the model region. It also reflects the average of a generic heavy oceanic crust profile of 40 km and a generic light continental crust profile of 40 km. The profiles were considered as 4 km water, 2 km sediment, 8 km oceanic crust, and 26 km mantle, respectively 2 km sediment, 10 km upper continental crust, 20 km lower continental crust, and 8 km mantle. The model was initialized with an identical assumed profile for all planes of the layers shown in Table 5.1. In addition two spare layers were introduced each with the same density of the mantle and a thickness of 1 m in case additional layers might be needed later. Then the bathymetry and sediment maps were digitized in the model to obtain the position of the respective interfaces. 5.3 Choice of densities The model has been adapted to fit the seismic refraction profiles in the southern part of the region of interest. This means that the confidence with which the model reflects the structure of the southern part is rather high. In order to get an idea of the parameter dependence of the model on different densities, it has been attempted to model the same seismic refraction profile structures with slightly increased or decreased densities. The model response showed that density changes up to ±0.05*10 3 kg/m 3 can also represent the observed structure. However, the model misfit increases compared to the densities that were chosen in the end. After the parameter dependence checks, the densities shown in Table 5.1 were chosen to be used for all subsequent modeling steps. Table 5.1: Geological layers used in the model with their densities. The uncertainty of the densities is ±0.05*10 3 kg/m 3. Geological layer Density in 10 3 kg/m 3 Water 1.00 Postrift sediment 2.30 Synrift sediment 2.60 Upper continental crust 2.65 Lower continental crust 2.75 Oceanic crust 2.85 Underplate 3.10 Mantle 3.30 For the purpose of gravity modeling, these p-wave velocity profiles have to be converted into density profiles. There is no direct one-to-one conversion as different minerals may lead to different densities at the same p-wave velocity. Nafe and Drake (1957) have empirically determined a relationship for sedimentary rocks while Christensen and Mooney (1995) have determined a relationship for igneous and metamorphic rocks. These relationships are empirical, but they have been tested thoroughly 23

Choice of densities since their introduction and they are widely accepted. For the purpose of this work, the curve shown in Figure 5.2 based on Funck et al. (2003) is used. A generic density value for the semi-light mantle was taken from Fowler (2005) to be 3.30*10 3 kg/m 3. The oceanic crust density increases with age of the crust. As the oceanic crust present in the region of interest is more than 100 Myrs old, a value of roughly 2.85*10 3 kg/m 3 is chosen as an initial guess which is rather at the lower end of the range given in Fowler (2005). 3.5 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 3.5 3.0 3.0 3 3 Density in 10 kg/m 2.5 2.0 2.5 2.0 1.5 1.0 ND57 ND57 min/max CM95 0 15 km CM95 15 25 km CM95 25 35 km CM95 35 45 km CM95 45 50 km Funck 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 Velocity in km/s 1.5 1.0 Figure 5.2: Relation between p-wave velocity and density of several rocks. ND57 is the range given by Nafe and Drake (1957) for sedimentary rocks. CM95 shows the values obtained by Christensen and Mooney (1995) for igneous rocks in several different depth bands. Funck is the generic formula for the relation obtained by Funck et al. (2003). In addition, the specific gravity model type used in this study only works with bodies of constant density and it cannot handle the continuous density profile that would be the outcome of a direct conversion of the velocity profile using the curve in Figure 24

Results 5.2. Therefore, the average density in between layer boundaries defined by refracted seismic rays is taken as a first guess for the density of the layer. 6 Results 6.1 Structure of Southern Part Figure 6.1: Modeled plane at model kilometer -300 in lower panel and gravity anomalies along the plane in upper panel. Densities of the bodies are shown at the right. The refraction seismic profiles 95301 and 95302 cross the plane at model kilometer +60 and +200, respectively. The different layers are labeled. VS = Vema seamount, COB = Continent-ocean boundary. Figure 6.1 shows the modeled plane at model kilometer -300 and the gravity anomalies along the plane. It represents a generic plane of the southern part. The seismic refraction profiles cross the plane at model kilometer +60 and +200 respectively. In this region the underplate could be established with its density. The thickness of the oceanic plate and the Vema seamount at model kilometer -400 can also be seen. The upper panel shows the agreement between measured (solid line) and modeled 3D (dotted line) gravity anomaly and it can be observed that the correlation is very well on long wavelengths and fair on short wavelengths. The dashed line shows the 2D gravity anomaly computed along the plane. It is not a goal to have the 2D modeled gravity anomaly agree with the 3D measured gravity anomaly. The model of the southern part shows that there is an underplate along the continentocean boundary (COB). The underplate reaches a maximum thickness of 10 km and is seen over an along shelf distance of 300 km. Two parts of the southern basin can be observed. The bathymetry is shallower in the part that is closer to the Walvis 25