We have extended our earlier derivative analysis method to higher derivatives to estimate the depth and shape (shape factor) of a buried structure from selfpotential (SP) data. We show that numerical second, third, and fourth horizontal-derivative anomalies obtained from SP data using filters of successive window lengths can be used to simultaneously determine the depth and the shape of a buried structure. The depths and shapes obtained from the higher derivatives anomaly values can be used to determine simultaneously the actual depth and shape of the buried structure and the optimum order of the regional SP anomaly along the profile. The method is semi-automatic and it can be applied to residuals as well as to observed SP data.We have also developed a method (based on a leastsquares minimization approach) to determine, successively, the depth and the shape of a buried structure from the residual SP anomaly profile. By defining the zero anomaly distance and the anomaly value at the origin, the problem of depth determination has been transformed into the problem of finding a solution of a nonlinear equation of form f (z) = 0. Knowing the depth and applying the least-squares method, the shape factor is determined using a simple linear equation.Finally, we apply these methods to theoretical data with and without random noise and on a known field example from Germany. In all cases, the depth and shape solutions obtained are in good agreement with the actual ones.

Saqqara is one of the most important archaeological sites in Egypt. The monuments in this area are suffering from the effects of urbanization and temporal and spatial variations in the groundwater level. In an attempt to understand better the problems associated with the groundwater, a geoelectrical DC resistivity survey, comprising 47 vertical electrical soundings using a Schlumberger array, has been conducted. These data have been inverted using a 3D code based on a smoothness‐constrained least‐squares method. To determine the reliability of the inversion results, a range of tests has been performed. The final 3D resistivity model obtained for the study area provides useful new subsurface geological and hydrogeological information. The new model allows a more integrated image and interpretation of the complex hydrogeological conditions. It also depicts the mutual relationship between the two water‐bearing units in the area that was not clear in the previous 1D and 2D interpretations.

Mastabas were large rectangular structures built for the funerals and burials of the earliest Pharaohs.One such mastaba was the basic building block that led to the first known stone pyramid, the >4600-yearoldStep Pyramidwithinthe Saqqaranecropolisof Egypt.Wehavetestedanumberofshallowgeophysical techniques for investigating in a non-invasive manner the subsurface beneath a large Early Dynastic mastabalocated closeto the Step Pyramid.Afterdiscoveringthat near-surface sedimentary rocks with unusually high electrical conductivities precluded the use of the ground-penetrating radar method, a very high-resolution seismic data set was collected along a profile that extended the 42.5 m length of the mastaba. A sledgehammer source was used every 0.2 m and the data were recordedusinga 48-channelarrayofsinglegeophonesspacedat 0.2 mintervals.Inversionsofthe directand refracted-wave travel times provided P-wave velocity tomograms of the shallow subsurface, whereas relatively standard processing techniques yielded a high-fold (50^80) ultrashallow seismic reflection section. The tomographic and reflection images were jointly interpreted in terms of loose sand and friable limestone layers with low P-wave velocities of150^650 m s À1 overlying consolidated limestoneandshalewithvelocities >1500 m s À1.The sharp contact betweenthelow-andhigh-velocity regimes was approximately horizontal at a depth of ca. 2 m. This contact was the source of a strong seismic reflection. Above this contact, the velocity tomogram revealed moderately high velocities at the surface location of a friable limestone outcrop and two low-velocity blocks that probably outlined sand-filled shafts.Below the contact, threeregularly spacedlow velocity blocksprobably represented tunnels and/or subsurface chambers

Numerical horizontal self-potential gradients obtained from self-potential data using filters of successive window lengths can be used to determine the depth and width of a 2-D plate. For a fixed window length the depth is determined iteratively using a simple formula for each half width value. The computed depths are plotted against the half width values representing a continuous window curve. The solution for the depth and the half width of the buried structure is read at the common intersection of the window curves. The method is applied to synthetic data with and without random errors.

The interpretation of actual geophysical field data still has a problem for obtaining a unique solution. In order to investigate the groundwater potentials in Saqqara archaeological area, vertical electrical soundings with Schlumberger array have been carried out. In the interpretation of VES data, 1D resistivity inversion has been performed based on a horizontally layered earth model by El-Qady (1995). However, some results of 1D inversion are not fully satisfied for actual 3D structures such as archaeological tombs. Therefore, we have carried out 2D inversion based on ABIC least squares method for Schlumberger VES data obtained in Saqqara area. Although the results of 2D cross sections were correlated with the previous interpretation, the 2D inversion still shows a rough spatial resistivity distribution, which is the abrupt change in resistivity between two neighboring blocks of the computed region. It is concluded that 3D interpretation is recommended for visualizing ground water distribution with depth in the Saqqara area.