A sample of approximately 100 predominantly metal-weak giants, identified in a high-latitude field towards the galactic center using an automated objective-prism survey technique, is presented. Abundances and radial velocities have been measured for these giants, whose distances from the Sun range from 1 to 18 kpc. While the extremely metal-weak stars in the field have halo kinematics, the majority of the stars with intermediate abundance ([Fe/H] between - 1.0 and - 1.6) have thick disk kinematics, despite the fact that their average distance from the galactic plane is 3 kpc. The most satisfactory explanation for this effect is that the inner halo is moderately flattened, and the metal-weak stars of the thick disk have a scale height of approximately 2 kpc. Because this field is not in the solar neighborhood, it is difficult to make direct comparisons with the more common metal-strong thick disk stars. However, if the scale height of the thick disk remains constant for Galactocentric distances of 4-8 kpc, it follows that the thick disk has a vertical abundance gradient. This suggests that the thick disk may have formed in a dissipational collapse, rather than in a separate event such as the accretion of a small satellite galaxy.