Multifractal properties of the epicenter and hypocenter distribution and also of the energy distribution of earthquakes are studied for California, Japan, and Greece. The calculated D q −q curves (the generalized dimension) indicate that the earthquake process is multifractal or heterogeneous in the fractal dimension. Japanese earthquakes are the most heterogeneous and Californian earthquakes are the least. Since the earthquake process is multifractal, a single value of the so-called fractal dimension is not sufficient to characterize the earthquake process. Studies of multifractal models of earthquakes are recommended. Temporal changes of the D q −q curve are also obtained for Californian and Japanese earthquakes. The D q −q curve shows two distinctly different types in each region; the gentle type and the steep type. The steep type corresponds to a strongly heterogeneous multifractal, which appears during seismically active periods when large earthquakes occur. D q for small q or negative q is considerably more sensitive to the change in fractal structure of earthquakes than D q for q ≥ 2. We recommend use of D q at small q to detect the seismicity change in a local area.