For the most part, an earthquake will be most intense at the epicenter, but the is not always the case.
The intensity of an earthquake is defined as the amount of damage that is caused by the quake. This is different from the magnitude, which is simply how strong the quake was.
The intensity of an earthquake can be affected by things other than the distance from the epicenter. One major factor is the local geology of the area of the quake. For example, earthquake intensity is greatest in areas where the soil can liquify easily. When soil liquifies, it shakes more than other soils do and the impact on buildings is much greater.
The greatest intensity of an earthquake as measured on Richter scale is at the epicenter of the earthquake. The reason for this are very simple. The earthquake is due to the disturbances in the upper crust of the earth that take place at the epicenter. These disturbances release energy which spread out i all direction around the epicenter in form of shock waves. The intensity of these shock waves reduces as they move away from the epicenter of the earthquake for two reasons. As the the shock waves move away from epicenter, they cover an enlarging circle of area, with the result that the same energy is distributed over a larger area, resulting in lower energy per unit area. Second, as the shock wave progresses, part of the energy is absorbed by the land covered by them. Incidentally if the earthquake intensity did not reduce in this way as it spreads from the epicenter, every earthquake would spread to the entire earth and have the same high intensity everywhere.
The damage caused by earth quake is definitely dependent to a great extent on the intensity of the earthquake, but it is not equivalent to it. For example, landslides take place only in hilly area, is very much related to the type of rocks or soils. Similarly tsunami can cause damage only in coastal area. Also damages in terms of human life can take place only in populated area. Thus it is not correct to equate intensity of earthquake to its intensity
An earthquake is the result of a sudden release of energy in the earth' crust that creates seismic waves. Earthquakes are recorded with as seismometer, also known as a seismograph. The term epicenter refers to the point at ground level directly above the hypocenter or focus, the point where an earthquake or underground explosion originates. In the case of earthquakes, the epicenter is directly above the point where the fault begins to rupture, and in most cases, it is the area of greatest damage. However, in larger events, the length of the fault rupture is much longer, and damage can be spread across the rupture zone.
During an earthquake seismic waves propagate spherically out from the hypocenter. Seismic shadowing occurs on the opposite side of the Earth from the earthquake epicenter because the liquid outer core refracts the longitudinal or compressional (P-waves) while it absorbs the transverse or shear waves. At the Earth's surface, earthquakes manifest themselves by shaking and sometimes displacing the ground. When a large earthquake epicenter is located offshore, the seabed sometimes suffers sufficient displacement to cause a tsunami. The shaking in earthquakes can also trigger landslides and occasionally volcanic activity.