Record overlay

Overlay is one of the most common and powerful GIS functions.  It investigates the spatial association of features by “vertically stacking” feature layers to investigate geographic patterns and determine locations that meet specific criteria.
Overlay operations belong to the most frequently used functions in a GIS application. They allow to combine two different layers and apply the set theoretic operations of intersection, union, difference, and complement.
It is the best-known GIS function. Vector and raster models both perform overlay, but their overlay functions differ considerably.

Vector (Logical) Overlay
Vector overlay predominantly overlays polygons in one layer over polygons in another layer, but it can also be used to overlay point or line features over polygon layers.  Sometimes referred to as topological or logical overlay, it is conceptually and mathematically more demanding than raster overlay.  There are three types of vector overlay operations:
Line on polygon is similar to point in polygon, but lines are superimposed on polygons.  This type of spatial join either appends polygon attributes to line features falling within them or counts and aggregates line attribute data to the polygon layer’s data file.

1. Polygon on polygon is where one polygon layer is superimposed over another polygon layer to create a new output polygon layer.  The resultant polygons may contain some or all of the attributes from the polygons in which they were created.  Several types of polygon on polygon overlay exist, including intersection (A and B), union (A or B), and clip (A not B).  These Boolean operators work both on the attribute table and the geography. 
1. Intersection computes the geometric intersection of all of the polygons in the input layers. Only those features that share a common geography are preserved in the output layer.  Any polygon or portion of a polygon that falls outside of the common area is discarded from the output layer.  The new polygon layer can possess the attribute data of the features in the input layers.
2. Union combines the features of input polygon layers.  All polygons from the input layers are included in the output polygon layer.  It can also possess the combined attribute data of the input polygon layers.
3. Clip removes those features (or portions of features) from an input polygon layer that overlay with features from a clip polygon layer.  The clip layer acts as a cookie cutter to remove features (and portions of features) that fall inside the clip layer. 
2. Point in polygon is where a layer of point features is superimposed over a layer of polygon features.  The two layers produce a point layer that includes attributes from the surrounding input layer polygons. Alternatively, the number of point features falling within each polygon are counted and stored as a new attribute in the polygon layer.  Other point attributes can be aggregated (summed, averaged, etc.) and included as attributes in the polygon’s data file.  The transferring of attributes based on their geographic position is called a spatial join.
3. Line on polygon is similar to point in polygon, but lines are superimposed on polygons.  This type of spatial join either appends polygon attributes to line features falling within them or counts and aggregates line attribute data to the polygon layer’s data file.

Raster (Arithmetic) Overlay

Raster overlay superimposes at least two input raster layers to produce an output layer.  Each cell in the output layer is calculated from the corresponding pixels in the input layers.  To do this, the layers must line up perfectly; they must have the same pixel resolution and spatial extent.  If they do not align, they can be adjusted to fit by the pre-processing functions. After preprocessing, raster overlay is flexible, efficient, quick, and offers more overlay possibilities than vector overlay. 

Raster overlay, frequently called map algebra, is based on calculations which include arithmetic expressions and set and Boolean algebraic operators to process the input layers to create an output layer.  The most common operators are addition, subtraction, multiplication, and division, but other popular operators include maximum, minimum, average, AND, OR, and NOT.  Raster overlay simply uses arithemetic operators to compute the corresponding cells of two or more input layers together, uses Boolean algebra like AND or OR to find the pixels that fit a particular query statement, or executes statistical tests like correlation and regression on the input layers