gdalbuildvrt -a_srs epsg:3857 ortho_3857.vrt ortho-*.tif

Driver: VRT/Virtual Raster
Files: ortho_3857.vrt
       /Users/jeremyeastwood/Desktop/debug/ortho-0-0.tif
       /Users/jeremyeastwood/Desktop/debug/ortho-0-1.tif
       /Users/jeremyeastwood/Desktop/debug/ortho-1-0.tif
       /Users/jeremyeastwood/Desktop/debug/ortho-1-1.tif
Size is 9191, 7284
Coordinate System is:
PROJCS["WGS 84 / Pseudo-Mercator",
    GEOGCS["WGS 84",
        DATUM["WGS_1984",
            SPHEROID["WGS 84",6378137,298.257223563,
                AUTHORITY["EPSG","7030"]],
            AUTHORITY["EPSG","6326"]],
        PRIMEM["Greenwich",0,
            AUTHORITY["EPSG","8901"]],
        UNIT["degree",0.0174532925199433,
            AUTHORITY["EPSG","9122"]],
        AUTHORITY["EPSG","4326"]],
    PROJECTION["Mercator_1SP"],
    PARAMETER["central_meridian",0],
    PARAMETER["scale_factor",1],
    PARAMETER["false_easting",0],
    PARAMETER["false_northing",0],
    UNIT["metre",1,
        AUTHORITY["EPSG","9001"]],
    AXIS["X",EAST],
    AXIS["Y",NORTH],
    EXTENSION["PROJ4","+proj=merc +a=6378137 +b=6378137 +lat_ts=0.0 +lon_0=0.0 +x_0=0.0 +y_0=0 +k=1.0 +units=m +nadgrids=@null +wktext  +no_defs"],
    AUTHORITY["EPSG","3857"]]
Origin = (-122.318962274868440,37.873466153295041)
Pixel Size = (0.000000446142119,-0.000000446142119)
Corner Coordinates:
Upper Left  (-122.3189623,  37.8734662) (  0d 0' 3.96"W,  0d 0' 1.22"N)
Lower Left  (-122.3189623,  37.8702165) (  0d 0' 3.96"W,  0d 0' 1.22"N)
Upper Right (-122.3148618,  37.8734662) (  0d 0' 3.96"W,  0d 0' 1.22"N)
Lower Right (-122.3148618,  37.8702165) (  0d 0' 3.96"W,  0d 0' 1.22"N)
Center      (-122.3169120,  37.8718413) (  0d 0' 3.96"W,  0d 0' 1.22"N)
Band 1 Block=128x128 Type=Byte, ColorInterp=Red
  NoData Value=0
Band 2 Block=128x128 Type=Byte, ColorInterp=Green
  NoData Value=0
Band 3 Block=128x128 Type=Byte, ColorInterp=Blue
  NoData Value=0
Band 4 Block=128x128 Type=Byte, ColorInterp=Alpha
  NoData Value=0