def remove_repeat_coordinates(x, y, z):
    r"""Remove all x, y, and z where (x,y) is repeated and keep the first occurrence only.

    Will not destroy original values.

    Parameters
    ----------
    x: array_like
        x coordinate
    y: array_like
        y coordinate
    z: array_like
        observation value

    Returns
    -------
    x, y, z
        List of coordinate observation pairs without
        repeated coordinates.

    """
    coords = []
    variable = []

    for (x_, y_, t_) in zip(x, y, z):
        if (x_, y_) not in coords:
            coords.append((x_, y_))
            variable.append(t_)

    coords = np.array(coords)

    x_ = coords[:, 0]
    y_ = coords[:, 1]

    z_ = np.array(variable)

    return x_, y_, z_