Customize Site Header in Genesis

Remove the Site Title

//* Remove the site title
remove_action( 'genesis_site_title', 'genesis_seo_site_title' );

Remove the Site Description

//* Remove the site description
remove_action( 'genesis_site_description', 'genesis_seo_site_description' );

Remove the Header Widget Area

//* Remove the header right widget area
unregister_sidebar( 'header-right' );

Modify the Header URL

//* Modify the header URL
add_filter( 'genesis_seo_title', 'child_header_title', 10, 3 );
function child_header_title( $title, $inside, $wrap ) {
    $inside = sprintf( '<a href="http://example.com/" title="%s">%s</a>', esc_attr( get_bloginfo( 'name' ) ), get_bloginfo( 'name' ) );
    return sprintf( '<%1$s class="site-title">%2$s</%1$s>', $wrap, $inside );
}