In the terminology of the geometry
package, the paper<*>
parameters refer to the physical size of the sheets of paper the document will be printed on. The layout<*>
parameters, by contrast, refer to the logical size of the "paper", which will (one hopes) be no larger than the physical size of the sheet of paper. (Put differently, with regard to paper
and layout
, your terminology and that of the geometry
package are exactly reversed...)
You will need to use the parameters layoutvoffset
and layouthoffset
to indicate where on the physical page the logical page is supposed to be placed. Assuming that the logical page should be centered on the physical page, and given that the differences between the physical and logical dimensions are 100mm and 80mm, respectively, the values of layoutvoffset
and layouthoffset
should be 50mm and 40mm.
By the way, if the logical page is supposed to be exactly centered on the physical page, you needn't load the crop
package; specifying the option showcrop=true
(as you already do) suffices.
Addendum, to address the follow-up request to make the text block margins be zero: To make the text block occupy the entire logical layout, while still showing the header and footer lines, you need to specify the options margin=0pt
and includeheadfoot
when loading the geometry package.

\documentclass{book}
\usepackage{lipsum}
\usepackage[ paperheight =297mm,paperwidth =210mm, % or: "paper=a4paper"
layoutheight =197mm,layoutwidth =130mm,
layoutvoffset= 50mm,layouthoffset= 40mm,
margin=0pt, includeheadfoot,
showframe=true, showcrop=true]{geometry}
%% \usepackage[a4,center]{crop} %% not needed if logical page is centered on physical page
\begin{document}
\chapter{In the Beginning}
\lipsum
\end{document}
layoutvoffset
andlayouthoffset
.