After a system restoration Acronis makes new backup replacing existing one.

Vladimir Sokolov,
In my experience, the best solution after a restore is to stop using the old task and start a new task. It is the cleanest and most predictable solution. This prevents the old backups from being contaminated with newer backups. The best choice by far is to start over with new backus pointing to a new storage folder.

However, if you wish the backups to continue correctly, what worked for me the once I tried it was after the restore to immediately move the backup used for the restore and all newer backups to a different folder so the only backup that the program would see is those which existed at snapshot time . So if you used the Wednesday backup to do the restore, then move Wedsday and any newer diff to a different folder.

The reason being is that after the restore, TrueImage does not know about the backups which were created after Tuesday as the Wednesday backup was a snapshot of the system prior to the Wednesday backup. Essentially, the restore of the Wednesday backup put the system back to what at snapshot time.

No guarantees but it is something you can try or test.

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Added:

GroverH wrote:

However, if you wish the backups to continue correctly, what worked for me the once I tried it was after the restore to immediately move the backup used for the restore and all newer backups to a different folder so the only backup that the program would see is those which existed at snapshot time . So if you used the Wednesday backup to do the restore, then move Wedsday and any newer diff to a different folder.

Another option would be to make a copy of the backup folder used for the restore and copy to another location. Then you could delete the Wednesday and newer backups so all that remained in the old backup folder was the Full plus any diff up and including Tuesday but not Wednesday or newer. By doing this, you have preserved your old copy for possible later use.

GroverH,
thank you very much for prompt reply!

Note I added some edits to the prior postings.

GroverH,
Thanks again!

Vladimir,

How did you specific that the full backups should be done on Mondays, and the differential backups should be done the other days? Are you using 2 different tasks? Are they backing up in the same directory the same content? That is going to lead to problems...

Pat L,
I simply create and run this task first time on Sunday. The rest is provided by default by the "Version chain" backup scheme. On first Sunday it makes first full backup that will never be deleted, on Monday it makes Full backup, on Tuesday to Sunday it makes differential backups, on Monday it makes Full backup, on Tuesday to Sunday it makes differential backups, and the weekly cycle goes on.
I did use 2 different tasks backing up in the same directory the same content when I used Acronis True Image Home 11 (perhaps, I simply didn't know about its advanced features). The situation was quite the same, moreover I didn't know how to keep backups older than one week (the full backup was weekly overwritten on Mondays) and risked having the full backup overwritten by defective one; this taught me to keep backups stored on different media. After Acronis version Upgrade these risks are gone, I use one "Version chain" task. Now I decided to add date and time to the filename, and change the scheduling type from "Daily on 3 am" with Missed Backups: run at system Startup to "Upon event - system startup" with Once a day only checkbox checked. I wonder what the result will be. The folder is still the same for all backups.

Some general comments.

Acronis permits editing of tasks and permits backups from seveal tasks to be stored in one folder and yet both of those practices which I recommend to the users that they DO NOT do.

The mixing of backups is confusing both to the user and can be confusing to the program especially when the user often created additional backup tasks of the same name, etc. The rule I practice and recommend is that each task has its own folder or sub-folder or no mixing of backup files inside one folder and makes a review of the folder much easier.

Editing a task most often produces unexpected results or no results or confusion. The program will try to make changes based on the edit but the changes it can make are dependent upon the computers exact settings at the time. Often the user wants to make changes to reduce the number of backups to avoid a disk full error. Most often, the progrem will simply restart at that point and add more backkups onto the existing one to create the edit request set of desired. Nowhere is there any guidance from the program on what can be expected to occur.

The rule I practice and recommend to others is that if a task needs editing, do not do it (schedule changes excepted which can be done from the main GUI).If changes needed, stop using the old task and recreate a new task pointing to a new empty sub-folder.

For my own use, I also avoid using all of the default backup schemes.
I find better results and more predictable results by creating a custom backup scheme and most often it is the Custom/Differential scheme. Before I leave the scheme settings, I save the Custom scheme with a name for possible reuse latter.

In all my tasks, I prefer to use the Custom backup scheme with automatic cleanup enabled. Using automatic cleanup enables me to control both how many backups I wish to retain before the automatic cleanup begins deleting files on a revolving escalator basis.

Likewise, I avoid all consolidation settings. Again, this is a setting offered by the program but it is a setting which I refuse to use. The merging of data into another backup has the possibility of contamining of the orignal backup plus it is lengthy in time and the program sometimes goes looking for the merged files so I won't use consolidation. Automatic cleanup is a neat way of maintaining the desired numher of backups.

Look at this nex example of a custom/differential scheme in practice.
I elected to keep the original full and then additionally keep 4 more most recent chains. I have my backups numbered by the program for easy tracking.
The initial and ongoing deletion did not occur until after the number retain exceeds the retain requirement. This picture was taken immediately following the last full at which time the oldest chin of 7 files was deleted.

http://forum.acronis.com/system/files/forum/2009/11/5940/example-folder…

I would encourage you to set up an automatic cleanup backup scheme.
The link below is an extract from my signature link #2 guide below.

Figure 11-Dif: -Example of custom/differential backup method settings

If using differential type backups (which is full + X Diff), the 11-Diff illustration is my recommended method. Change the 6 or 4 to fit your available storage.
These automatic cleanup settings will provide for automatic deletion of the oldest backups after the "Store no more than X number of chains" quota has been reached.
In this example, deletion of oldest backup chain will occur immediately following creation of backup #29.

Allow space for 1 more full backup in addition to "Store no more than X number of chains" as the program will NOT delete the oldest full until its replacement has been successfully created.

In this example, one chain or one recent version chain =1 full plus 6 diff or 7 files per chain.
If keeping 4 recent version chains (4 chains of 7 each) retention would be 28 files. Deletion begins after backup 29.

When restoring, a single diff file is selected and that specific diff plus its full backup base will be restored (2 files restored).

GroverH,
Thank you again for detailed explanation!