"We remain committed to locating Shirley, and are supportive of anything that will help us do that.
"We're also extremely grateful for the support shown by the community in the search for Shirley."
They said police will not hesitate to initiate further physical searches as new information comes to hand.
Granddaughter Aleisha Hofman says her family does suspect something "not nice" has happened to her.
"You go through all these different scenarios. We talk about it a lot but she had her wits about her, if she was lost she would've followed the light, she would've knocked on somebody's door.
"We're lost, we don't know, it's been a month and we thought we would've found her in the first week," she said.
Hofman said it has been a very hard experience for her and the family.
"It's still quite a surreal thing to be going through. Quite odd really, you kind of need to carry on with things in your life. for me, I've got a daughter and you've got work and things but at the same time, you feel like you shouldn't be because nothing's been resolved with nana, she's still out there missing."
The Herald previously reported was nothing strange about Shirley and Wally Warrington's decision to go for a drive on July 10.
They left their Burwood home and at 7.30pm, the Warringtons were stopped at Rolleston by police, driving slowly on State Highway 1 towards Christchurch with their headlights on full beam, and well under the speed limit.
They were doing nothing wrong, but the police would have been remiss not to pull them over in the circumstances.
After a quick chat, the Warringtons were back on the road.
At 8.34pm their car was captured on CCTV camera on Ferry Rd - Wally driving and Shirley in the front passenger seat.
At 10.19pm another camera picked the car up near the Ferrymead Bridge.
More than 40 people and dogs - police dogs, search dogs and some that have worked both disciplines - combed Ferrymead, the surrounding areas, bush tracks and waterways for her.
Police Search and Rescue teams are hunting the area around Ferrymead Park for missing Christchurch woman Shirley Warrington. Photo / George Heard
Detective Senior Sergeant Damon Wells wants to be clear - very - about one thing.
"There is absolutely no indication Wally's involved in doing something sinister," he stated.
"Quite the opposite, in fact - he was a doting husband.
"Shirley has wanted to go for a walk and while he's been waiting for her to get back he's fallen asleep.
"When he woke up she wasn't back… he's guilt-stricken."
