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Note 2 - Revenue Recognition (Details Textual) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Mar. 31, 2025	Mar. 31, 2024	Mar. 31, 2025	Mar. 31, 2024	Oct. 01, 2024	Sep. 30, 2024	Oct. 01, 2023
Write-off of Rent Receivable	$ 2,200
Operating Lease, Lease Income (Reversal)	(700)
Contract with Customer, Liability, Current	0		$ 0			$ 0
Capitalized Contract Cost, Net, Current	200		200			$ 0
Contract with Customer, Liability, Revenue Recognized, Including Balance	0		0
Contract with Customer, Liability, Cost of Revenue Recognized	0	$ 0	0	$ 0
Contract with Customer, Liability, Revenue Recognized		1,000		1,000
Contract with Customer, Receivable, after Allowance for Credit Loss	13,200	12,500	13,200	12,500	$ 12,600		$ 11,100
Transferred over Time [Member]
Contract with Customer, Liability, Revenue Recognized	$ 0	$ 1,000	$ 0	$ 1,000

X

- Definition

Amount of cost of revenue recognized that was previously included in balance of obligation to transfer good or service to customer for which consideration from customer has been received or is due.

+ References

No definition available.

+ Details

Name:	geos_ContractWithCustomerLiabilityCostOfRevenueRecognized
Namespace Prefix:	geos_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

X

- Definition

Amount of revenue recognized that was previously included in balance of obligation to transfer good or service to customer for which consideration from customer has been received or is due.

+ References

No definition available.

+ Details

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Namespace Prefix:	geos_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

X

- Definition

Amount of operating lease income (reversal) from lease payments and variable lease payments paid and payable to lessor. Includes, but is not limited to, variable lease payments not included in measurement of lease receivable.

+ References

No definition available.

+ Details

Name:	geos_OperatingLeaseLeaseIncomeReversal
Namespace Prefix:	geos_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

X

- Definition

Amount of write-off of rent receivable.

+ References

No definition available.

+ Details

Name:	geos_WriteoffOfRentReceivable
Namespace Prefix:	geos_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	duration

X

- Definition

Amount, after accumulated amortization and accumulated impairment loss, of asset recognized from cost incurred to obtain or fulfill contract with customer; classified as current.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 340
-SubTopic 40
-Name Accounting Standards Codification
-Section 50
-Paragraph 3
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479483/340-40-50-3

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

X

- Definition

Amount of obligation to transfer good or service to customer for which consideration has been received or is receivable, classified as current.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 11
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479806/606-10-50-11

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479837/606-10-45-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479806/606-10-50-8

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 2
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479837/606-10-45-2

+ Details

Name:	us-gaap_ContractWithCustomerLiabilityCurrent
Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	instant

X

- Definition

Amount of revenue recognized that was previously included in balance of obligation to transfer good or service to customer for which consideration from customer has been received or is due.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479806/606-10-50-8

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	credit
Period Type:	duration

X

- Definition

Amount, after allowance for credit loss, of right to consideration in exchange for good or service transferred to customer when right to consideration is unconditional.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 11
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479806/606-10-50-11

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Topic 954
-SubTopic 310
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479196/954-310-45-1

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 4
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479837/606-10-45-4

Reference 4: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 45
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479837/606-10-45-1

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Topic 606
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 8
-Subparagraph (a)
-Publisher FASB
-URI https://asc.fasb.org/1943274/2147479806/606-10-50-8

+ Details

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Namespace Prefix:	us-gaap_
Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

X

- Details

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Namespace Prefix:
Data Type:	na
Balance Type:
Period Type: