<PAGE>   1
                                                                      EXHIBIT 10



                       FIRST AMENDMENT TO LOAN AGREEMENT

       This First Amendment to Loan Agreement (the "First Amendment"), dated as
of April 15, 1997, is made and entered into by and between Dawson Geophysical
Company, a Texas corporation (the "Borrower"), and Norwest Bank Texas, N.A., a
national banking association (the "Lender").

                             W I T N E S S E T H :

       WHEREAS, the Borrower and the Lender entered into that certain Loan
Agreement, dated as of April 1, 1996 (as amended, renewed and extended by this
First Amendment, the "Agreement");

       WHEREAS, pursuant to the terms of the Agreement, the Borrower executed,
issued and delivered to the Lender (i) that certain Revolving Line of Credit
Promissory Note, dated April 1, 1996, in the original principal amount of
$5,000,000 and (ii) that certain Term Promissory Note, dated April 1, 1996, in
the original principal amount of $6,000,000;

       WHEREAS, the Borrower has requested that the Lender (i) renew, extend
and increase the principal amount of the indebtedness evidenced by the
Revolving Line of Credit Promissory Note dated April 1, 1996, (ii) make
available to the Borrower an additional six-year term loan facility in the
principal amount of $5,000,000 and (iii) amend certain provisions of the
Agreement;

       WHEREAS, the Lender is willing to amend the Agreement and provide the
additional financing requested by the Borrower, but only upon and subject to
the terms of the Agreement as provided therein and in this First Amendment;

       NOW, THEREFORE, in consideration of the foregoing and the mutual
covenants and agreements herein contained, and intending to be legally bound
hereby, the parties hereto hereby agree as follows:

SECTION 1. DEFINED TERMS.

       All terms defined in the Agreement, and not otherwise defined in this
First Amendment, shall have the meanings given them in the Agreement when used
herein.

<PAGE>   2
SECTION 2. AMENDMENTS TO AGREEMENT.

       (a) Section 1.1 of the Agreement is amended by deleting the defined
terms "Prime Rate" and "Cash Flow", and by adding the following new defined
terms:

       "EBITDA" means for any period, the revenues of the Borrower for such
period from continuing operations, minus associated costs (generally excluding
Interest Expense, income taxes, unallocated depreciation, depletion, and
amortization and other non-cash expenses), determined in each case on a
consolidated basis in accordance with generally accepted accounting principles.

       "FIXED CHARGES" means for any period, the sum (without duplication) of
(i) Interest Expense for such period, (ii) provision for cash income taxes made
by the Borrower on a consolidated basis in respect of such period and (iii)
scheduled payments required to be made during such period on account of
principal of Debt of the Borrower.

       "INTEREST EXPENSE" means for any period, the amount of interest expense,
both expensed and capitalized, of the Borrower determined on a consolidated
basis in accordance with generally accepted accounting principles, for such
period on the aggregate principal amount of Borrower's Debt, determined on a
consolidated basis in accordance with generally accepted accounting principles.

       "PRIME RATE" shall mean that variable rate of interest per annum
published in the Money Rates section of The Wall Street Journal as its "prime
rate". In the event that the Money Rates section of The Wall Street Journal
does not have a rate designated by it as its "prime rate," then the "Prime
Rate" shall be deemed to be the variable rate of interest per annum which is
the general reference rate designated by Lender as its "reference rate", "base
rate", or other similar rate and which is comparable to the "Prime Rate" as
described above.

       (b) Section 2.1(a) of the Agreement is amended to read in its entirety
as follows:

       (a) TERM LOANS - (i) Contemporaneously with the execution and delivery
hereof, Borrower shall execute and deliver to the Lender the Term Promissory
Note in the form of Exhibit A hereto in the principal amount of $6,000,000.00
(the "Term Promissory Note"). Subject to and upon the terms and conditions of
this Agreement and the Term Promissory Note, Borrower may, at any time and from
time to time during the period from the date hereof until December 31, 1996,
request one or more Advances and borrow (without the ability to reborrow
amounts prepaid under the Term Promissory Note) under the Term Promissory Note;
provided, however, the cumulative aggregate principal amount of all



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<PAGE>   3

Advances under the Term Promissory Note shall not exceed $6,000,000.00. The
Term Promissory Note, including the loans evidenced thereby, is a multiple
advance term loan facility and shall not be construed as a revolving line of
credit as reborrowings are not permitted. The Term Promissory Note shall be
stated to mature seven years from the date of such note and shall bear interest
on the unpaid principal amount thereof from time to time outstanding at the
applicable interest rate per annum as provided in the Term Promissory Note.
Principal and interest on the Term Promissory Note shall be payable in the
manner and on the dates specified therein.

       (ii) Contemporaneously with the execution and delivery hereof, Borrower
shall execute and deliver to the Lender the Term Promissory Note in the form of
Exhibit A-1 hereto in the principal amount of $5,000,000.00 (the "Second Term
Promissory Note"). Subject to and upon the terms and conditions of this
Agreement and the Second Term Promissory Note, Borrower may, at any time and
from time to time during the period from the date hereof until April 15, 1998,
request one or more Advances and borrow (without the ability to reborrow
amounts prepaid under the Second Term Promissory Note) under the Second Term
Promissory Note; provided, however, the cumulative aggregate principal amount
of all Advances under the Second Term Promissory Note shall not exceed
$5,000,000.00. The Second Term Promissory Note, including the loans evidenced
thereby, is a multiple advance term loan facility and shall not be construed as
a revolving line of credit as reborrowings are not permitted. The Second Term
Promissory Note shall be stated to mature six years from the date of such note
and shall bear interest on the unpaid principal amount thereof from time to
time outstanding at the applicable interest rate per annum as provided in the
Second Term Promissory Note. Principal and interest on the Second Term
Promissory Note shall be payable in the manner and on the dates specified
therein.

       (c) Section 2.1(b) of the Agreement is amended to read in its entirety
as follows:

       (b) Contemporaneously with the execution and delivery hereof, Borrower
shall execute and deliver to the Lender the Revolving Line of Credit Promissory
Note in the form of Exhibit B hereto in the maximum principal amount of
$6,000,000.00 (the "Revolving Line of Credit Promissory Note"). Subject to and
upon the terms and conditions of this Agreement and the Revolving Line of
Credit Promissory Note, Borrower may request one or more Advances and borrow,
prepay and reborrow at any time and from time to time under the Revolving Line
of Credit Promissory Note; provided, however, the aggregate principal amount of
all Advances outstanding at any one time under the Revolving Line of Credit
Promissory Note shall never exceed the lesser of (i) $6,000,000.00 or (ii) the
Borrowing Base then in effect. The Revolving Line of Credit Promissory Note
shall be stated to mature on April 15, 1999 and shall bear interest on the
unpaid principal amount thereof from time to time outstanding at the applicable
interest rate per annum as provided in the Revolving




                                      -3-
<PAGE>   4

Line of Credit Promissory Note. Principal and interest on the Revolving Line of
Credit Promissory Note shall be payable in the manner and on the dates
specified therein.

       (d) Section 5.1(d) of the Agreement is hereby amended by deleting the
reference to "Cash Flow" therein and substituting in place thereof "Fixed
Charge Coverage".

       (e) Section 6.10 of the Agreement is hereby amended by deleting said
Section in its entirety and substituting in place thereof the following new
Section 6.10:

       6.10 FIXED CHARGE COVERAGE. Borrower shall not permit the ratio of (i)
EBITDA to Fixed Charges to be less than 1.25 to 1.0 for each moving three-month
period (each such period a "Test Period") ending on the date such ratio is to
be calculated, with the first such calculation to be made and dated as of May
31, 1997, followed by a similar calculation at the end of each succeeding Test
Period.

SECTION 3. REPRESENTATIONS AND WARRANTIES.

       The Borrower hereby represents and warrants to the Lender as follows:

       (a) ORGANIZATION, EXISTENCE AND GOOD STANDING OF BORROWER. Borrower is
duly organized, validly existing and in good standing under the laws of its
state of organization, having all corporate powers required to enter into and
carry out the transactions contemplated by this First Amendment. Borrower is
duly qualified, in good standing and authorized to do business in all other
jurisdictions wherein the character of Borrower's operations, transaction of
business or ownership of property makes such qualification necessary, except
where the absence of qualification, good standing or authorization would not
have a Material Adverse Effect on the business, properties or financial
condition of Borrower.

       (b) AUTHORIZATION. Borrower is duly authorized and empowered to create
and issue the Revolving Line of Credit Promissory Note and the Second Term
Promissory Note pursuant to this First Amendment, and to execute and deliver
this First Amendment, the Revolving Line of Credit Promissory Note, Second Term
Promissory Note and all other instruments referred to or mentioned herein, and
all action (corporate or otherwise) on Borrower's part requisite for the due
execution, delivery and performance of this First Amendment, the Revolving Line
of Credit Promissory Note, Second Term Promissory Note and the other Loan
Papers executed and delivered in connection with this First Amendment has been
duly and effectively taken.




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<PAGE>   5
       (c) ENFORCEABLE OBLIGATIONS. This First Amendment is, and the other Loan
Papers to be executed in connection with this First Amendment when duly
executed and delivered will be, the legal, valid and binding obligation of
Borrower, enforceable in accordance with their respective terms (subject to
applicable bankruptcy, insolvency or other laws generally affecting the
enforcement of creditors' rights).

       (d) NO CONFLICTS OR CONSENTS. The execution and delivery by Borrower of
this First Amendment, the Revolving Line of Credit Promissory Note and the
Second Term Promissory Note, the performance by Borrower of its obligations
under such Loan Papers, and the consummation of the transactions contemplated
thereby, do not and will not (1) conflict with any provision of the articles of
incorporation or bylaws of Borrower, or (2) except as to matters that could not
reasonably be expected to have a Material Adverse Effect, result in the
acceleration of any Debt owed by Borrower, or conflict with any law, statute,
rule, regulation or Material Agreement, judgment, license, order or permit
applicable to or binding upon Borrower or any of its properties or assets, or
require the consent, approval, authorization or order of, or notice to or
filing with, any Governmental Authority or third party, or result in or require
the creation of any Lien upon any material assets or properties of Borrower,
except as permitted in the Loan Papers.

       (e) USE OF PROCEEDS. The proceeds of the loans to be made to the
Borrower shall be used by the Borrower for the following purposes:

                 (i)      with respect to loans made pursuant to and evidenced
                          by the Second Term Promissory Note, for the purchase
                          of seismic survey equipment and machinery to be used
                          in the ordinary course of Borrower's business; and

                 (ii)     with respect to loans made pursuant to and evidenced
                          by the Revolving Line of Credit Promissory Note, for
                          general working capital purposes.

       The Borrower will not use any of the loan proceeds to purchase any
vehicle subject to a certificate of title law of any state.

       (f) REPRESENTATIONS AND WARRANTIES. The representations and warranties
contained in Article IV of the Agreement are true and correct on and as of the
date hereof as though made on and as of the date hereof; and

       (g) NO EVENT OF DEFAULT. No Event of Default has occurred and is
continuing (before and after giving effect to this First Amendment).



                                      -5-
<PAGE>   6

       (h) NO MATERIAL ADVERSE CHANGES. Since April 1, 1996, there have been no
events, circumstances or other developments of any nature that have had a
Material Adverse Effect.

SECTION 4. RATIFICATION AND AMENDMENT OF SECURITY AGREEMENT.

       The Borrower hereby (i) ratifies and confirms in all respects all of the
terms, provisions and covenants of that certain Security Agreement, dated as of
April 1, 1996, between the Borrower and the Lender (the "Security Agreement"),
including, without limitation, the grant and conveyance to the Lender of Bank
Liens in and to Collateral (as defined in the Security Agreement); (ii)
acknowledges and agrees that all of the Notes, including the Second Term
Promissory Note, are now and shall remain subject to all of the terms and
provisions of the Security Agreement and that the security interests and Bank
Liens in and to the Collateral now secure and shall continue to secure the
prompt and complete payment and performance when due (whether at the stated
maturity, by acceleration or otherwise) of the Obligation; and (iii) represents
and warrants that the representations and warranties contained in Section 3 of
the Security Agreement are true and correct as of the date hereof as though
made on and as of the date of this First Amendment.

SECTION 5. CONDITIONS PRECEDENT.

       This First Amendment shall be effective only upon satisfaction of the
following conditions precedent:

       (a)    the Lender shall have received the Second Term Promissory Note in
              the form of Exhibit A-1 hereto, executed and delivered by a duly
              authorized officer of Borrower;

       (b)    the Lender shall have received the Revolving Line of Credit
              Promissory Note in the form of Exhibit B hereto, executed and
              delivered by a duly authorized officer of Borrower;

       (c)    the Lender shall have received counterparts of this First
              Amendment duly executed and delivered by the Borrower;

       (d)    no Event of Default shall have occurred and be continuing as of
              the date of this First Amendment, both before and after giving
              effect to this First Amendment;




                                      -6-
<PAGE>   7
       (e)    the Lender shall have received a copy of the resolutions, in form
              and substance satisfactory to the Lender, of the Board of
              Directors of the Borrower authorizing (i) the execution, delivery
              and performance of this First Amendment and the other Loan Papers
              to be entered into in connection herewith, and (ii) the
              additional borrowings contemplated by this First Amendment, such
              resolutions to be certified by its Secretary or Assistant
              Secretary as of the date hereof, which certificate shall state
              that the resolutions thereby certified have not been amended,
              modified, revoked or rescinded as of the date of such certificate
              and such certificate shall be in form and substance satisfactory
              to the Lender;

       (f)    the Lender shall have received the favorable opinion of counsel
              for Borrower covering the matters requested by Lender; and

       (g)    the Lender shall have received such other agreements, documents,
              certificates and instruments as Lender may require.

SECTION 6. NO OTHER AMENDMENTS; RATIFICATION.

       Except as expressly amended and modified by this First Amendment, all of
the provisions and covenants of the Agreement, all exhibits thereto and all
other Loan Papers are and shall continue to remain in full force and effect in
accordance with the terms thereof and all of such provisions, covenants,
exhibits and Loan Papers are hereby ratified and confirmed by the Borrower as
of the date of this First Amendment as if the Agreement were executed as of the
date of this First Amendment.

SECTION 7. COUNTERPARTS.

       This First Amendment may be executed by one or more of the parties
hereto in any number of separate counterparts and all of said counterparts
taken together shall be deemed to constitute one and the same instrument.

SECTION 8. GOVERNING LAW.

       THIS FIRST AMENDMENT SHALL BE GOVERNED BY AND CONSTRUED AND INTERPRETED
IN ACCORDANCE WITH THE LAWS OF THE STATE OF TEXAS.




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SECTION 9. GLOBAL AMENDMENT OF LOAN PAPERS.

       All of the Loan Papers are hereby modified wherever necessary or
appropriate, and even though not specifically addressed herein, so as to
conform to the amendments to the Agreement as set forth herein, and the
Borrower covenants to observe, comply with and perform each and all of the
terms and provisions of the Loan Papers, as modified hereby. Each Loan Paper is
hereby amended so that any reference in each such Loan Paper to the Agreement
shall mean a reference to the Agreement as amended hereby.

       Without limiting the generality of the foregoing paragraph:

       (a) all references to the "Notes" appearing in the Agreement and in the
Security Agreement shall mean and be deemed to include the Term Promissory
Note, Second Term Promissory Note and the Revolving Line of Credit Promissory
Note; and

       (b) the references to "Term Promissory Note" in Sections 1.1, 2.2, 2.7,
3.2, 4.10, 5.4 and 5.12 of the Agreement shall be deemed to include and
constitute separate references to each of the Term Promissory Note and the
Second Term Promissory Note, and the provisions of each such Section shall
apply to the Second Term Promissory Note with full force and effect as if
express reference to the Second Term Promissory Note were contained in each
such Section.

       THIS FIRST AMENDMENT AND THE OTHER LOAN PAPERS REPRESENT THE ENTIRE
AGREEMENT BETWEEN THE PARTIES AND MAY NOT BE CONTRADICTED BY EVIDENCE OF PRIOR,
CONTEMPORANEOUS OR SUBSEQUENT ORAL AGREEMENTS BETWEEN THE PARTIES. THERE ARE NO
UNWRITTEN AGREEMENTS BETWEEN THE PARTIES.




                                      -8-
<PAGE>   9
       IN WITNESS WHEREOF, the parties hereto have caused this First Amendment
to be executed and delivered by their respective duly authorized officers as of
the date and year first above written.




                                             NORWEST BANK TEXAS, N.A., a
                                               national banking association



                                             By: /s/ Mark D. McKinney
                                                -----------------------------
                                                 Mark D. McKinney, Senior
                                                   Vice President



                                             DAWSON GEOPHYSICAL COMPANY



                                             By: /s/ L. Decker Dawson
                                                -----------------------------
                                                L. Decker Dawson, President




                                      -9-
<PAGE>   10

                                  EXHIBIT A-1

                              TERM PROMISSORY NOTE

$5,000,000.00                                                   April 15, 1997

       FOR VALUE RECEIVED, in the manner, on the dates and in the amounts
herein stipulated, DAWSON GEOPHYSICAL COMPANY, a Texas corporation
("Borrower"), hereby promises and agrees to pay to the order of NORWEST BANK
TEXAS, N.A, a national banking association ("Lender"), in Midland, Midland
County, Texas, the principal sum of FIVE MILLION AND NO/100 DOLLARS
($5,000,000.00) or, if less, the aggregate unpaid principal amount outstanding
hereunder, in lawful money of the United States of America, which shall be
legal tender in payment of all debts and dues, public and private, at the time
of payment, together with interest on the unpaid principal amount hereof from
time to time outstanding until maturity at a rate per annum which shall from
day to day be equal to the lesser of (a) the Prime Rate in effect from day to
day (calculated on the basis of actual days elapsed, but computed as if each
calendar year consisted of 360 days) or (b) the Highest Lawful Rate. Each
change in the rate of interest charged under this Term Promissory Note (this
"Note") shall, subject to the terms hereof, become effective, without notice to
Borrower, upon the effective date of each change in the Prime Rate or the
Highest Lawful Rate, as the case may be. Notwithstanding the foregoing, if at
any time the Prime Rate exceeds the Highest Lawful Rate, the rate of interest
on this Note shall be limited to the Highest Lawful Rate, but any subsequent
reductions in the Prime Rate shall not reduce the rate of interest hereon below
the Highest Lawful Rate until the total amount of interest accrued hereon
approximately equals the amount of interest which would have accrued hereon if
the Prime Rate had at all times been in effect. In the event that at maturity
(stated or by acceleration), or at final payment of this Note, the total amount
of interest paid or accrued hereon is less than the amount of interest which
would have accrued if the Prime Rate had at all times been in effect, then, at
such time and to the extent permitted by applicable laws, Borrower shall pay to
Lender an amount equal to the difference between (a) the lesser of the amount
of interest which would have accrued if the Prime Rate had at all times been in
effect or the amount of interest which would have accrued if the Highest Lawful
Rate had at all times been in effect, and (b) the amount of interest actually
paid or accrued on this Note. All of the past-due principal and accrued
interest hereunder shall, at the option of Lender, bear interest from maturity
(stated or by acceleration) until paid at a rate per annum equal to the Highest
Lawful Rate. Interest calculations may be made ten days prior to any interest
installment due date under this Note, in which event, if there is an adjustment
in the interest rate in accordance with the terms hereof during such ten-day
period, then Borrower shall subsequently, on demand, pay to Lender any
underpayment, or Lender shall pay to Borrower, any overpayment, as the case may
be, as a result of any adjustment during such ten-day period.



<PAGE>   11
       This Note is the Term Promissory Note referred to in the Loan Agreement,
dated as of April 1, 1996, as amended by that certain First Amendment to Loan
Agreement, dated as of the date hereof (as the same may be further amended,
supplemented or otherwise modified from time to time, the "Loan Agreement"), by
and between Borrower and Lender, and is subject to the terms and conditions
thereof. Reference is made to the Loan Agreement for provisions for the
disbursement of funds hereunder and for a further statement of the rights,
remedies, powers, privileges, benefits, duties and obligations of Borrower and
Lender under the Loan Agreement and this Note. Terms used herein which are
defined in the Loan Agreement shall have such defined meanings unless otherwise
defined herein. The holder of this Note shall be entitled to the benefits of
the Loan Agreement.

       Subject to the terms hereof and of the Loan Agreement, from the date of
this Note until April 15, 1998, the Lender will make Advances and Subsequent
Advances under this Note in accordance with the provisions of the Loan
Agreement. The aggregate principal amount of all such Advances as may be made
by the Lender to the Borrower under this Note shall never exceed Five Million
and No/100 Dollars ($5,000,000.00).

       The principal of this Note shall be due and payable (a) in seventy-one
consecutive monthly installments of $69,400.00 each (the "Monthly Payment
Amount"), with the first such installment being due and payable on May 15,
1997, and a like installment being due and payable on the fifteenth day of each
succeeding calendar month to and including March 15, 2003; provided that, if on
the due date of any such monthly installment the principal amount then
outstanding on this Note is less than the Monthly Payment Amount, such lesser
amount shall be due and payable on such installment due date, and (b) one final
installment in an amount equal to all unremaining unpaid principal and accrued
and unpaid interest on this Note shall be due and payable on April 15, 2003.
Interest, computed on the unpaid balance of this Note, shall be due and payable
as it accrues, on the same dates as, but in addition to, the installments of
principal. All payments and prepayments shall be applied first to accrued
interest, the balance to principal. If partial prepayments are applied to
principal, installments of principal shall continue as scheduled. All past due
principal and interest shall bear interest at the lesser of the Prime Rate plus
two percent (2%) or the Highest Lawful Rate.

       This Note is secured as provided in the Loan Agreement and in the other
Loan Papers, to which reference is hereby made for a description of the
properties and assets in which a lien and security interest has been granted,
the nature and extent of the security, the terms and conditions upon which the
liens and security interest were granted and the rights of the holder of this
Note with respect thereto.

       Time is of the essence of this Note. Upon the occurrence of any one or
more of the Events of Default specified in the Loan Agreement, all amounts then
remaining unpaid on



                                      -2-
<PAGE>   12

this Note shall become, or may be declared to be, immediately due and payable,
all as provided therein.

       Borrower and any and all co-makers, endorsers, guarantors and sureties
severally waive notice (including, but not limited to, notice of protest,
notice of dishonor, notice of intent to accelerate and notice of acceleration),
demand, presentment for payment, protest, diligence in collecting or bringing
suit and the filing of suit for the purpose of fixing liability, and consent
that the time of payment hereof may be extended and re-extended from time to
time without notice to them or any of them, and each agrees that his, her or
its liability on or with respect to this Note shall not be affected, diminished
or impaired by any (a) release of any security at any time existing for this
Note, (b) substitution for any security at any time existing for this Note, or
(c) failure to perfect (or to maintain perfection of) any lien on or security
interest in any such security, in each case in whole or in part, with or
without notice, before or after maturity.

       It is the intention of Borrower and Lender that Lender shall conform
strictly to usury laws applicable to it. Accordingly, if the transactions
contemplated by the Loan Agreement and this Note would be usurious as to Lender
under laws applicable to it (including the laws of the United States of America
and the State of Texas or any other jurisdiction whose laws may be mandatorily
applicable to Lender notwithstanding the other provisions of the Loan Agreement
and this Note), then, in that event, notwithstanding anything to the contrary
in this Note, the Loan Agreement or any other Loan Paper or other agreement
entered into in connection with or as security for this Note, (i) the aggregate
of all consideration which is contracted for, taken, reserved, charged or
received by Lender under this Note, the Loan Agreement or any other Loan Paper
or agreement entered into in connection with or as security for this Note shall
under no circumstances exceed the maximum amount allowed by such applicable
law, and any excess shall be credited by Lender on the principal amount of the
Obligation to Lender (or, to the extent that the principal amount of the
Obligation shall have been or would thereby be paid in full, refunded by Lender
to the Borrower); and (ii) in the event that the maturity of this Note is
accelerated by reason of an Event of Default under the Loan Agreement or
otherwise, or in the event of any prepayment, then such consideration that
constitutes interest under law applicable to Lender may never include more than
the maximum amount allowed by such applicable law, and excess interest, if any,
provided for in this Note, the Loan Agreement or otherwise shall be cancelled
automatically by Lender as of the date of such acceleration of prepayment and,
if theretofore paid, shall be credited by Lender on the principal amount of the
Obligation (or, to the extent that the principal amount of such Obligation
shall have been or would thereby be paid in full, refunded by Lender to the
Borrower).

       To the extent that Article 5069-1.04 of the Texas Revised Civil Statutes
is relevant to Lender for the purpose of determining the Highest Lawful Rate,
the applicable rate ceiling



                                      -3-
<PAGE>   13
under such Article shall be determined by the indicated (weekly) rate ceiling
from time to time in effect, subject to Lender's right subsequently to change
such method in accordance with applicable law.

       This Note is performable and payable in the County of Midland, State of
Texas, and shall be construed in accordance with, and governed by, the laws of
the State of Texas; provided, however, that the laws pertaining to allowable
rates of interest may, from time to time, be governed by the laws of the United
States of America.




                                               DAWSON GEOPHYSICAL COMPANY



                                               By: /s/ L. Decker Dawson
                                                  -----------------------------
                                                  L. Decker Dawson, President




                                      -4-
<PAGE>   14
                                   EXHIBIT B

                    REVOLVING LINE OF CREDIT PROMISSORY NOTE

$6,000,000.00                                                   April 15, 1997

       FOR VALUE RECEIVED, in the manner, on the dates and in the amounts
herein stipulated, DAWSON GEOPHYSICAL COMPANY, a Texas corporation
("Borrower"), hereby promises and agrees to pay to the order of NORWEST BANK
TEXAS, N.A., a national banking association ("Lender"), in Midland, Midland
County, Texas, the principal sum of SIX MILLION AND NO/100 DOLLARS
($6,000,000.00) or, if less, the aggregate unpaid principal amount outstanding
hereunder, in lawful money of the United States of America, which shall be
legal tender in payment of all debts and dues, public and private, at the time
of payment, together with interest on the unpaid principal amount hereof from
time to time outstanding until maturity at a rate per annum which shall from
day to day be equal to the lesser of (a) the Prime Rate in effect from day to
day (calculated on the basis of actual days elapsed, but computed as if each
calendar year consisted of 360 days) or (b) the Highest Lawful Rate. Each
change in the rate of interest charged under this Revolving Line of Credit
Promissory Note (this "Note") shall, subject to the terms hereof, become
effective, without notice to Borrower, upon the effective date of each change
in the Prime Rate or the Highest Lawful Rate, as the case may be.
Notwithstanding the foregoing, if at any time the Prime Rate exceeds the
Highest Lawful Rate, the rate of interest on this Note shall be limited to the
Highest Lawful Rate, but any subsequent reductions in the Prime Rate shall not
reduce the rate of interest hereon below the Highest Lawful Rate until the
total amount of interest accrued hereon approximately equals the amount of
interest which would have accrued hereon if the Prime Rate had at all times
been in effect. In the event that at maturity (stated or by acceleration), or
at final payment of this Note, the total amount of interest paid or accrued
hereon is less than the amount of interest which would have accrued if the
Prime Rate had at all times been in effect, then, at such time and to the
extent permitted by applicable laws, Borrower shall pay to Lender an amount
equal to the difference between (a) the lesser of the amount of interest which
would have accrued if the Prime Rate had at all times been in effect or the
amount of interest which would have accrued if the Highest Lawful Rate had at
all times been in effect, and (b) the amount of interest actually paid or
accrued on this Note. All of the past-due principal and accrued interest
hereunder shall, at the option of Lender, bear interest from maturity (stated
or by acceleration) until paid at a rate per annum equal to the Highest Lawful
Rate. Interest calculations may be made ten days prior to any interest
installment due date under this Note, in which event, if there is an adjustment
in the interest rate in accordance with the terms hereof during such ten-day
period, then Borrower

<PAGE>   15
shall subsequently, on demand, pay to Lender any underpayment, or Lender shall
pay to Borrower, any overpayment, as the case may be, as a result of any
adjustment during such ten-day period.

       This Note (i) is given in renewal, extension and increase in principal
amount, but not in extinguishment, of that certain Revolving Line of Credit
Promissory Note, dated April 1, 1996, in the original principal amount of
$5,000,000, and (ii) is the Revolving Line of Credit Promissory Note referred
to in the Loan Agreement, dated as of April 1, 1996, as amended by that certain
First Amendment to Loan Agreement, dated as of the date hereof (as the same may
be further amended, supplemented or otherwise modified from time to time, the
"Loan Agreement"), by and between Borrower and Lender, and is subject to the
terms and conditions thereof. Reference is made to the Loan Agreement for
provisions for the disbursement of funds hereunder and for a further statement
of the rights, remedies, powers, privileges, benefits, duties and obligations
of Borrower and Lender under the Loan Agreement and this Note. Terms used
herein which are defined in the Loan Agreement shall have such defined meanings
unless otherwise defined herein. The holder of this Note shall be entitled to
the benefits of the Loan Agreement.

       Advances and Subsequent Advances under this Note shall be made in
accordance with the provisions of the Loan Agreement. Subject to the terms
hereof and of the Loan Agreement, Borrower may borrow, repay and reborrow at
any time and from time to time under this Note; provided, however, that the
principal sum outstanding hereunder at any one time shall never exceed the
lesser of $6,000,000.00 or the Borrowing Base then in effect.

       Interest on the outstanding principal balance of this Note shall be due
and payable monthly on the fifteenth day of each calendar month, commencing May
15, 1997. The then outstanding principal balance of this Note and all accrued
and unpaid interest shall be due and payable on April 15, 1999.

       This Note is secured as provided in the Loan Agreement and in the other
Loan Papers, to which reference is hereby made for a description of the
properties and assets in which a lien and security interest has been granted,
the nature and extent of the security, the terms and conditions upon which the
liens and security interest were granted and the rights of the holder of this
Note with respect thereto.

       Time is of the essence of this Note. Upon the occurrence of any one or
more of the Events of Default specified in the Loan Agreement, all amounts then
remaining unpaid on this Note shall become, or may be declared to be,
immediately due and payable, all as provided therein.




                                      -2-
<PAGE>   16
       Borrower and any and all co-makers, endorsers, guarantors and sureties
severally waive notice (including, but not limited to, notice of protest,
notice of dishonor, notice of intent to accelerate and notice of acceleration),
demand, presentment for payment, protest, diligence in collecting or bringing
suit and the filing of suit for the purpose of fixing liability, and consent
that the time of payment hereof may be extended and re-extended from time to
time without notice to them or any of them, and each agrees that his, her or
its liability on or with respect to this Note shall not be affected, diminished
or impaired by any (a) release of any security at any time existing for this
Note, (b) substitution for any security at any time existing for this Note, or
(c) failure to perfect (or to maintain perfection of) any lien on or security
interest in any such security, in each case in whole or in part, with or
without notice, before or after maturity.

       It is the intention of Borrower and Lender that Lender shall conform
strictly to usury laws applicable to it. Accordingly, if the transactions
contemplated by the Loan Agreement and this Note would be usurious as to Lender
under laws applicable to it (including the laws of the United States of America
and the State of Texas or any other jurisdiction whose laws may be mandatorily
applicable to Lender notwithstanding the other provisions of the Loan Agreement
and this Note), then, in that event, notwithstanding anything to the contrary
in this Note, the Loan Agreement or any other Loan Paper or other agreement
entered into in connection with or as security for this Note, (i) the aggregate
of all consideration which is contracted for, taken, reserved, charged or
received by Lender under this Note, the Loan Agreement or any other Loan Paper
or agreement entered into in connection with or as security for this Note shall
under no circumstances exceed the maximum amount allowed by such applicable
law, and any excess shall be credited by Lender on the principal amount of the
Obligation to Lender (or, to the extent that the principal amount of the
Obligation shall have been or would thereby be paid in full, refunded by Lender
to the Borrower); and (ii) in the event that the maturity of this Note is
accelerated by reason of an Event of Default under the Loan Agreement or
otherwise, or in the event of any prepayment, then such consideration that
constitutes interest under law applicable to Lender may never include more than
the maximum amount allowed by such applicable law, and excess interest, if any,
provided for in this Note, the Loan Agreement or otherwise shall be canceled
automatically by Lender as of the date of such acceleration of prepayment and,
if theretofore paid, shall be credited by Lender on the principal amount of the
Obligation (or, to the extent that the principal amount of such Obligation
shall have been or would thereby be paid in full, refunded by Lender to the
Borrower).

       To the extent that Article 5069-1.04 of the Texas Revised Civil Statutes
is relevant to Lender for the purpose of determining the Highest Lawful Rate,
the applicable rate ceiling under such Article shall be determined by the
indicated (weekly) rate ceiling from time to time in effect, subject to
Lender's right subsequently to change such method in accordance with applicable
law.




                                      -3-
<PAGE>   17
       This Note is performable and payable in the County of Midland, State of
Texas, and shall be construed in accordance with, and governed by, the laws of
the State of Texas; provided, however, that the laws pertaining to allowable
rates of interest may, from time to time, be governed by the laws of the United
States of America.


                                                DAWSON GEOPHYSICAL COMPANY




                                                By: /s/ L. Decker Dawson
                                                   ---------------------------
                                                   L. Decker Dawson, President





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