How can I eliminate this costly index seek operation from my query?
In addition to the T-SQL techniques discussed in Aaron Bertrands article, "Best approaches for grouped running totals", you might want to look at a SQLCLR procedure (if you are running less than SQL Server 2012).

The main advantages are that a SQLCLR procedure requires only a single scan of the source records, and benefits from the increased execution speed of compiled code. The sample below is taken from Aaron's post:

DDL

CREATE TABLE dbo.SpeedingTickets
(
  IncidentID    INT IDENTITY(1,1) PRIMARY KEY,
  LicenseNumber INT          NOT NULL,
  IncidentDate  DATE         NOT NULL,
  TicketAmount  DECIMAL(7,2) NOT NULL
);

CREATE UNIQUE INDEX x 
ON dbo.SpeedingTickets(LicenseNumber, IncidentDate) 
INCLUDE(TicketAmount);


Sample data

;WITH TicketAmounts(ID,Value) AS 
(
  -- 10 arbitrary ticket amounts
  SELECT i,p FROM 
  (
    VALUES(1,32.75),(2,75), (3,109),(4,175),(5,295),
          (6,68.50),(7,125),(8,145),(9,199),(10,250)
  ) AS v(i,p)
),
LicenseNumbers(LicenseNumber,[newid]) AS 
(
  -- 1000 random license numbers
  SELECT TOP (1000) 7000000 + number, n = NEWID()
    FROM [master].dbo.spt_values 
    WHERE number BETWEEN 1 AND 999999
    ORDER BY n
),
JanuaryDates([day]) AS 
(
  -- every day in January 2014
  SELECT TOP (31) DATEADD(DAY, number, '20140101') 
    FROM [master].dbo.spt_values 
    WHERE [type] = N'P' 
    ORDER BY number
),
Tickets(LicenseNumber,[day],s) AS
(
  -- match *some* licenses to days they got tickets
  SELECT DISTINCT l.LicenseNumber, d.[day], s = RTRIM(l.LicenseNumber) 
    FROM LicenseNumbers AS l CROSS JOIN JanuaryDates AS d
    WHERE CHECKSUM(NEWID()) % 100 = l.LicenseNumber % 100
    AND (RTRIM(l.LicenseNumber) LIKE '%' + RIGHT(CONVERT(CHAR(8), d.[day], 112),1) + '%')
    OR (RTRIM(l.LicenseNumber+1) LIKE '%' + RIGHT(CONVERT(CHAR(8), d.[day], 112),1) + '%')
)
INSERT dbo.SpeedingTickets(LicenseNumber,IncidentDate,TicketAmount)
SELECT t.LicenseNumber, t.[day], ta.Value 
  FROM Tickets AS t 
  INNER JOIN TicketAmounts AS ta
  ON ta.ID = CONVERT(INT,RIGHT(t.s,1))-CONVERT(INT,LEFT(RIGHT(t.s,2),1))
  ORDER BY t.[day], t.LicenseNumber;


SQL CLR procedure DDL

CREATE ASSEMBLY [Demo] AUTHORIZATION [dbo]
FROM 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WITH PERMISSION_SET = SAFE;
GO
CREATE PROCEDURE [dbo].[TicketRunningTotals] 
AS EXTERNAL NAME [Demo].[StoredProcedures].[TicketRunningTotals];


Usage

EXECUTE dbo.TicketRunningTotals;


Output



Execution plan



SQL CLR source code

using System.Data;
using System.Data.SqlClient;
using Microsoft.SqlServer.Server;

public partial class StoredProcedures
{
    [SqlProcedure]
    public static void TicketRunningTotals()
    {
        using (var conn = new SqlConnection("context connection = true"))
        {
            conn.Open();

            using (var cmd = new SqlCommand())
            {
                cmd.Connection = conn;
                cmd.CommandText =
                    @"
                    SELECT
                        ST.LicenseNumber,
                        ST.IncidentDate,
                        ST.TicketAmount
                    FROM dbo.SpeedingTickets AS ST
                    ORDER BY
                        ST.LicenseNumber,
                        ST.IncidentDate
                    ";

                var columns = new SqlMetaData[4]
                {
                    new SqlMetaData("LicenseNumber", SqlDbType.Int),
                    new SqlMetaData("IncidentDate", SqlDbType.Date),
                    new SqlMetaData("TicketAmount", SqlDbType.Decimal, 7, 2),
                    new SqlMetaData("RunningTotal", SqlDbType.Decimal, 9, 2)
                };

                int licenseNumber, lastLicenseNumber;
                var ticketAmount = 0m;
                var runningTotal = 0m;

                var pipe = SqlContext.Pipe;
                var reader = cmd.ExecuteReader(CommandBehavior.SingleResult);
                var record = new SqlDataRecord(columns);

                pipe.SendResultsStart(record);

                if (reader.Read())
                {
                    lastLicenseNumber = reader.GetInt32(0);

                    do
                    {
                        licenseNumber = reader.GetInt32(0);
                        ticketAmount = reader.GetDecimal(2);

                        if (licenseNumber != lastLicenseNumber)
                        {
                            runningTotal = 0m;
                            lastLicenseNumber = licenseNumber;
                        }

                        record.SetInt32(0, licenseNumber);
                        record.SetDateTime(1, reader.GetDateTime(1));
                        record.SetDecimal(2, ticketAmount);
                        record.SetDecimal(3, runningTotal += ticketAmount);

                        pipe.SendResultsRow(record);
                    }
                    while (reader.Read());
                }

                pipe.SendResultsEnd();

            }
        }
    }
}